TopCoder Statistics - Problem Statement

Problem Statement

Warning: This problem statement contains superscripts and/or subscripts. It may not display properly outside of the applet.

King Dengklek is the perfect king of Kingdom of Ducks, where slimes and ducks live together in peace and harmony.

The palace has N rooms, conveniently numbered 0 through N-1. The rooms are occupied by the ducks King Dengklek loves the most. There are ducks[i] ducks in room i.

Today, King Dengklek realized that two magic spells are affecting the palace. Being a perfect king, he quickly learned that on each day, exactly one of the two magic spells will take place with the same probability (i.e., 50%). The effects of the two magic spells are as follows:

Spell 1: For each i, let D be the number of ducks in room i right before the spell's effect takes place. The number of ducks in room i will become D XOR spellOne[i] (see the Notes section for the definition of XOR).
Spell 2: For each i, all ducks in room i will move to room spellTwo[i]. All these movements will happen simultaneously. This will permute the ducks (i.e., no two elements of spellTwo will be equal).

King Dengklek is worried about these odd magic spells. He is especially worried about room 0, because he has promised that he will grant all ducks in this room to his successor. You are given the int[]s ducks, spellOne, spellTwo, and the int K. Return the expected number of ducks in room 0 after the magic spells have affected the palace for K days.

Definition

Class:: KingXMagicSpells
Method:: expectedNumber
Parameters:: int[], int[], int[], int
Returns:: double
Method signature:: double expectedNumber(int[] ducks, int[] spellOne, int[] spellTwo, int K)
(be sure your method is public)

Notes

The returned value must have an absolute or relative error less than 10-9.
If a and b are single bits then a XOR b is defined as (a + b) modulo 2. For two integers, A and B, in order to calculate A XOR B, they need to be represented in binary: A = (an...a1)2, B = (bn...b1)2 (if the lengths of their representations are different, the shorter one is prepended with the necessary number of leading zeroes). Then A XOR B = C = (cn...c1)2, where ci = ai XOR bi. For example, 10 XOR 3 = (1010)2 XOR (0011)2 = (1001)2 = 9.

Constraints

ducks, spellOne, and spellTwo will contain the same number of elements, between 1 and 50, inclusive.
Each element of ducks will be between 0 and 1,000,000,000, inclusive.
Each element of spellOne will be between 0 and 1,000,000,000, inclusive.
Each element of spellTwo will be between 0 and N-1, inclusive, where N is the number of elements in ducks.
All elements of spellTwo will be distinct.
K will be between 1 and 50, inclusive.

Examples

{5, 3, 7}

{1, 7, 4}

{1, 0, 2}

1

Returns: 3.5

We want to know the expected number of ducks in room 0 after K=1 day. Exactly one spell will take place. Depending on which spell takes place, there are two possible outcomes: Spell 1: The numbers of ducks in the rooms become {5 XOR 1, 3 XOR 7, 7 XOR 4} = {4, 4, 3}. Spell 2: The numbers of ducks in the rooms become {3, 5, 7}. Therefore, the expected number of ducks in room 0 is (4 + 3)/2 = 3.5.
{5, 8}

{53, 7}

{1, 0}

2

Returns: 21.5

There are four possible outcomes, depending on which two spells take place: Spell 1 and then spell 1: {48, 15} and then {5, 8}. Spell 1 and then spell 2: {48, 15} and then {15, 48}. Spell 2 and then spell 1: {8, 5} and then {61, 2}. Spell 2 and then spell 2: {8, 5} and then {5, 8}. Therefore, the expected number of ducks in room 0 is (5 + 15 + 61 + 5)/4 = 21.5.
{123, 456, 789, 1234, 56789}

{0, 0, 0, 0, 0}

{0, 1, 2, 3, 4}

50

Returns: 123.0

In this case, the number of ducks in each room will never change.
{83291232, 3124231, 192412, 3813249, 629231, 9998989}

{58, 37, 44, 66, 72, 19}

{2, 0, 1, 5, 4, 3}

11

Returns: 2.888186784716797E7
{58}

{58}

{0}

37

Returns: 29.0
{58}

{58}

{0}

36

Returns: 29.0
{236395817}

{657803532}

{0}

1

Returns: 4.63255719E8
{107568287}

{488200094}

{0}

5

Returns: 2.83947984E8
{359258121}

{632183651}

{0}

50

Returns: 5.888198975E8
{916034202, 542018767, 462858069, 604784364, 448675548}

{50086587, 56379590, 420237754, 783315271, 398242782}

{1, 0, 2, 3, 4}

7

Returns: 7.215634865625E8
{383895486, 214327610, 737231581, 274127900, 453490876}

{319050962, 735723580, 689886693, 829370848, 200418373}

{4, 3, 1, 0, 2}

50

Returns: 5.3043290712040865E8
{405425313, 777780011, 196806066, 868283382, 382564375}

{497997968, 770886324, 291460319, 918235722, 406717948}

{2, 1, 3, 4, 0}

18

Returns: 5.905663454109497E8
{748983707, 69010537, 334060977, 486215287, 195654791, 787551853, 657782603, 931378372, 477438546, 487153451}

{131796744, 127409879, 657240746, 992606923, 989155689, 312028046, 250548589, 766935700, 361350466, 971348326}

{9, 4, 3, 2, 7, 5, 8, 1, 0, 6}

1

Returns: 6.036107385E8
{136597953, 639846189, 294854499, 470658931, 126061475, 490509291, 110727137, 636360433, 274404016, 588165683, 123513883, 406200760, 568091917}

{633270983, 251324037, 409763959, 797815383, 354388980, 29216012, 159165849, 325737305, 31232440, 18514283, 920488308, 177225541, 501131147}

{4, 7, 3, 9, 0, 2, 11, 12, 8, 6, 10, 5, 1}

8

Returns: 4.6751497796875E8
{3566218, 529178146, 748667136, 262283333, 949786417, 234454473, 513607370, 359550376, 32269855, 867996350, 388766388, 43952058, 46250009}

{272515183, 62466341, 819254671, 449740724, 416113843, 446244637, 167695175, 934109577, 111580731, 258977234, 293735971, 121795722, 645113793}

{10, 9, 3, 0, 1, 4, 5, 6, 8, 7, 11, 12, 2}

50

Returns: 5.3665608903167635E8
{898616906, 579278328, 997347795, 942568965, 625528337, 269862977, 857551660, 297299362, 572120056, 273665502, 743543999, 739815231, 60291432, 707641085, 998792466, 354027404, 829436807, 496422612, 478048701, 87508995}

{723214961, 543082461, 118218083, 953573529, 989810721, 750110661, 298731783, 386325397, 616457711, 10013761, 994906804, 367590970, 589292090, 992254599, 310159934, 67336780, 114633929, 20227948, 364636142, 686753985}

{11, 13, 18, 5, 14, 1, 6, 8, 7, 15, 4, 2, 17, 0, 10, 9, 16, 12, 3, 19}

6

Returns: 7.46167029578125E8
{464867389, 510451785, 995209868, 54159478, 355222737, 157886156, 121496258, 322373021, 178114104, 338648755, 9127005, 472007554, 446828896, 140728929, 678708791, 115166475, 418606964, 91953785, 612940861, 45423964, 983247481, 50740596, 395455926, 122656344, 459274769}

{551577770, 399359575, 617919602, 858947751, 914904557, 98054853, 176331493, 277872695, 93264721, 83007325, 485611787, 251150877, 57019938, 807984808, 429264981, 395668693, 669628167, 753788889, 842497589, 810357097, 285014034, 810180418, 81480414, 376967819, 275637632}

{5, 16, 18, 3, 19, 24, 10, 17, 13, 7, 21, 15, 9, 2, 8, 4, 22, 0, 6, 14, 23, 20, 1, 11, 12}

1

Returns: 5.43697288E8
{111172097, 871660017, 855140342, 192652512, 101144189, 130777974, 319556891, 166392197, 309672557, 694433550, 501780196, 947841909, 473404332, 89044122, 56447216, 111322864, 296245314, 410591024, 778089245, 928802847, 710515906, 675346597, 899488520, 114108019, 482140240, 530675354, 946965113, 832086223, 978974001, 386127449}

{729562501, 90146098, 110303819, 437219197, 135314964, 63964363, 420513525, 454871855, 230356560, 730186082, 1821758, 732136756, 530544344, 327742444, 673697233, 586991561, 291581662, 969942547, 997582585, 69670907, 751261747, 560614844, 597533858, 503266620, 527239217, 79674097, 33941973, 326720684, 764276674, 865432328}

{24, 21, 17, 3, 27, 23, 28, 5, 11, 9, 18, 1, 10, 13, 22, 2, 14, 15, 26, 29, 25, 12, 19, 6, 20, 8, 16, 4, 7, 0}

7

Returns: 5.492173076484375E8
{614766555, 586881114, 434487589, 275377689, 262549420, 218062314, 71303786, 2182089, 422150564, 322101739, 824687673, 208941249, 427237803, 379330012, 526276278, 860116312, 460185938, 283119222, 437092836, 363500764, 37544749, 83740267, 870593691, 205101475, 327921556, 880953237, 899897419, 651776942, 630287464, 773930399}

{592425356, 245054019, 360811512, 879429299, 520431708, 475877286, 97491612, 591735494, 330575729, 372158530, 766353587, 155263402, 433616133, 46107744, 387109768, 959892412, 906224056, 847295707, 95527987, 195833245, 63312824, 133072736, 279573512, 933906516, 190690566, 607495068, 667376106, 90587984, 111788363, 150179924}

{27, 11, 21, 16, 13, 5, 1, 9, 6, 2, 18, 15, 8, 17, 0, 26, 4, 3, 22, 25, 28, 23, 20, 29, 14, 10, 19, 7, 24, 12}

38

Returns: 5.3670977337341475E8
{351325280, 936297486, 535055853, 746559223, 866660089, 971215226, 367257581, 125416331, 209898918, 579691434, 862231950, 968224787, 558478873, 606827324, 12683142, 435890410, 738532467, 869550264, 219526002, 570049669, 821945372, 51511193, 464879696, 759929571, 310553542, 146132592, 36087980, 29607312, 199794303, 107867083}

{860449446, 551119583, 896680923, 248021653, 150195160, 615857365, 71753232, 517452741, 741273696, 281652150, 97144174, 603505646, 102393290, 508139401, 62849323, 115076433, 944029811, 801381790, 837143051, 16072166, 371431459, 511604777, 67583359, 688827509, 124050701, 378136901, 687476456, 12655035, 260260567, 887270759}

{9, 27, 19, 23, 18, 2, 29, 6, 3, 10, 14, 7, 20, 1, 25, 8, 22, 0, 15, 26, 12, 21, 17, 4, 13, 16, 11, 24, 28, 5}

20

Returns: 5.3623906215787506E8
{887142457, 103131515, 55663697, 178049152, 972850910, 276911717, 766634653, 310944023, 717396615, 725189249, 537794478, 292050016, 633404374, 73183286, 969096709, 49758899, 818905064, 613736187, 410143235, 218524985, 95518716, 786599738, 989576366, 793938731, 230639600, 301971609, 763893092, 905332718, 301843307, 599018843, 840286402, 188985764, 554666712, 895950100, 367034916, 380033975, 25378170, 986185923, 690977998, 742774786, 563891526, 81288829, 887341156, 197295899, 154472115, 856437864, 247054798, 973377180, 322690405, 657198033}

{191902164, 270725475, 296314125, 33994884, 64664206, 526953725, 335966493, 681073652, 284802796, 637809800, 280092494, 125089197, 826795564, 834759206, 873555651, 46346833, 67309535, 898933822, 32532756, 758287533, 494224961, 448940636, 839576363, 381566116, 646236535, 994048478, 90520334, 745807687, 967425657, 413210739, 255522073, 11844175, 683936214, 551836198, 45839059, 601116774, 78789922, 381805552, 282190426, 216109072, 19615351, 414799274, 341198270, 698927270, 102074834, 67270274, 597790457, 169384369, 966204096, 482839567}

{2, 32, 28, 46, 34, 1, 31, 44, 38, 41, 42, 6, 17, 29, 18, 49, 11, 21, 35, 13, 27, 23, 37, 24, 19, 12, 15, 20, 33, 22, 36, 8, 40, 43, 16, 45, 25, 5, 30, 3, 39, 48, 26, 10, 4, 14, 0, 47, 7, 9}

1

Returns: 6.567459495E8
{857675094, 492883062, 275053507, 595509443, 670228438, 276905436, 287934979, 62327733, 24031468, 297228531, 125663832, 106513421, 86710338, 796912634, 973291931, 495956763, 15189315, 270603531, 519016284, 871014212, 744255910, 975830911, 630114415, 502287492, 730761172, 123909785, 96534477, 829646128, 511066158, 605786788, 506807684, 368741252, 951186205, 781861191, 816767049, 621414642, 58766627, 104702027, 536258729, 935314450, 254446912, 661922561, 894344225, 341157250, 311351549, 720152509, 837114014, 179057218, 990756041, 208646651}

{902587785, 735011950, 184477561, 532702199, 89815795, 915238733, 509128338, 186350273, 597401215, 20194496, 792137061, 104208898, 241452102, 595839619, 738586443, 58219150, 69770614, 649869424, 15437531, 606029343, 437700227, 269884444, 120468258, 184560805, 463558048, 284336161, 904713315, 153188415, 463393379, 895469355, 361835066, 218497517, 482997658, 546312627, 751199717, 572813453, 314067714, 112844408, 759163726, 911468929, 985555259, 403817141, 868194181, 79523714, 999656760, 606780623, 137742864, 69427374, 109166401, 5696750}

{22, 21, 46, 5, 19, 7, 18, 43, 12, 47, 24, 32, 35, 17, 28, 33, 30, 41, 8, 25, 27, 42, 37, 3, 13, 15, 29, 10, 9, 20, 26, 36, 40, 2, 14, 38, 11, 31, 34, 16, 45, 4, 0, 39, 44, 1, 48, 49, 23, 6}

5

Returns: 5.10929303375E8
{497590035, 987283049, 708758237, 658057530, 291554637, 662615137, 523214493, 55123203, 606731256, 457798829, 927858170, 556544124, 772872591, 347459764, 486970895, 441420390, 351005146, 9053261, 42745678, 990691276, 275979639, 597790898, 867020215, 649585094, 472537211, 462989621, 381214962, 270700689, 56445656, 784936956, 105125740, 554035691, 772220005, 666400332, 64609575, 916290996, 329015468, 587824068, 971414199, 935746724, 45622896, 751788723, 344807202, 671011842, 99248486, 831778097, 112432231, 302769987, 840831358, 7694263}

{293461262, 116810996, 458001515, 12997831, 618912444, 783055080, 475987452, 852643760, 53755769, 532433108, 637580716, 11397863, 86468799, 262317074, 530314549, 3594728, 31124423, 859330018, 591418796, 2538622, 647593095, 489558046, 606843699, 844916651, 13086241, 558608539, 529211101, 125518472, 861378526, 222558812, 985729090, 7356142, 191886162, 296246958, 20353973, 810798607, 79302038, 496341425, 515958720, 985574162, 881290888, 6055789, 849488379, 820276041, 268372863, 232319282, 823870769, 299497287, 91649299, 415289564}

{14, 22, 11, 43, 12, 16, 27, 28, 21, 3, 36, 41, 6, 32, 48, 45, 4, 31, 17, 39, 1, 46, 13, 42, 35, 30, 8, 0, 2, 25, 7, 26, 5, 20, 49, 44, 19, 47, 29, 37, 9, 38, 24, 23, 10, 40, 18, 15, 34, 33}

28

Returns: 5.3605213329934543E8
{370372217, 269916518, 176088129, 641065869, 624807592, 140638685, 180132384, 64534301, 929060009, 871212541, 595910310, 985287251, 716844960, 571561420, 798878456, 28906048, 836404284, 382919866, 660971638, 919650001, 715446308, 179452960, 896373738, 782186872, 739189806, 958461657, 584421223, 213052499, 916712365, 53967753, 97382467, 139600935, 323884271, 273470597, 780666805, 801208217, 266625636, 960799189, 865742518, 48201998, 684528084, 461652827, 33489248, 253889397, 33214247, 684884058, 282795446, 722134885, 920320278, 943767084}

{494301239, 635766586, 123220043, 243191330, 270469811, 862409849, 201652986, 707407388, 75462348, 118365351, 761375141, 25361169, 110482640, 85259412, 298831766, 891149445, 738983983, 565457402, 704464988, 604726501, 613659401, 388993071, 918895682, 499665003, 642882468, 804626283, 37065415, 925677914, 526761167, 957385693, 721961351, 21062405, 445668632, 845181395, 116770089, 568654797, 560107597, 318423076, 276062184, 488086299, 289304781, 37437325, 513447469, 399787421, 975213092, 664795589, 143453220, 566713428, 82769345, 847918208}

{32, 42, 33, 5, 40, 1, 36, 43, 35, 2, 9, 23, 44, 34, 46, 38, 17, 41, 20, 31, 3, 48, 45, 49, 19, 15, 18, 30, 4, 25, 22, 39, 24, 21, 37, 11, 28, 6, 29, 7, 27, 13, 26, 8, 14, 10, 16, 47, 0, 12}

50

Returns: 5.36871162712527E8
{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}

{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}

{1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14, 17, 16, 19, 18, 21, 20, 23, 22, 25, 24, 27, 26, 29, 28, 31, 30, 33, 32, 35, 34, 37, 36, 39, 38, 41, 40, 43, 42, 45, 44, 47, 46, 49, 48}

50

Returns: 5.0E8
{65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535}

{536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376, 536805376}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0}

50

Returns: 2.68468223E8
{632968311, 604654573, 409332134, 413917875, 654008467, 238984737, 22596885, 368157949, 64606913, 50505677, 17593130, 885630944, 102370751, 363457057, 648598959, 97087790, 757931086, 996393429, 839283076, 943113341, 854692266, 413266837, 23873159, 650489530, 135068771, 3428237, 376450260, 679008032, 892884308, 297714762, 658474984, 378368972, 902369335, 67807118, 792286848, 408894155, 159308209, 667400087, 777052104, 223915122, 570422118, 794645234, 962062420, 672792869, 10618644, 463177733, 769880659, 768549731, 459571161, 461680088}

{564179425, 166779781, 874946925, 440568939, 817269311, 862532051, 443997176, 46235924, 541540082, 189397837, 196467040, 52531419, 567766810, 98836374, 972854892, 212570011, 360246884, 132163100, 879970098, 137298987, 208594577, 302908569, 784460576, 23173350, 975701438, 795079220, 486351083, 745582097, 416145304, 945922245, 59778538, 980324730, 965218380, 934725464, 273410022, 635004044, 797257514, 717407198, 681239968, 191313949, 906805035, 877707008, 96361722, 474571844, 829059736, 69216614, 687141855, 41822973, 53896068, 419628306}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 0, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 25}

36

Returns: 5.368224116584623E8
{190434465, 500376769, 198962052, 409901582, 70070133}

{521848074, 52679923, 263665307, 231556990, 176157901}

{4, 1, 0, 2, 3}

7

Returns: 2.280705376875E8
{499700690, 706826993, 511088540, 64759259, 159623559}

{563867421, 378543219, 256799908, 792081884, 391702920}

{2, 0, 3, 1, 4}

50

Returns: 5.368865323290219E8
{537529908, 381127629, 776022336, 589008314, 791029211}

{846092469, 110856388, 843709134, 109757775, 194929732}

{1, 0, 3, 2, 4}

18

Returns: 4.4503533848339844E8
{79602854, 600006163, 380159804, 443207748, 664765422, 539783364, 859591523, 895824995, 796583272, 504189760}

{140044268, 729356652, 95553266, 377256379, 920049816, 371198833, 914786287, 153693798, 147221169, 356310954}

{0, 5, 1, 9, 3, 8, 4, 2, 6, 7}

1

Returns: 1.48009976E8
{704000917, 493188988, 66159873, 84160720, 936396737, 583441649, 623944084, 648504613, 479266643, 273043710, 152694373, 619310912, 854916716}

{100763993, 996567291, 627482885, 324479181, 763869931, 781176683, 324216704, 120180884, 578416045, 22563049, 292380935, 71880894, 830667171}

{6, 12, 9, 7, 10, 4, 2, 5, 3, 11, 0, 8, 1}

8

Returns: 5.1285972928515625E8
{32751007, 104033768, 156397914, 504578273, 811466838, 257161908, 353661917, 438949722, 581641089, 970048202, 72642758, 905857793, 942745440}

{651058803, 928420842, 235126374, 722939697, 611604367, 894637092, 160668829, 177972350, 115217587, 212035317, 448341251, 828987072, 182078033}

{0, 5, 11, 7, 10, 12, 9, 2, 1, 6, 4, 8, 3}

50

Returns: 3.455592375E8
{35606806, 154150856, 618503079, 941464599, 96896296, 122078236, 722401795, 184539024, 845017933, 186522515, 79176115, 5686761, 217011219, 46910057, 70238433, 665352470, 728413483, 252316466, 173256049, 912599484}

{840395217, 659633334, 100489025, 313741329, 955077095, 592260127, 291665713, 61987692, 46225845, 475768369, 460364367, 81832651, 482435579, 78867446, 23297250, 431848229, 53462036, 598215399, 616387254, 898479969}

{8, 4, 14, 0, 9, 1, 6, 7, 16, 18, 5, 19, 17, 11, 2, 12, 15, 10, 3, 13}

6

Returns: 5.1699055559375E8
{705841319, 387485555, 761843103, 188276897, 318869355, 637656707, 620125127, 372331391, 88388459, 89028734, 270811360, 725642727, 489624811, 27494444, 432424567, 937130946, 854415962, 804558878, 113050562, 933653945, 349949238, 54086016, 705803498, 407489285, 95610495}

{791694381, 272622781, 581911455, 21767330, 199743969, 114438260, 727608649, 587229524, 728797717, 768401900, 906098880, 218970777, 241043380, 278430270, 307359236, 330072114, 401757984, 885518317, 819696926, 429252428, 317942883, 609344225, 136184743, 122501761, 574911141}

{14, 2, 1, 11, 20, 0, 24, 16, 10, 22, 5, 9, 21, 23, 18, 3, 15, 8, 17, 7, 12, 4, 6, 19, 13}

1

Returns: 3.618860865E8
{365141535, 142128065, 200369212, 501326279, 117146180, 775280353, 423681320, 294629887, 256793863, 904356214, 879602879, 686434223, 29241841, 737198652, 550502392, 175894799, 647054747, 381525174, 50156405, 144140366, 88829319, 397852620, 547324865, 867620595, 134075860, 81455988, 806287461, 52887568, 17345095, 630472642}

{643912557, 382486630, 772600707, 844281769, 736329263, 742263241, 619562122, 12526937, 36893127, 728872339, 916883151, 916496007, 267822916, 946124993, 506211012, 818325308, 122019791, 5782112, 52366835, 24692551, 149922479, 141196154, 422545171, 697247344, 861333104, 409137385, 778703332, 520136918, 462024953, 796048427}

{0, 26, 29, 17, 12, 28, 16, 13, 27, 20, 8, 1, 5, 11, 22, 21, 10, 25, 7, 9, 14, 19, 2, 3, 4, 6, 18, 23, 24, 15}

7

Returns: 6.157244885E8
{962842763, 225542656, 599338530, 993894174, 1269276, 254590516, 613791201, 371775491, 529404624, 393698812, 779174834, 533091071, 943005928, 955586537, 657116787, 438438035, 490725605, 599467811, 908406288, 31646786, 446702024, 403067092, 869974092, 435132391, 172789420, 110581449, 137412216, 351649134, 277375785, 212345312}

{845050155, 92734901, 437887968, 296905038, 939145429, 291673598, 551495555, 552936629, 663449090, 80900178, 799151795, 442623923, 466507603, 742157722, 250726814, 123624390, 33112110, 741452419, 575608555, 941518399, 773099205, 22310578, 197101844, 495589651, 309959323, 222407618, 606171100, 299887893, 574056752, 883546885}

{17, 9, 18, 26, 1, 23, 29, 8, 27, 13, 6, 2, 24, 22, 12, 4, 5, 16, 19, 7, 25, 10, 11, 3, 20, 28, 15, 21, 14, 0}

38

Returns: 5.368823299195055E8
{508519273, 68604641, 364591467, 189833767, 871242169, 933119766, 957777335, 818069649, 905659973, 983690240, 428346218, 959100358, 808754940, 481246711, 479048346, 228493715, 637390371, 975137079, 681344601, 534986450, 46834365, 928230240, 205681734, 140842230, 224734075, 224483022, 397325773, 891129176, 996939057, 953697209}

{836613737, 357974684, 22301849, 53721557, 547808451, 746060372, 986841323, 358102139, 416646375, 745017649, 194308733, 844992593, 704118006, 3063672, 178755657, 35682706, 231557387, 816146029, 10819784, 912901988, 351132478, 910170505, 693648581, 409330566, 903529089, 918382657, 633813589, 153371215, 662028186, 483268999}

{24, 20, 0, 11, 21, 15, 2, 14, 22, 18, 7, 6, 27, 5, 23, 9, 4, 16, 1, 26, 28, 12, 13, 17, 10, 29, 25, 3, 8, 19}

20

Returns: 5.3528101928505707E8
{419582345, 371563948, 124269167, 113342382, 205966928, 529149000, 207427223, 786430281, 773386510, 659614204, 783540008, 762641667, 306109917, 478158682, 308531184, 808185657, 351533013, 890103408, 541818783, 41053372, 335011770, 40870251, 934222564, 542606990, 86086654, 89238675, 653731299, 49685713, 25552021, 918226824, 675312958, 297650721, 142307125, 652098479, 410993103, 348274053, 33763833, 618420326, 134704334, 807150343, 130550884, 770760696, 422308363, 436660801, 101435731, 730839548, 97362812, 452968744, 620942955, 639181595}

{346538470, 808471079, 532568200, 133277388, 351078069, 471171208, 222516063, 4809367, 520856921, 100584439, 775552545, 48686233, 398235160, 917859670, 553301066, 809228263, 266133723, 587064899, 280164942, 253354411, 246731595, 410715826, 24115106, 669039959, 699892982, 125550838, 252395860, 797255794, 431035936, 873338815, 288953742, 777574407, 534326248, 821521943, 763368149, 885404317, 145209504, 985884212, 742730038, 666066426, 86468650, 370798937, 567269013, 337220164, 288658606, 120570078, 146448426, 407308683, 560151332, 279129723}

{44, 39, 15, 35, 46, 5, 1, 49, 4, 21, 34, 31, 6, 10, 25, 19, 2, 26, 9, 32, 37, 40, 48, 33, 29, 0, 45, 17, 12, 3, 23, 16, 11, 30, 47, 8, 24, 7, 20, 41, 14, 13, 18, 38, 43, 27, 28, 42, 22, 36}

1

Returns: 1.59096449E8
{646368358, 964240421, 407478525, 43867225, 50320786, 861940851, 730024700, 109487585, 315367956, 676007212, 728805716, 47924785, 282652817, 7523127, 175359871, 574076623, 614679778, 545049841, 380862175, 655187881, 806766843, 134045409, 2386252, 249464618, 758684379, 895633847, 547181464, 575696294, 367818627, 845126885, 718449011, 866703339, 661883659, 125927535, 910570564, 564720799, 840384740, 493111618, 526724739, 155752696, 21635183, 255530454, 56193835, 304288000, 263053581, 231553706, 878364623, 877733359, 776603547, 111743151}

{385437594, 583370390, 245788560, 240340200, 685351362, 856989294, 135974046, 85049180, 432685587, 356309027, 930176065, 3650951, 223012365, 444576077, 129578487, 986099284, 861813230, 822479581, 331727255, 388537968, 978232277, 353362438, 496584777, 34426111, 657650438, 759638358, 118496171, 388531414, 489888071, 895099719, 500274565, 875325665, 330986462, 598579479, 115665864, 16337823, 455568772, 104156264, 101387003, 740770713, 460465292, 884079422, 744421665, 535994011, 181171852, 726516506, 522093294, 42985082, 548996086, 853820549}

{4, 24, 13, 7, 45, 10, 1, 22, 31, 26, 35, 18, 19, 39, 38, 46, 17, 29, 15, 9, 34, 27, 43, 32, 25, 41, 36, 12, 20, 23, 37, 16, 8, 5, 14, 42, 3, 11, 28, 33, 40, 6, 49, 44, 0, 48, 47, 30, 2, 21}

5

Returns: 2.4482536203125E8
{78458445, 40616885, 865347745, 249081290, 891145978, 249687219, 600875987, 173224283, 8636341, 995655766, 4298675, 473922367, 674474948, 215117783, 146391379, 986434666, 545140428, 241242877, 691173276, 112862780, 589459212, 131095203, 813384559, 248864011, 181526112, 977692225, 965520400, 663164575, 474639956, 900029858, 532683210, 405614755, 940646743, 398030954, 654696045, 684309075, 500234527, 108088385, 857533358, 508870868, 103744150, 861832033, 982793236, 630735453, 76949816, 981700969, 617170118, 474606598, 75460199, 160859748}

{439985733, 664919411, 291954951, 253370291, 766299777, 473481064, 83578870, 584336530, 989161993, 558218826, 484366387, 521845202, 963833581, 277529484, 772392510, 471045980, 961838559, 272627036, 579134365, 819371916, 634014259, 682878516, 533720303, 469323848, 166130322, 463186473, 303541170, 783300440, 937793071, 379001369, 944160188, 230295157, 43920779, 88631493, 483665449, 662736910, 562112557, 567244319, 247073440, 403790903, 125463144, 583956181, 925636106, 941813079, 861485665, 550544969, 412859058, 823324223, 823172006, 991993424}

{44, 29, 22, 46, 48, 1, 37, 25, 4, 28, 7, 15, 16, 31, 34, 41, 5, 11, 35, 6, 45, 2, 9, 26, 19, 33, 30, 32, 43, 21, 27, 3, 8, 36, 40, 24, 39, 20, 42, 14, 49, 47, 12, 23, 18, 13, 38, 0, 10, 17}

28

Returns: 5.367688946415316E8
{579462207, 261642825, 237380993, 136267583, 72858540, 278356248, 554558624, 287135579, 732190562, 648690241, 177100977, 883051007, 90550705, 524252639, 561299744, 561343964, 502947120, 785583450, 229289199, 416725590, 191718918, 32179480, 792073064, 723866336, 200309965, 377943029, 323173551, 69862456, 984556041, 551753119, 60597626, 416534602, 665912298, 297978619, 552802185, 591287193, 576334867, 107360808, 878422772, 161041783, 756051049, 55523749, 44092789, 846601754, 432292742, 457908888, 260462072, 787756217, 96008691, 342267625}

{204481806, 287727609, 374447105, 996554871, 864110300, 427273424, 227014253, 39800204, 497135880, 64086647, 591553323, 557733506, 480621249, 109981975, 855712125, 33423433, 701269168, 284563345, 140784241, 432208293, 445605128, 749351645, 340248396, 489697918, 448469752, 772541139, 947606806, 561448178, 412813709, 43615496, 903715803, 617295515, 183859460, 130679261, 466366739, 47969759, 557952685, 693380992, 87769963, 55088564, 757467640, 531839640, 465338424, 90605242, 641821615, 173566902, 124028676, 195607136, 458130248, 117329271}

{30, 19, 23, 35, 46, 22, 48, 28, 14, 33, 20, 36, 6, 17, 12, 1, 31, 38, 8, 13, 41, 37, 25, 4, 49, 21, 0, 5, 27, 16, 47, 34, 43, 15, 26, 11, 3, 7, 45, 40, 10, 29, 42, 9, 39, 18, 32, 44, 2, 24}

50

Returns: 5.3687035733788276E8
{221369623, 418600362, 989826617, 370120909, 202811010, 600927857, 918616867, 925325387, 805735494, 177393014, 824314100, 374136901, 327354457, 311786365, 592007785, 742588222, 89211849, 297457400, 68703098, 487339235, 124230997, 361225680, 63484227, 650003857, 756378908, 19918802, 817052653, 101432531, 473761576, 47538843, 285889392, 695131199, 318655559, 128232362, 65252107, 521466569, 729160219, 836385328, 299308309, 387412066, 13778342, 123622408, 761548967, 193649153, 287925128, 206073105, 936237375, 229653331, 503530506, 4940473}

{716992566, 480277857, 218682507, 632993147, 130281713, 827577770, 505428303, 799850721, 929010301, 979189879, 699905918, 67416046, 526837432, 18561476, 195648408, 444605893, 540028046, 777324982, 280991221, 839336355, 164737047, 147285917, 815475118, 778802369, 193451424, 955916600, 984875474, 129688799, 185569930, 340922333, 987145627, 755078850, 821200191, 58344487, 240588350, 803998258, 885922257, 746016653, 456365332, 667448911, 577722885, 156271249, 734864957, 104560316, 27349080, 930513366, 401682564, 567377126, 560354701, 682673785}

{1, 2, 3, 4, 0, 6, 7, 8, 9, 5, 11, 12, 13, 14, 10, 16, 17, 18, 19, 15, 21, 22, 23, 24, 20, 26, 27, 28, 29, 25, 31, 32, 33, 34, 30, 36, 37, 38, 39, 35, 41, 42, 43, 44, 40, 46, 47, 48, 49, 45}

50

Returns: 5.370525822588782E8
{259229834, 725091748, 682476056, 927221306, 356410470, 875927480, 883137905, 341285944, 858132633, 921224189, 682208277, 697794613, 676303038, 355924821, 756139101, 916891388, 12439433, 494577711, 515424394, 468804765, 14542976, 945663634, 477592369, 749407933, 902740304, 504941449, 532437652, 304422867, 72318574, 92792352, 839613006, 184064762, 670400455, 522089061, 111286068, 26810924, 250532895, 846940327, 220613222, 108665527, 620680870, 902821500, 806460141, 149500261, 111262674, 415115595, 66391649, 123702107, 762209660, 434332397}

{445023227, 776752636, 232512384, 922615596, 526160569, 135252688, 280073398, 58598220, 292191909, 204908326, 3906927, 131804915, 388973088, 674307382, 506410330, 352775510, 553634660, 756943225, 52232191, 774247883, 865608753, 672913061, 529585736, 524585247, 822413322, 640848410, 792217196, 741321325, 617066872, 554426855, 28170076, 914606453, 183695845, 260682460, 689738402, 709856414, 248451502, 969811800, 620970988, 540643412, 174720125, 477394269, 672448327, 416209567, 4218004, 31375010, 768985078, 557852665, 788318236, 673733623}

{1, 0, 4, 2, 3, 9, 5, 6, 7, 8, 16, 10, 11, 12, 13, 14, 15, 27, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 40, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 49, 41, 42, 43, 44, 45, 46, 47, 48}

47

Returns: 5.468263794892577E8
{332100547, 506443342, 199163037, 861686283, 31028588, 21576358, 355051046, 675762138, 615414038, 824634272, 82705346, 496100468, 739240724, 266401191, 756782928, 281495479, 976257605, 5234430, 251307278, 449744947, 398394196, 278543757, 927139216, 70842522, 694753325, 931357221, 102217532, 316254756, 341726239, 743052122, 989988379, 673826786, 249495463, 189151415, 388029422, 133040405, 63244127, 595596822, 808802543, 531174519, 420231094, 891507890, 27274986, 11988171, 10425434, 636574269, 293483651, 986683040, 494325053, 397307283}

{288944340, 892719249, 675851041, 68599909, 816078125, 370604365, 852473484, 770812011, 686859121, 194199722, 513864133, 529363853, 720542862, 615875950, 718515268, 108572283, 748916356, 634275749, 556685460, 410235252, 165450268, 976916554, 154259495, 45241608, 841421079, 164684930, 681815877, 134904729, 3884323, 176140929, 384728367, 145345017, 68860177, 60579407, 213944926, 737454656, 283700126, 66418410, 508266667, 970559247, 113134486, 874647154, 352439453, 833677349, 490523103, 70954720, 794765986, 91955812, 557746823, 203967799}

{1, 0, 4, 2, 3, 9, 5, 6, 7, 8, 16, 10, 11, 12, 13, 14, 15, 27, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 40, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 49, 41, 42, 43, 44, 45, 46, 47, 48}

47

Returns: 5.463809445039065E8
{354707419, 723197091, 33400706, 508966914, 768438700, 874821786, 526168198, 302770930, 862242869, 530052521, 478911860, 246971235, 675397538, 400288391, 160066996, 741858819, 137743047, 443767122, 660793583, 498526068, 266842722, 773928069, 225689575, 619282175, 460121771, 716212678, 542753249, 107404111, 660684845, 100500072, 311371910, 15392263, 676213517, 344772617, 376875531, 297168570, 72110756, 903043730, 599939501, 934353625, 285612604, 78851360, 33841214, 961010143, 331656105, 193908210, 555385315, 321915506, 637675333, 216178897}

{672957928, 904518055, 842623320, 898647503, 523800230, 155261445, 467376535, 66553478, 262665556, 128061379, 19569904, 426553820, 143453642, 695783422, 771326437, 372845527, 992951992, 843437193, 275889256, 445407846, 630307172, 561501861, 376775560, 664148386, 375028357, 708431666, 858056596, 930413672, 882863526, 495731928, 999108923, 555821454, 252766337, 841732242, 306985310, 776566567, 996993687, 774361845, 695636399, 112175596, 902423224, 567722658, 538729417, 898393220, 116022433, 162572207, 123755101, 108974424, 858525755, 399644357}

{1, 0, 4, 2, 3, 9, 5, 6, 7, 8, 16, 10, 11, 12, 13, 14, 15, 27, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 40, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 49, 41, 42, 43, 44, 45, 46, 47, 48}

47

Returns: 8.055684077968707E8
{406898625, 488832926, 813662572, 783674185, 5497665, 41207282, 344622204, 863554261, 971620954, 227485730, 211802543, 823246230, 635823538, 464568880, 517494826, 942808848, 93651800, 367004866, 717170693, 789288199, 479180463, 472110270, 209527210, 870426234, 223019844, 325549643, 32998440, 346774945, 287040422, 744040549, 598935656, 693939047, 85389828, 412598228, 477613231, 90887493, 453805510, 822235436, 954441755, 277942818, 902237520, 166244297, 101189047, 538061057, 630813177, 471200227, 333386258, 724464977, 838205094, 50556950}

{366269529, 169901910, 375183575, 575796740, 40328143, 450719773, 901346383, 925842938, 797494718, 40903158, 669883487, 248946727, 734842205, 755273315, 661544955, 64971790, 846160809, 967866820, 887207226, 653118917, 98325991, 641961099, 819363214, 52031392, 32538509, 302692744, 523231620, 365924767, 879674075, 361436713, 268998072, 98459957, 531338623, 644181647, 674256697, 424183120, 94901419, 428119434, 350026057, 744912491, 469022592, 872425898, 993859218, 56381151, 480215567, 507920527, 121352941, 178892729, 328303700, 8560166}

{1, 0, 4, 2, 3, 9, 5, 6, 7, 8, 16, 10, 11, 12, 13, 14, 15, 27, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 40, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 49, 41, 42, 43, 44, 45, 46, 47, 48}

47

Returns: 2.681426262500462E8
{152740425, 801299943, 779614462, 299578043, 414681414, 543391110, 846986761, 970088385, 835351434, 194225397}

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

{0, 1, 2, 6, 3, 9, 4, 8, 5, 7}

5

Returns: 1.52740425E8
{843782475, 380503668, 402568651, 302722278, 357293784, 337970904, 494091252, 121777092, 600303548, 238800422, 93245060, 753043973, 40100364, 872859522, 52622016, 307298133, 268766986, 752125131, 129902871, 104118419, 946350529, 981383315, 694348915, 553520977, 381490080, 8607802, 758114236, 735541356, 31007055, 888330779}

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

{9, 27, 29, 14, 24, 6, 16, 20, 10, 25, 4, 18, 13, 17, 5, 8, 12, 21, 2, 19, 1, 23, 0, 28, 22, 26, 15, 7, 11, 3}

28

Returns: 4.133377164162045E8
{504803506, 945972367, 663263089, 773637952, 545812014, 545807604, 252282535, 631106210, 774959725, 852704212, 21736662, 95428622, 398887302, 165411087, 455997885, 817929914, 214223882, 123865279, 505739512, 15161807, 626668254, 2700236, 614966616, 110854542, 341493522, 620808754, 976530912, 393927318, 237281482, 430264990, 477368169, 742084988, 228753710, 140631257, 368239294, 774565724, 538955215, 473038183, 258188288, 166431294}

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

{28, 19, 37, 35, 10, 18, 1, 22, 14, 31, 26, 13, 7, 29, 30, 23, 36, 6, 12, 17, 0, 33, 5, 34, 4, 16, 39, 8, 25, 2, 32, 11, 24, 9, 38, 15, 21, 20, 27, 3}

8

Returns: 4.091754193359375E8
{750051758, 127222962, 777318160, 506083823, 121944012, 61596744, 456125765, 589990170, 174922594, 800095026, 295317809, 718513434, 473948809, 595246790, 343374338, 140950203, 115931419, 742800966, 199423167, 109654231, 105448589, 424327425, 281635791, 895504809, 911091600, 30763401, 835929773, 820746283, 27483329, 435914655, 424640400, 630051441, 415653971, 54474913, 136135264, 537597983, 116071658, 444777383, 127588152, 290994252, 97388762, 275422315, 9507686, 423853925, 723185460, 205398378, 564804129, 839116879, 948199344, 764227296}

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

{14, 17, 21, 4, 26, 41, 5, 22, 43, 1, 47, 27, 49, 3, 39, 6, 36, 30, 8, 24, 7, 16, 18, 45, 38, 40, 28, 15, 20, 0, 12, 2, 10, 42, 23, 34, 19, 35, 37, 29, 33, 13, 46, 48, 31, 44, 9, 32, 11, 25}

37

Returns: 4.550832247053232E8
{404205969, 790604997, 334354934, 96563682, 869268279, 470313466, 659590501, 5846292, 23592479, 766766906, 90623649, 46131497, 675230774, 81565292, 257225236, 519134250, 874176030, 272998003, 181757091, 9418341, 914196081, 690582626, 923206883, 457976222, 380695003, 31195623, 958813342, 388229487, 723498903, 385295450, 10479814, 980221226, 28416800, 344834749, 76784907, 750201433, 667664569, 588891762, 756047725, 543773402, 355658667, 846671374, 589904900, 30889440, 928236666, 847130136, 402540044, 654929049, 120128139, 584297135}

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

{44, 41, 34, 45, 36, 48, 21, 32, 16, 8, 17, 24, 18, 6, 31, 2, 46, 13, 20, 3, 30, 29, 7, 39, 40, 47, 9, 22, 25, 23, 37, 42, 33, 11, 5, 10, 35, 49, 38, 19, 4, 0, 27, 43, 12, 14, 15, 1, 26, 28}

50

Returns: 5.890456595151919E8
{145705171, 631958997, 905562023, 626033504, 242486096, 247871298, 34598501, 552659685, 992720619, 98092547, 982961413, 321867074, 530966691, 300103713, 778409644, 256427814, 814579165, 595559684, 158187895, 485201106, 14063036, 812262190, 402297697, 191883161, 198871922, 741769382, 326371161, 247318355, 106333948, 937707959, 546493250, 104555473, 422183310, 304571626, 730588978, 664669406, 404959278, 765187479, 69845444, 397679897, 715796381, 52806856, 572063325, 99279425, 205426923, 202989322, 208223594, 20006087, 798549006, 366411489}

{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

{48, 26, 16, 39, 35, 5, 8, 19, 24, 30, 41, 46, 25, 13, 12, 21, 11, 9, 44, 40, 20, 7, 18, 3, 1, 6, 32, 10, 15, 28, 31, 22, 49, 2, 47, 33, 38, 0, 34, 23, 42, 4, 45, 27, 17, 37, 29, 14, 36, 43}

50

Returns: 4.4166076890211535E8
{0, 1, 0, 0, 0, 1, 1, 1, 0, 0}

{0, 1, 1, 1, 0, 0, 0, 1, 0, 0}

{0, 3, 2, 9, 5, 4, 8, 1, 6, 7}

50

Returns: 0.0
{1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1}

{0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0}

{28, 21, 7, 24, 9, 17, 26, 22, 20, 15, 13, 27, 11, 0, 23, 1, 10, 2, 3, 8, 29, 18, 4, 19, 14, 25, 12, 6, 16, 5}

50

Returns: 0.500595191484301
{0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1}

{0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1}

{32, 4, 19, 34, 2, 27, 36, 9, 17, 8, 5, 13, 33, 12, 16, 20, 23, 1, 28, 22, 14, 24, 10, 37, 18, 31, 7, 25, 39, 11, 29, 0, 35, 15, 26, 3, 38, 6, 21, 30}

50

Returns: 0.5000000162221045
{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1}

{0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0}

{26, 4, 35, 29, 30, 38, 22, 32, 19, 39, 16, 28, 34, 5, 14, 18, 7, 9, 2, 49, 27, 37, 20, 24, 11, 45, 48, 44, 23, 3, 43, 1, 17, 15, 6, 46, 12, 0, 13, 8, 33, 25, 41, 21, 40, 47, 42, 10, 31, 36}

50

Returns: 0.5000006407145943
{0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1}

{0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0}

{38, 6, 0, 31, 7, 26, 25, 45, 10, 39, 33, 2, 20, 13, 4, 15, 47, 41, 8, 16, 29, 18, 40, 17, 19, 49, 3, 24, 12, 44, 9, 36, 23, 32, 43, 5, 42, 27, 11, 28, 21, 37, 30, 48, 46, 14, 35, 34, 22, 1}

50

Returns: 0.4999683461319364
{557480818, 915304306, 236021483, 266079838, 876453626, 338938109, 950974265, 134976492, 625694185, 82382801, 638279580, 236790808, 478567102, 498800021, 286663392, 595204616, 616360261, 58449757, 230776168, 251223929, 394419654, 883129693, 941936029, 456178658, 381986552, 814121587, 375834004, 850890755, 503149662, 559678128, 993061591, 495657080, 877089720, 43817652, 678175240, 862503657, 981492203, 440724319, 108022659, 219906704, 533306377, 385242936, 294835345, 525182911, 165715283, 267333869, 744519054, 738868531, 940295734, 139469153 }

{15154958, 423055723, 657636268, 601618647, 174344001, 451471630, 662892226, 152289906, 219566047, 272138699, 867881164, 502186189, 974391975, 35678190, 534509453, 291277535, 949347878, 78374387, 94891018, 748625452, 67033305, 524264641, 209242748, 681795417, 686922074, 945842079, 198622207, 156167696, 468982326, 374983708, 70768810, 10805416, 381486261, 582555264, 334314003, 967174302, 35490289, 768403187, 435013519, 116994720, 515235371, 298824246, 101196383, 546073484, 448902097, 272682927, 690643371, 561866783, 638303546, 928120607 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.368702307114401E8
{11469200, 171092839, 54028366, 525344220, 36060392, 123986172, 882842555, 153115321, 388590479, 940526812, 583755882, 945527302, 602282880, 415242187, 225775235, 978011148, 893221412, 518158763, 763459036, 535252067, 800238306, 791967215, 252976259, 274037365, 568618895, 428102175, 75383093, 359625734, 621704949, 790852181, 247470571, 608154538, 596511058, 292638145, 475937352, 159494987, 89559766, 307846437, 711099436, 304218791, 639245867, 174527832, 590065189, 840979915, 156787945, 55470023, 116865528, 260065185, 887005213, 919029999 }

{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 267803826, 118184380, 806837793, 713494570, 486109402, 738075947, 218440138, 798402503, 130486769, 924491158, 150564127, 302486934, 158862338, 703891035, 416159579, 92773226, 487422093, 412221928, 115678560, 883857006 }

{37, 18, 12, 42, 22, 44, 38, 3, 46, 8, 33, 35, 19, 32, 15, 10, 28, 23, 1, 21, 11, 9, 45, 26, 31, 20, 27, 7, 0, 43, 6, 17, 13, 40, 47, 4, 24, 5, 36, 49, 34, 16, 41, 29, 25, 48, 39, 14, 30, 2 }

42

Returns: 4.559194893730465E8
{101579248, 729605492, 286977090, 671999882, 397752276, 328778697, 240594394, 59897458, 591568885, 345872567, 447953811, 115324572, 7753033, 351528380, 247369160, 705387425, 609521265, 50256586, 353531365, 114233991, 121080266, 330424601, 294947419, 167748855, 338600986, 256627408, 563293415, 917818335, 239044323, 51315978, 709056632, 58040939, 746213368, 362558502, 867841692, 492758128, 263407213, 364809429, 451715767, 731280385, 332051326, 489561328, 989967867, 29183604, 25679480, 832754549, 353657169, 448550794, 938642252, 535819709 }

{848325428, 259034081, 878917078, 687227982, 909248438, 351612040, 624394880, 541424205, 383601556, 586917330, 352018244, 102017797, 633914301, 250009641, 599146172, 366106491, 947188997, 33468956, 866520381, 776607870, 984058492, 220684131, 222208184, 679473729, 252357936, 991211773, 515896920, 832662244, 839485621, 20080443, 62914948, 263742945, 887927880, 792915172, 907354208, 23009518, 548323053, 308757277, 23669340, 628975404, 394439521, 92454505, 66128373, 253127217, 534442784, 688496478, 525489963, 940810982, 902826623, 58170455 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.368701618999068E8
{234623459, 645634799, 435755699, 564573459, 345756729, 123346499, 945634576, 235324599, 994564569, 934563129, 234643759, 342523469, 923452345, 576749999, 234523459, 324542599, 235645999, 923453245, 923452369, 923452345, 996435399, 234569999, 234569999, 934569999, 999534539, 245724579, 999992346, 912359999, 999923462, 935684999, 935685369, 999945799, 999923459, 999345799, 999453879, 999574599, 999345699, 999969999, 999956899, 999957999, 999993457, 949679999, 999658999, 999938999, 999994569, 999956999, 979999999, 999799999, 969999299, 999949994 }

{234623459, 645634799, 435755699, 564573459, 345756729, 123346499, 945634576, 235324599, 994564569, 934563129, 234643759, 342523469, 923452345, 576749999, 234523459, 324542599, 235645999, 923453245, 923452369, 923452345, 996435399, 234569999, 234569999, 934569999, 999534539, 245724579, 999992346, 912359999, 999923462, 935684999, 935685369, 999945799, 999923459, 999345799, 999453879, 999574599, 999345699, 999969999, 999956899, 999957999, 999993457, 949679999, 999658999, 999938999, 999994569, 999956999, 979999999, 999799999, 969999299, 999949994 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.471117769310151E8
{162037696, 191451497, 235452021, 326366258, 321692440, 180584811, 73086742, 101699959, 28560172, 473715784, 112252469, 158841514, 365207742, 267843234, 433464895, 191820576, 73226451, 299615447, 467822519, 141720078, 348171402, 225483313, 12351033, 185841236, 203998296, 484321975, 199341297, 419577351, 203234381, 402457472, 131634268, 384758679, 379853419, 493833394, 479941559, 365585010, 333668658, 282330750, 522029677, 145149921 }

{1024, 524288, 268435456, 32768, 134217728, 268435456, 2097152, 268435456, 65536, 2, 268435456, 268435456, 2048, 1, 4, 262144, 268435456, 32, 16384, 16777216, 128, 268435456, 4096, 268435456, 268435456, 268435456, 67108864, 512, 8, 1048576, 16, 4194304, 268435456, 64, 131072, 33554432, 8388608, 268435456, 256, 8192 }

{6, 2, 39, 9, 14, 17, 28, 26, 11, 12, 10, 1, 8, 18, 23, 25, 15, 16, 4, 22, 13, 7, 29, 35, 33, 0, 20, 24, 19, 31, 21, 5, 32, 38, 30, 3, 34, 37, 27, 36 }

49

Returns: 2.6959897387830424E8
{397140766, 1007545, 181423094, 517423764, 242555231, 239694559, 20817063, 646702213, 721223145, 925413493, 576175796, 391559, 573507834, 832034837, 60547372, 566223552, 535355847, 373863114, 166938384, 947298317, 152793112, 913464196, 20007923, 397347667, 943144245, 54306215, 401983167, 913697350, 360176779, 533446915, 891139870, 133402167, 395068154, 592088524, 238153003, 938338727, 764350329, 18749347, 16760304, 465892662, 516892557, 104871848, 933434759, 9441829, 806354751, 620993601, 846080983, 323688538, 540213043, 31529458 }

{477284541, 712393236, 447365887, 19638358, 474604343, 628989919, 22463585, 598720813, 455579401, 914017466, 816382613, 41638180, 290929603, 800380121, 530818023, 432037632, 480848839, 264727191, 712861346, 418127564, 588726217, 436514952, 72392241, 312707313, 912559159, 27642042, 363202692, 105937742, 141667026, 142293, 995542539, 716103207, 395851966, 399990244, 31875370, 188732986, 996064967, 248019047, 275304436, 387465643, 654211344, 487179233, 488293246, 343662709, 828666518, 132770790, 523074981, 97714209, 919724694, 660126135 }

{41, 15, 11, 37, 43, 19, 36, 31, 49, 4, 32, 7, 17, 18, 28, 16, 38, 22, 42, 23, 35, 30, 6, 48, 44, 29, 33, 39, 2, 46, 9, 27, 14, 12, 10, 1, 0, 26, 40, 20, 24, 47, 5, 8, 25, 3, 21, 13, 34, 45 }

50

Returns: 5.36843892268904E8
{569933734, 207763660, 152454210, 729262581, 144139128, 249547202, 649604549, 235116564, 488197459, 830363961, 418025585, 757666882, 732318277, 142793614, 64032981, 883832806, 741974576, 290368137, 857286099, 327992911, 528813092, 954803385, 238264795, 88791913, 159625357, 297019259, 29052793, 340242638, 165107635, 179158922, 995289768, 200888192, 739751417, 952173561, 871624134, 886614153, 159198787, 615248857, 989108089, 363435632, 568747074, 46807270, 235443142, 250505135, 912569724, 688490414, 150531539, 179839421, 227653157, 807801589 }

{545708229, 770424238, 483437507, 294901246, 210260610, 716797526, 909545425, 558361075, 731978186, 900606571, 955674687, 269288995, 498368922, 606018850, 130951709, 6255265, 444794780, 363273946, 534292395, 969403930, 913967426, 607777403, 788685593, 76127620, 983966995, 97551199, 157661983, 70168344, 174478631, 719951326, 508903882, 686441198, 754735790, 809816692, 631331671, 115536180, 931678609, 798880056, 572192779, 969806269, 198946814, 469520127, 246364444, 102695399, 575013546, 220836896, 958473379, 196269193, 526799861, 25683680 }

{47, 9, 38, 2, 37, 3, 23, 25, 29, 22, 0, 13, 49, 20, 43, 33, 17, 14, 1, 45, 30, 12, 15, 48, 34, 44, 16, 19, 41, 27, 42, 18, 40, 6, 26, 4, 24, 11, 32, 21, 5, 46, 31, 36, 7, 8, 28, 10, 39, 35 }

50

Returns: 5.0354342253941244E8
{375156976, 90712533, 81681207, 553842178, 145846347, 621003691, 384621538, 671140025, 973029649, 878818988, 146380559, 146961659, 937401588, 738484778, 143853829, 704965265, 257642803, 295463871, 827868428, 128833251, 35703504, 660810951, 34749087, 34111817, 71535156, 119924094, 739859383, 968446369, 946052275, 270888345, 323078966, 84471224, 147197123, 268247728, 609866260, 1099748, 130704459, 75762186, 134162152, 857490948, 86247170, 67154523, 120200973, 556053276, 113911800, 4716993, 374942177, 60219474, 76090079, 47208808 }

{79176543, 610576179, 504443421, 60838140, 118192, 609108918, 92033137, 875375161, 530884366, 645095123, 285180330, 139066310, 17080752, 519923122, 191238989, 67721035, 146851402, 911552988, 811981175, 293612867, 3221985, 604593823, 179144818, 853790614, 80580849, 67081824, 543709993, 95047749, 543325783, 152364914, 147202976, 469048162, 9565818, 8923842, 68442421, 109122302, 559489553, 92129305, 62159238, 129625681, 39005904, 135497553, 3438672, 167801499, 143266738, 391667583, 71836981, 67519468, 30015721, 102781160 }

{49, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48 }

50

Returns: 5.368656463089642E8
{444305032, 654534040, 507472054, 469872354, 592218042, 753483318, 937460258, 410753064, 327843203, 357579521, 112911241, 785959964, 122991975, 287915881, 355817805, 461057818, 660573153, 322209107, 787334334, 264617485, 456043541, 476761127, 424009146, 147871420, 146084411, 193827384, 552347451, 759461338, 887062250, 342730654, 816177339, 184765175, 679459578, 871315813, 987521600, 878217912, 103590233, 837320501, 948519222, 36586206, 267742267, 135974968, 603458764, 60196542, 703081976, 773704871, 705250107, 823468769, 480217452, 35884658 }

{234608618, 53913947, 133520130, 658657517, 535232390, 500783706, 534468020, 45680051, 358527961, 522964968, 322028412, 320491893, 215848798, 754933377, 856895525, 726286391, 173788128, 502948604, 860367284, 917588176, 552246682, 466247123, 369902733, 387873815, 698349020, 351144163, 814592010, 148633650, 458980796, 240263929, 808174882, 564385947, 687215569, 48163141, 133757219, 513381558, 752185160, 501458137, 513914683, 943701563, 760636458, 731109597, 540092714, 870580730, 56284923, 797083442, 869853199, 239618818, 687711229, 215431033 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

49

Returns: 5.368704568178051E8
{1361955, 207579012, 628145516, 376140462, 883515280, 186969585, 762888635, 326402539, 98152102, 158176572, 61402892, 127860889, 9580638, 570870044, 646139319, 178509022, 484027666, 61263304, 841082555, 558212774, 940563715, 26389629, 579113528, 496147999, 925801172, 837151740, 70301173, 656585275, 285845005, 902071050, 403573723, 727123762, 9467290, 296231662, 631265400, 899374333, 520690249, 798571510, 491747709, 799313372, 643215695, 789204466, 614608448, 162733264, 456517316, 555253431, 806956091, 181457954, 528156706, 751354013 }

{158398859, 152040410, 743974602, 458000642, 37883250, 164556873, 882264704, 205461189, 877444309, 167035008, 785986538, 300206284, 732553407, 775142614, 132099860, 896205950, 555144412, 457641318, 19344367, 590064713, 506507263, 909420687, 489726669, 55434270, 793692316, 210461042, 901329638, 537850352, 29523791, 614794871, 570497239, 905203769, 706091347, 904237001, 118054686, 337246324, 307178252, 150625749, 896162463, 644505508, 271356542, 1738703, 865692962, 226102988, 593986003, 122173997, 807688147, 583502197, 468916697, 747545898 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.3686159266661096E8
{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912 }

{1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 0 }

50

Returns: 3.675260633931588E8
{127964236, 193294433, 367693164, 878819442, 876602606, 553990294, 648514736, 19867475, 248974455, 600977938, 75517326, 835113965, 785369435, 304869191, 840367159, 913727604, 89207564, 326071327, 895875451, 224029243, 572821934, 49942133, 407352928, 26460441, 574775331, 179692521, 653064867, 627955544, 259309282, 83495267, 870817371, 725403610, 17225825, 200357736, 246634125, 67792545, 327239897, 856194563, 240608511, 194022239, 768726581, 265201748, 167199056, 860648236, 298205274, 270116093, 374890252, 918005705, 235353457, 6794358 }

{34937010, 595477635, 457969408, 551633226, 339826559, 597822973, 171948429, 74581787, 352524367, 99766772, 27970647, 500209407, 260853269, 534669942, 337287794, 256096576, 229377390, 974711988, 777096630, 82577357, 412607158, 447083386, 394958133, 548998820, 970605027, 665185301, 228463897, 808460814, 486565650, 99609866, 764466755, 245828987, 119345865, 339774453, 265123809, 319357806, 833632642, 370060809, 868975609, 36275999, 641290946, 326280622, 134151433, 157305151, 531506378, 830384705, 483232878, 295420029, 80329543, 2962604 }

{12, 1, 9, 49, 0, 27, 36, 31, 29, 45, 18, 46, 32, 40, 23, 33, 26, 41, 48, 17, 8, 47, 22, 34, 30, 7, 6, 11, 5, 4, 2, 21, 42, 35, 10, 39, 25, 3, 43, 16, 38, 37, 14, 13, 24, 15, 28, 19, 20, 44 }

50

Returns: 5.35351279631081E8
{43513, 32434, 32422, 43214, 234, 232, 3, 23, 342, 3241, 43513, 32434, 32422, 43214, 234, 232, 3, 23, 342, 3241, 43513, 32434, 32422, 43214, 234, 232, 3, 23, 342, 3241, 43513, 32434, 32422, 43214, 234, 232, 3, 23, 342, 3241, 43513, 32434, 32422, 43214, 234, 232, 3, 23, 342, 3241 }

{932459, 1413, 4324, 12345, 2583, 3248, 32148, 23448, 6193, 3249, 3249, 123, 439, 2359, 13249, 3460324, 14912, 41127, 14883, 12388, 1248, 1238, 1238, 48148, 1248, 1237, 3127, 124, 2148, 1248, 4128, 1248, 1427, 4568, 258253, 2358, 2358, 2358, 253813, 132, 142, 1248, 4128, 5932, 259, 1248, 1428, 3258, 6304, 3469 }

{21, 31, 41, 1, 11, 22, 32, 42, 2, 12, 20, 30, 40, 0, 10, 23, 33, 43, 3, 13, 24, 34, 44, 4, 14, 35, 45, 5, 15, 36, 46, 6, 16, 26, 37, 47, 7, 17, 27, 28, 29, 8, 9, 18, 19, 38, 39, 48, 49, 25 }

50

Returns: 456954.3337116209
{804289383, 846930886, 681692777, 714636915, 957747793, 424238335, 719885386, 649760492, 596516649, 189641421, 25202362, 350490027, 783368690, 102520059, 44897763, 967513926, 365180540, 540383426, 304089172, 303455736, 35005211, 521595368, 294702567, 726956429, 336465782, 861021530, 278722862, 233665123, 145174067, 468703135, 101513929, 801979802, 315634022, 635723058, 369133069, 125898167, 59961393, 89018456, 628175011, 656478042, 131176229, 653377373, 859484421, 914544919, 608413784, 756898537, 734575198, 973594324, 149798315, 38664370 }

{129566413, 184803526, 412776091, 424268980, 911759956, 749241873, 137806862, 42999170, 982906996, 135497281, 511702305, 84420925, 937477084, 827336327, 572660336, 159126505, 805750846, 632621729, 100661313, 433925857, 141616124, 84353895, 939819582, 1100545, 998898814, 548233367, 610515434, 585990364, 374344043, 760313750, 477171087, 356426808, 945117276, 889947178, 780695788, 709393584, 491705403, 918502651, 752392754, 474612399, 53999932, 264095060, 411549676, 843993368, 943947739, 984210012, 855636226, 749698586, 469348094, 956297539 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.368702412046428E8
{757148, 167851001, 301413357, 336971125, 659598369, 160567226, 391749388, 4890852, 35766291, 26239573, 473038165, 597007, 3615545, 326051437, 392289611, 118341523, 170427799, 37215529, 675016434, 168544291, 683447134, 950090227, 82426873, 116752252, 194041605, 706221269, 69909135, 257655784, 84970744, 21417563, 37379061, 40873981, 8670529, 80835681, 436291073, 653352031, 106923811, 374079501, 466701607, 86546365, 247776868, 480572137, 222071041, 36629217, 366496749, 549646417, 278840199, 119255907, 33557677, 379268590 }

{150378796, 137583463, 225450721, 32230963, 709031779, 144328646, 513494529, 36547831, 416998222, 84161665, 318773941, 170724397, 553666286, 368402971, 48581613, 31452501, 368026285, 47903381, 939151438, 204145360, 189920160, 288159400, 133145006, 314295423, 450219949, 160203213, 358403181, 478734385, 29331901, 31051111, 110710191, 567314089, 139695685, 111511396, 87708701, 317333277, 103301481, 110400517, 634446253, 481551313, 39202255, 105948, 738066085, 26137201, 8465310, 55521105, 554160985, 43110748, 94689271, 217042883 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.331598021814339E8
{2675798, 356535037, 217775399, 557879438, 135222824, 823807584, 298019527, 54948381, 344819270, 872817022, 72004243, 417934506, 418871721, 913007600, 510613051, 784832938, 870296037, 87313714, 483200500, 409991732, 400938710, 580489, 801379392, 419242038, 950469884, 379839028, 347104842, 811339761, 18334663, 398088272, 763469422, 21010461, 607139660, 981244821, 431406250, 594878836, 657568756, 729425776, 649827216, 2388025, 602242797, 574347810, 272838882, 873630869, 487355409, 783451932, 658463806, 210167797, 723281997, 141664306 }

{472675880, 124220706, 994761146, 126571623, 543462743, 797747381, 506410651, 743083936, 461603493, 524745313, 141172207, 77589266, 545755773, 600828218, 58834086, 977162023, 195707053, 568919193, 559104150, 845534268, 423823569, 13863299, 272398430, 696662450, 887494167, 759753838, 332630733, 398474325, 822437987, 55912729, 392654982, 295113866, 32649786, 239932479, 421685489, 428628880, 37679859, 928096139, 171712815, 499283351, 305357803, 165401373, 576872616, 851113576, 766229591, 488223054, 680791950, 814452995, 57142246, 92412451 }

{27, 3, 18, 9, 21, 32, 48, 36, 46, 8, 0, 6, 28, 13, 24, 47, 4, 12, 2, 19, 49, 14, 11, 38, 40, 44, 26, 33, 10, 41, 15, 5, 29, 17, 22, 31, 16, 25, 23, 37, 34, 20, 1, 35, 42, 45, 30, 43, 39, 7 }

50

Returns: 5.370935502796258E8
{235960473, 867870674, 18115101, 763488091, 769057341, 606036895, 524678817, 770950989, 807518898, 129598016, 315830550, 660621059, 472955407, 542286188, 743737278, 526788449, 361038276, 908496327, 616874575, 853867645, 125203580, 343566883, 436849299, 734101098, 274305537, 490957270, 527511652, 302354111, 223665808, 305603292, 238607248, 223467457, 432463505, 580021969, 903965499, 957356859, 98820590, 328351972, 296276386, 969542956, 242009011, 991467166, 721516746, 126828145, 429179511, 490563696, 364461941, 44755697, 616907865, 512885711 }

{309336457, 341976866, 550578736, 178517625, 236390287, 179902800, 64776337, 802150094, 296021890, 599288172, 516419422, 349758193, 118913846, 989620732, 123492206, 45536709, 528116878, 323341529, 481082834, 146544893, 981430686, 828742753, 914879354, 916306096, 805689966, 247225166, 622047989, 663163369, 473877108, 196870754, 789213700, 569109417, 54721745, 423424302, 671729431, 194710228, 961541622, 538163061, 858245825, 261789385, 729655291, 324313480, 563034051, 295216759, 282550950, 473227844, 720233291, 162326695, 933353543, 939322862 }

{35, 45, 8, 47, 41, 19, 16, 15, 36, 23, 1, 44, 40, 30, 12, 29, 42, 18, 13, 34, 9, 24, 17, 37, 7, 25, 49, 11, 27, 22, 43, 39, 38, 46, 10, 48, 26, 21, 2, 0, 31, 4, 14, 6, 32, 33, 28, 3, 20, 5 }

50

Returns: 5.368720762036266E8
{770629206, 798942531, 119487847, 319390108, 436364455, 808182870, 904968425, 120934605, 418190371, 914475532, 391136889, 397802736, 144205162, 12534041, 973706069, 936324827, 566206620, 856203250, 101231693, 39893175, 923806016, 421198967, 146423070, 883510277, 289317699, 244607611, 346085743, 222683697, 615877068, 333430661, 204078422, 449037490, 39539011, 521606189, 136792872, 124572998, 969354278, 621597791, 617674675, 684323730, 31859542, 164193013, 867261699, 427650634, 322501314, 830626895, 325452077, 969637728, 342199390, 381741884 }

{819278790, 446250189, 68427868, 575196951, 635738401, 772572249, 481102810, 563944864, 2307578, 545927182, 492151094, 23851471, 863087190, 554874220, 113995247, 900792731, 856646122, 46202315, 559928730, 132738484, 537756444, 821409762, 973684156, 927016787, 852800607, 14612118, 708479295, 45665364, 95666637, 443500117, 673217624, 566170690, 357576838, 778077797, 952306797, 650064626, 229749681, 866867030, 2091682, 705813325, 500002575, 155370134, 290880044, 54920509, 83737379, 103306303, 464533340, 671474566, 407788379, 593366584 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.3687071829191947E8
{11087255, 977090921, 849562017, 117388474, 19361008, 143384740, 128522870, 539330883, 20981150, 700519698, 234988919, 124950840, 835732762, 917261587, 63546688, 584687338, 67271479, 341705732, 493947642, 82538970, 908961433, 385651889, 77956321, 37461315, 6242107, 226975711, 551253199, 929917586, 94279912, 783038657, 531801764, 81688548, 249271749, 150167940, 832195296, 557342860, 768106691, 261134276, 104280338, 891188119, 251810861, 714420501, 310538840, 557547068, 874539039, 525930875, 136278510, 792431727, 3636489, 379811314 }

{225659134, 87179779, 1024, 2048, 470054845, 8192, 1048576, 512, 525690566, 81945210, 269332702, 67108864, 8, 109335770, 16777216, 16384, 130834923, 82391323, 536870912, 8388608, 594835188, 2, 264375317, 678115520, 4, 4194304, 524288, 400298820, 134217728, 200677301, 4096, 16, 32, 2097152, 65536, 64, 131072, 206398840, 904673339, 39626683, 1, 32768, 268435456, 33554432, 599550711, 945844606, 262144, 128, 256, 241176446 }

{8, 11, 39, 15, 42, 36, 1, 21, 9, 23, 35, 31, 0, 37, 10, 22, 18, 20, 38, 4, 2, 49, 47, 32, 19, 34, 33, 24, 29, 27, 26, 6, 13, 40, 43, 5, 14, 17, 45, 28, 46, 12, 44, 16, 41, 7, 25, 48, 3, 30 }

50

Returns: 5.369492751004112E8
{922338501, 693863603, 251224975, 835097230, 238096473, 193535118, 750323680, 743578632, 21876332, 781671748, 654291075, 947519536, 372108093, 927835576, 952577000, 325039668, 316033706, 130074797, 894252144, 90606020, 433704476, 954888464, 999906561, 426216130, 987987702, 528231082, 610569311, 325331798, 310675598, 412114850, 989296057, 997181290, 821558032, 910867139, 355224996, 188806225, 559740401, 779935410, 467637320, 393550331, 439591849, 949416895, 588675973, 561621593, 431495319, 971112949, 174502213, 678349512, 935642144, 221471327 }

{519173604, 257946220, 544880913, 871195252, 775574665, 228393865, 188139038, 70570361, 186919482, 36550984, 220144569, 233592694, 310605342, 990302236, 394398386, 614639, 652974631, 561477846, 34588197, 78506300, 570468703, 287086, 919243469, 835924580, 902591836, 290183496, 681906392, 960877925, 192999400, 999461174, 255296857, 954560817, 822340497, 628416018, 357359093, 792762866, 149105943, 783531024, 46586182, 114032243, 15515521, 519148379, 924437796, 512581339, 654079999, 605006216, 439068691, 549118398, 391238888, 141933962 }

{11, 33, 31, 39, 44, 16, 22, 17, 9, 13, 47, 37, 41, 24, 10, 6, 46, 26, 23, 25, 8, 1, 12, 49, 38, 0, 30, 28, 3, 2, 27, 5, 42, 45, 19, 32, 18, 35, 43, 40, 15, 48, 7, 4, 21, 36, 20, 29, 14, 34 }

50

Returns: 5.3687040922450286E8
{1, 2, 3 }

{0, 0, 0 }

{1, 2, 0 }

1

Returns: 2.0
{1361955, 207579012, 628145516, 376140462, 883515280, 186969585, 762888635, 326402539, 98152102, 158176572, 61402891, 127860889, 9580638, 570870044, 646139319, 178509022, 484027666, 61263304, 841082555, 558212774, 940563715, 26389628, 579113528, 496147999, 925801172, 837151740, 70301172, 656585275, 285845005, 902071050, 403573723, 727123762, 9467290, 296231662, 631265400, 899374333, 520690249, 798571510, 491747709, 799313372, 643215695, 789204466, 614608448, 162733264, 456517316, 555253431, 806956091, 181457954, 528156706, 751354013 }

{158398859, 152040410, 743974602, 458000642, 37883249, 164556873, 882264704, 205461189, 877444309, 167035008, 785986538, 300206284, 732553407, 775142614, 132099860, 896205950, 555144412, 457641318, 19344366, 590064713, 506507263, 909420687, 489726669, 55434269, 793692316, 210461042, 901329638, 537850352, 29523791, 614794871, 570497239, 905203769, 706091347, 904237001, 118054686, 337246324, 307178252, 150625749, 896162463, 644505508, 271356542, 1738703, 865692962, 226102988, 593986003, 122173997, 807688147, 583502197, 468916697, 747545898 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 0 }

50

Returns: 5.368615926666109E8

Statistics

Problem Statement for "KingXMagicSpells"

Problem Statement

Definition

Notes

Constraints

Examples