TopCoder Statistics - Problem Statement

Problem Statement

The galaxy contains an unlimited supply of habitable planets. These are numbered 0, 1, 2, ... in decreasing order of terraformation. Planet 0 is the origin of life in the galaxy, and it is still the planet best suitable for life.

There are multiple colonies in the galaxy. Their current state is described by the int[]s planet and colonySize. For each i, there is a colony on planet planet[i] with population colonySize[i].

At any moment, there can be multiple colonies on each planet (including planet 0). As soon as a colony becomes empty, it ceases to exist completely.

For some unspecified reason it became necessary to relocate all colonists back to planet 0.

It is unclear whether this is the responsibility of the Galactic High Command (below called "player A") or the Galactic Colonization Authority ("player B").

The two organizations discussed this and came to an agreement that they will issue alternating relocation orders. Each relocation order must move some positive number of colonists towards planet 0, using one of the moves described below.

The player after whose move all colonists are on the home planet will be celebrated as the one who successfully completed the relocation. (Equivalently, the player unable to make a valid move loses.)

Both players are trying to reach this goal and play optimally.

There are three types of allowed moves:

A normal move.
Select a colony on some planet P > 0 and another (currently existing, non-empty) colony on planet P-1.
Select a positive number X up to and inclusive the population of the first colony.
Move X colonists from the first colony to the second one.
 
A slow move.
Select a colony on some planet P > 0.
Select a positive number X up to and inclusive the population of that colony.
Build a new colony on planet P-1. While you do so, take X colonists from the old colony and move them slowly to the new one. As the move is slow, the colonists will multiply along the way and exactly 2*X of them will arrive to their destination.
 
A fast move.
Select a colony on some planet P > 0 such that P is an odd prime (3, 5, 7, 11, ...) and the population of the colony is at least P.
Relocate the entire colony to planet P-2 (as a new colony on that planet).
While adapting the colony to the new, different environment, P of the colonists will die. (If the original colony had X colonists, the new one will have X-P.)

A less precise but shorter version of the same rules:

Move any positive number of people from a colony on planet P to an existing colony on planet P-1.
Take X people from a colony on planet P, create a new colony on planet P-1 with 2*X people.
Take an entire colony of X people from planet P, where P is an odd prime, and create a new colony on planet P-2 with X-P people.

Two moves are different if you make different selections during the move.

For example, suppose there are four colonies: colony A and colony B on planet 4 with 1 person in each of them, colony C on planet 5 with 1 person, and colony D on planet 5 with 7 people. Then, the possible moves look as follows:

There are 16 ways to make a normal move. Three of them are "move 1 person from C to A", "move 1 person from C to B" and "move 4 people from D to B".
There are 10 ways to make a slow move. Two of them are "move 1 person from colony A (which ceases to exists) and create a new colony E on planet 3 with 2 people" and "take 4 people from colony D and create a new colony E on planet 4 with 8 people".
There is only 1 way to make a fast move: "take the entire colony D and instead create a new colony E on planet 3 with just 7-5 = 2 people".

Player A is the one to make the first move. Return the count of different winning first moves they can make. (In particular, return 0 if the current position is losing for them.)

Definition

Class:: Colonists
Method:: countMoves
Parameters:: int[], int[]
Returns:: long
Method signature:: long countMoves(int[] planet, int[] colonySize)
(be sure your method is public)

Notes

As shown in an example in the statement, relocating one colonist slowly produces two new colonists. Don't make any human-based assumptions about how the colonists multiply, just accept that their number always doubles during a slow move :)

Constraints

planet will have between 1 and 100 elements, inclusive.
colonySize will have the same number of elements as planet.
Each element of planet will be between 0 and 10^6, inclusive.
At least one element of planet will be positive.
Each element of colonySize will be between 1 and 10^9, inclusive.

Examples

{2, 2, 3, 3, 5, 5, 12, 12}

{12, 12, 5, 5, 8, 8, 3, 3}

Returns: 0

The second player has a fairly trivial winning strategy based on symmetry, so this is a losing position for the player whose turn it is.
{1}

{470}

Returns: 1

Relocate everyone to planet 0 using a slow move and win.
{0, 1, 1}

{30, 470, 420}

Returns: 2

One possible winning move is to relocate 50 people slowly from colony 1 to a new colony on planet 0. After the move we will have: on planet 0 a colony of size 30 and a colony of size 100, on planet 1 two colonies of size 420 each. It can be shown that this is a losing position (for the player whose turn it then is). The other possible winning move is to relocate 50 people quickly from colony 1 (on planet 1) to colony 0 (on planet 0). After the move we will have: on planet 0 a colony of size 80, and on planet 1 two colonies of size 420 each.
{3, 4, 5, 11}

{1, 7, 2, 14}

Returns: 2

One of the two winning moves here is a fast move.
{3, 4, 5, 9}

{1, 7, 2, 14}

Returns: 1
{10, 11}

{3, 11}

Returns: 3
{9, 9, 10, 11}

{1, 1, 23, 11}

Returns: 5

2 normal from planet 10, 3 of different types from planet 11
{9, 10, 11}

{3, 23, 15}

Returns: 4

one normal and one slow from planet 10, one normal and one slow from planet 11
{9, 10, 11}

{4, 23, 15}

Returns: 4

slow from planet 11 is impossible because adding a new pile on an odd planet only works if the new pile is 11, which is odd
{9, 10, 11}

{25, 100, 15}

Returns: 2

9: 25->15 (slow) 10 -> a new 9 of size 22 (slow)
{17}

{17}

Returns: 2

One of the two winning moves is to relocate the entire colony to planet 15 using a fast move. During this move all 17 colonists perish, and so the colony on planet 15 immediately stops existing. As there are now no colonists on planets other than planet 0, the game is now over.
{1, 1}

{470, 420}

Returns: 1
{65562, 451082, 580533, 475708, 598517, 360154, 269932, 537336, 405334, 411477, 645462, 42895, 833704, 438863, 690620, 24809, 107432, 656, 276621, 988439, 830728, 504944, 759019, 573243, 9579, 961967, 855335, 942395, 330907, 595138, 448475, 241221, 249290, 548687, 538918, 376524, 463702, 253806, 34879, 588194, 392342, 751548, 721002, 370621, 630168, 358522, 584885, 603039, 798908, 205503, 250210, 826916, 881458, 764568, 959398, 980978, 36992, 131595, 350148, 102704, 380463, 606446, 402211, 532997, 566365, 852477, 265116, 101815, 680324, 914300, 923912, 237982, 972044, 733173, 886702, 351125, 229170, 493910, 780328, 115496, 810627, 436899, 634026, 370198, 707636, 914726, 300226, 921855, 810482, 849306, 250591, 848416, 582238, 966795, 274296}

{383264904, 571965508, 607076113, 43067573, 519633100, 335229333, 604235496, 837158198, 424641142, 279434605, 784058148, 557700497, 858579683, 237229315, 651057818, 122337492, 673673333, 903481342, 222357207, 407879374, 521192988, 271805618, 648024764, 994029813, 599194166, 160204726, 476619357, 16310368, 182853534, 587328862, 673404584, 863645038, 817622290, 88879942, 80106252, 285346812, 548934240, 872583033, 668418987, 587191333, 511648896, 840026800, 861002057, 467735816, 392537041, 986210306, 815161858, 35628519, 652610127, 284556009, 965501522, 691803010, 653516179, 555088477, 723820367, 976562441, 506602157, 981853233, 760408747, 685395202, 857357004, 338221219, 890700443, 23872915, 619463998, 260940258, 226951149, 371476398, 463467162, 930735751, 742802514, 197585685, 189705945, 504436337, 988878480, 213327222, 137306117, 105675227, 146737413, 784281967, 842998322, 611626154, 369426273, 566292667, 421294033, 116055548, 286544299, 476656189, 485224, 700751159, 131400023, 444604327, 72117358, 396477634, 22249659}

Returns: 46
{43731, 147260, 189980, 775049, 536512, 876160, 514833, 210919, 821122, 810416, 851118, 518725, 553936, 475624, 590983, 594895, 10472, 728797, 77432, 183629, 876371, 157881, 966637, 569842, 354777, 666396, 909209, 48953, 920167, 652264, 245892, 746840, 64209, 397126, 129130, 23293, 92892, 317433, 56509, 921960, 574468, 322610, 250733, 642411, 940028, 769671, 560870, 158549, 576641, 607920, 799463, 286429, 649055, 899994, 598563, 84623, 590305, 515117, 359363, 583555, 54717, 999540, 120161, 433562, 437933, 370926, 950647, 317521, 591733, 885304, 796629, 513021, 626692, 146435, 66622, 532545, 122753, 947173, 483671, 684670, 825079, 475808, 863675, 18746, 455693, 849004, 591323, 547487, 800497, 69406, 819583, 827562, 301600, 821816}

{756726467, 526350672, 539442013, 122544573, 810623579, 263195266, 378160093, 854968509, 355526282, 179226443, 496671191, 24260176, 631062847, 105426213, 720412489, 493352293, 494488688, 297197666, 685081510, 585103879, 736604807, 746550456, 739996156, 986463311, 25537872, 601508805, 203243638, 884873257, 729714785, 308222627, 43901204, 828718828, 282674978, 582239741, 518276963, 411998380, 73514839, 775694912, 843957082, 117075130, 944031162, 559272525, 761348628, 633503746, 643082352, 512516893, 576767594, 799221061, 849100513, 388654384, 621118348, 334682125, 442484490, 826768667, 733157854, 962200197, 964545184, 219977311, 786368717, 679160797, 98188880, 110252491, 550176499, 868789570, 327488404, 434950848, 357293696, 578737880, 897908492, 386678573, 913854418, 116822058, 876386674, 100051729, 917869313, 668324193, 798837167, 457550044, 387115370, 53950147, 375574709, 625812829, 928943729, 60640905, 993976202, 420753701, 680685374, 866619588, 287670032, 273090582, 226141679, 311090681, 224634686, 499291495}

Returns: 31
{860853, 857489, 314063, 466873, 980465, 813383, 461847, 332872, 906811, 707258, 57431, 162819, 608474, 503001, 645, 28860, 443278, 908247, 479621, 545493, 459148, 643887, 854208, 901658, 270241, 308241, 107486, 317797, 129864, 978738, 177993, 443639, 353009, 521696, 446690, 245899, 527806, 597969, 538166, 275881, 328193, 581740, 24187, 963101, 638466, 705765, 915825, 397746, 897406, 958456, 623493, 617928, 730631, 623736, 723360, 654321, 962060, 484259, 646951, 585434, 188219, 715684, 735994, 395328, 854055, 44875, 190457, 642762, 974242, 190276, 654186, 81718, 508511, 430984, 63198, 235321, 484151, 184455, 975847, 626983, 417221, 4681, 654778, 145846, 779350, 76321, 587403, 408014, 791, 403040, 523582, 777893, 477231, 660368, 391328, 766115, 128434, 536081, 419936, 107067}

{92381311, 847718053, 451283483, 442330297, 955753428, 591098776, 111951380, 914736691, 662807301, 187723308, 970209760, 714165865, 535330824, 510886849, 471638319, 640306371, 889758905, 100636319, 424668444, 563196277, 542924253, 351539984, 464477859, 804158885, 980750911, 211144145, 339716497, 426400949, 910274886, 80090327, 142284814, 765291446, 523577853, 357621017, 697865347, 697184248, 112574390, 271115612, 521260086, 849335197, 99546048, 383493615, 31925669, 423641320, 670770888, 87319694, 645911310, 240774618, 553833416, 691563365, 226325724, 545243636, 276680943, 765865032, 921223554, 820193933, 329181420, 536941529, 650205374, 122125672, 980661602, 603609902, 67053697, 308060350, 772702300, 190339682, 524279704, 746861205, 259106282, 434185123, 655650969, 509022208, 7600387, 632549436, 937244481, 429046082, 653966170, 252599355, 671430482, 595262025, 401686913, 860241464, 845548683, 114584280, 362763679, 69033215, 168657968, 633379556, 113697938, 256607957, 906858948, 929270384, 196738985, 85869073, 152165060, 552954731, 180549571, 771786202, 177607407, 82929220}

Returns: 55
{132068, 617727, 412913, 904152, 365232, 127711, 434809, 309198, 575934, 671651, 230209, 712076, 962404, 363768, 805969, 94476, 672581, 329415, 106865, 37524, 211626, 850454, 586244, 142052, 346247, 981945, 95308, 874214, 334840, 806084, 750149, 695619, 984106, 990987, 960512, 449804, 530809, 572481, 600392, 789475, 807200, 713092, 944458, 369259, 836234, 546647, 544714, 446168, 668835, 460452, 457221, 709039, 433181, 763124, 514494, 23776, 204277, 342291, 51455, 628797, 983951, 449342, 945021, 106023, 460423, 810916, 611112, 130057, 100970, 887740, 350921, 458390, 774664, 955519, 61878, 349914, 826045, 791280, 196581, 958305, 852729, 701372, 428630, 491576, 777452, 958898, 970772, 543113, 498061, 726411, 541504}

{128335517, 990286839, 246358737, 213253710, 673613714, 28325500, 579735866, 529972179, 349194490, 988023004, 152479610, 725197700, 175900272, 831185721, 310391576, 77943947, 50425261, 801636736, 899480441, 971454461, 649218199, 320727333, 47475367, 689268660, 662912313, 915562150, 718682184, 6766888, 275073123, 370083200, 969893483, 206399913, 596475438, 230917734, 396613519, 968584734, 398019724, 143462529, 217322535, 480391205, 661634890, 37085385, 855177132, 796389968, 873907334, 323850330, 647074277, 718894195, 321677091, 452878616, 118965930, 453793777, 905792745, 449159157, 373129316, 812593218, 534486858, 275762578, 48742450, 777448047, 606607707, 774963801, 740287895, 979135682, 526985909, 246665393, 290525282, 435434485, 62786848, 937032332, 25771036, 422104354, 204805746, 822084015, 448078215, 393888245, 558562209, 95257111, 370603161, 775849258, 931345904, 670691069, 951449379, 673872988, 364001623, 473746334, 929842811, 898059515, 72777337, 946139114, 70281719}

Returns: 71
{279766, 67482, 170143, 214671, 238478, 974009, 442602, 495600, 831854, 207044, 311126, 6227, 119733, 633878, 591832, 854131, 12439, 263303, 559312, 223345, 558160, 390772, 493890, 960974, 224666, 348571, 419917, 955572, 40197, 705701, 677871, 614964, 434865, 341259, 850335, 843437, 563714, 361470, 938607, 7845, 114596, 21555, 326077, 830212, 50948, 638554, 229296, 862915, 861087, 885506, 549703, 906440, 641637, 3523, 36609, 914223, 581598, 616711, 51650, 402072, 936445, 800139, 486578, 200245, 94133, 290723, 986754, 707910, 975551, 666704, 930246, 414638, 534998, 364761, 39646, 929735, 68437, 318811, 630652, 749012, 326305, 54558, 639849, 961335, 463207, 485921, 426527, 763911, 755322, 348771, 754434, 94300, 265509, 894369, 934934, 993606, 440844}

{401042096, 105467296, 760537922, 405221553, 405306410, 189430593, 317497029, 31989629, 32726130, 617521431, 726017514, 619324220, 871948756, 951735768, 205501002, 135272467, 602537866, 239233695, 92667708, 8177954, 454128575, 459168225, 446959523, 759229788, 454231930, 620958490, 787641001, 136988491, 165344300, 830170090, 774867577, 794438710, 796228455, 914960510, 403416924, 578629391, 688684552, 973483088, 494006316, 282008120, 687581715, 886033332, 688680144, 158444828, 80619763, 42543235, 633350053, 259280605, 873094827, 784896456, 631112253, 137725855, 75703655, 974654824, 18824811, 147075428, 131683493, 556736525, 837370285, 136669035, 657283462, 917253377, 313656810, 611977491, 647129740, 945353534, 449164982, 587730181, 800411911, 524059222, 657631084, 916829794, 623784895, 934807900, 25189945, 179749844, 839551595, 864246082, 641872478, 581930458, 620904647, 884453280, 680032467, 777589860, 156614938, 998550954, 248279257, 911137235, 125931885, 162686523, 961925422, 975155806, 306166692, 662212724, 520043732, 963663276, 866417029}

Returns: 25
{513856, 482999, 864129, 895412, 634411, 324234, 429622, 790457, 970915, 471554, 634983, 192394, 13414, 448734, 847868, 826341, 979682, 914565, 511028, 513420, 767606, 427859, 360167, 393153, 582719, 316554, 838564, 940930, 322227, 413634, 872614, 867974, 394757, 37283, 654037, 800070, 551913, 281777, 148523, 490069, 411441, 106265, 876444, 924840, 808554, 691544, 112873, 621610, 35596, 385634, 983417, 669519, 860590, 934170, 356726, 696090, 710649, 599490, 787888, 154657, 1149, 273031, 368304, 167765, 650951, 900982, 41707, 835602, 844274, 432346, 504288, 752035, 339192, 154683, 278571, 988888, 268598, 346832, 428601, 689135, 116955, 215482, 946221, 701481, 980129, 185180, 651626, 921924, 241712, 966602, 295862, 696541, 257631, 483036, 729257, 803237, 553396, 357489, 968848, 163654}

{566868633, 387564735, 119742496, 962856224, 157283769, 989045510, 190822316, 606252559, 993325838, 244278499, 579712237, 907283298, 613552594, 841249331, 566383530, 892819225, 833095612, 344020032, 685975530, 849986755, 686313606, 581779981, 221132853, 849113147, 683837377, 267547180, 43809682, 392440296, 408431883, 963287788, 809727135, 184616434, 526358252, 653678608, 787348667, 967600909, 779413612, 182842245, 994013395, 937637266, 207557985, 432322631, 864005186, 781877103, 718940261, 57626285, 503487332, 350884232, 589017925, 980174541, 579282472, 80153799, 277949394, 102260531, 148720049, 912658137, 718362961, 882190773, 553349043, 802872131, 622248952, 717226781, 223613533, 293876823, 641316025, 418215817, 933805531, 119174042, 274407612, 593674311, 384081636, 128444744, 403558185, 399695760, 697295742, 572360429, 241576537, 312392337, 269443405, 653481057, 726880980, 750581443, 698581539, 344474779, 611678994, 41154510, 815750641, 663889713, 222756081, 318072460, 478939337, 829775836, 991922160, 936906408, 349184566, 809825376, 122641026, 157041995, 635679036, 196573589}

Returns: 27
{359711, 287299, 99271, 308873, 218105, 39705, 802495, 932033, 283692, 642966, 682240, 227602, 207990, 716130, 516264, 519256, 81203, 400291, 680572, 24412, 686188, 804230, 990362, 621625, 157184, 111597, 930464, 439685, 315618, 969436, 231030, 894366, 434158, 787588, 199009, 90341, 224620, 673523, 665122, 918376, 696784, 234366, 574662, 93613, 582541, 439649, 324065, 330682, 392069, 956124, 124513, 95496, 725745, 329531, 476688, 222149, 806907, 123170, 685016, 90850, 561846, 696585, 357211, 796946, 594200, 722418, 507774, 833562, 229565, 62248, 334462, 323389, 830199, 766240, 772385, 699552, 828968, 397401, 277692, 803417, 620657, 62248, 79608, 268498, 479435, 528551, 230956, 537835, 535887, 508918, 297158, 333985, 457621, 541347}

{267144961, 654921848, 730521680, 914819767, 754201963, 689727792, 944156015, 352830664, 612460485, 680788929, 225195980, 934987890, 613720296, 886058950, 190555654, 203371247, 256920390, 809231905, 44568549, 31547555, 746135705, 652946827, 914027477, 547139921, 923729021, 965378733, 872448898, 650364373, 279749953, 790175293, 653975628, 316428353, 963039860, 213199020, 368616927, 635579722, 928536538, 649265723, 676396199, 946956586, 600446389, 361553584, 541555156, 186630428, 802433617, 833335013, 910847219, 351951339, 400184363, 198432454, 168785932, 709487333, 780723746, 529817936, 81103306, 37782503, 419704491, 498449468, 998257390, 745713325, 483244204, 315973313, 667432713, 100871024, 848584237, 686573552, 747489349, 528621850, 869734476, 673666891, 921814484, 290424729, 358398436, 303088383, 746571564, 232994098, 880548957, 886913147, 973068820, 750897153, 912785634, 869474304, 459009037, 81042951, 274266983, 657022711, 410764215, 347421595, 493608954, 313460939, 172951438, 259903772, 195834967, 389412331}

Returns: 56
{968444, 323999, 38031, 227115, 723901, 602556, 496673, 25851, 372823, 9678, 660968, 298201, 287144, 579746, 435995, 794456, 555316, 967025, 247535, 476163, 476318, 55475, 860686, 956504, 86732, 756051, 136451, 769693, 421944, 464770, 196285, 259919, 48136, 421240, 705379, 474120, 558025, 549318, 104559, 584989, 27782, 570970, 470128, 566719, 509073, 882256, 617534, 169081, 166232, 826282, 794227, 995606, 249961, 288999, 704087, 333977, 203070, 584329, 708060, 893493, 517025, 533351, 839784, 778647, 288086, 482113, 267787, 353380, 550608, 122188, 231583, 798114, 266584, 822612, 994641, 236971, 34274, 819573, 144595, 256417, 722435, 772715, 923417, 970582, 747249, 980590, 469657, 771614, 748930, 912293, 815022, 88889, 339861}

{782066373, 588010766, 792594065, 693919127, 703996020, 231993630, 347371572, 672987831, 101020613, 850625277, 279436855, 556755569, 168658124, 298489062, 387453592, 149811814, 803695839, 176767640, 84539944, 936060169, 197845380, 873253680, 59908795, 915817695, 830211682, 546695398, 192797327, 648388737, 982778185, 984130081, 694548491, 869941946, 596447181, 657048495, 659111743, 110244359, 307193055, 45065367, 861668079, 344203211, 199147538, 92800142, 482794487, 296132580, 105909351, 320452293, 209762399, 636373934, 809649230, 809494948, 531432209, 670018416, 775254864, 154613846, 828429879, 928123569, 146306528, 261236478, 764189164, 578120340, 911521225, 258206410, 653448591, 335525631, 275785663, 722703084, 793874907, 964568269, 487871185, 869692514, 28229431, 331853798, 983452481, 202396398, 800223341, 981348322, 27309549, 462539401, 187131485, 288525764, 944663570, 750657729, 522820015, 202610552, 481592794, 13801158, 396785469, 682951183, 265601510, 431034016, 544656690, 192270658, 844502692}

Returns: 27
{187704, 632306, 52623, 225587, 330463, 639608, 422147, 687271, 314453, 768397, 280633, 656185, 97345, 317476, 241252, 45588, 587890, 494158, 974373, 943333, 854798, 320908, 247401, 310154, 873722, 478651, 187829, 185399, 581147, 317468, 830251, 482505, 303200, 305591, 641638, 777296, 54297, 875575, 321570, 952937, 39778, 691317, 907935, 71908, 640192, 628450, 419103, 594889, 530734, 445630, 153474, 396814, 403255, 690050, 569205, 235083, 555820, 587449, 433648, 725332, 466580, 565987, 853035, 928848, 191261, 264770, 420086, 335881, 959068, 351458, 942896, 130696, 396453, 456559, 147382, 94138, 770296, 454710, 261744, 247127, 3706, 269512, 568359, 857660, 26616, 840559, 353435, 415887, 901797, 557240, 317591, 747604}

{212617238, 272297391, 72661579, 728706102, 54359801, 260817298, 187496023, 655400073, 378584169, 371797147, 89760091, 734884755, 535993289, 280134610, 301299249, 825547802, 641592966, 395144936, 219442695, 873439308, 51486094, 885307929, 279650888, 523175053, 249946078, 713515653, 117424597, 567095307, 900685019, 328202785, 198192512, 426046960, 301908537, 795213017, 635367513, 981060515, 765388553, 216486917, 566987262, 300931477, 815929986, 172275959, 173352264, 343708249, 164534170, 298745039, 517629709, 105991854, 306762032, 745304563, 280681363, 162143874, 419878593, 724193896, 235521336, 238159964, 860849122, 808592009, 848136890, 191248812, 92590548, 987660076, 311456703, 554942739, 156493369, 876242436, 499431675, 834892399, 316968558, 33901619, 114449044, 952905551, 729813896, 595832881, 237159748, 222616950, 114139693, 211464672, 536220191, 411516943, 324732524, 769448532, 274169983, 13067810, 919717080, 360152609, 386949584, 450942183, 103822818, 94427180, 353892626, 995858021}

Returns: 66
{559217, 875209, 242995, 609248, 987420, 754325, 723612, 946210, 144428, 257893, 706146, 963143, 840208, 521424, 577616, 731971, 662846, 210390, 809509, 35769, 776900, 175857, 24852, 597012, 912227, 912610, 328981, 238595, 719396, 384607, 885185, 240198, 256567, 512371, 388487, 211578, 864533, 905560, 445300, 195492, 486123, 624483, 644779, 233275, 37282, 806924, 426453, 488771, 977214, 243093, 444108, 957916, 802853, 19065, 443297, 648242, 537552, 69143, 514438, 202759, 409829, 196627, 759682, 2159, 251216, 516154, 545047, 12307, 877321, 577269, 982191, 309941, 502642, 329506, 321283, 640757, 733945, 697220, 544275, 743900, 726038, 781635, 657278, 529367, 393769, 655047, 233232, 706931, 56487, 228077, 229125, 799191, 515100, 616470}

{473560129, 535136613, 908666816, 429421180, 583893765, 431799897, 150271761, 449470263, 383566399, 13877559, 747734428, 562817263, 364707773, 585987425, 798255605, 114938111, 821901445, 654620711, 388544003, 899541018, 547493939, 931847487, 414265721, 281294715, 164181215, 951306366, 56688851, 230979639, 56690751, 604562856, 281029826, 739067792, 277614974, 189250000, 401874114, 950060051, 658667778, 401158251, 248011407, 612564359, 621495514, 594568372, 872220175, 930006774, 994658876, 143127587, 253225510, 113920547, 952702929, 144266279, 385963701, 923636421, 55165533, 155823831, 786789267, 990476921, 187481096, 418898249, 826599392, 900571675, 825205549, 744611074, 713352710, 290524756, 560740182, 67494239, 669588349, 785950665, 571590226, 165324554, 965512135, 258641278, 345948915, 487992592, 919497848, 556632985, 792194210, 761415307, 282034524, 101148591, 376513443, 819631327, 275478583, 10155155, 677837919, 593916635, 299698976, 572832778, 287353557, 499217864, 563220040, 658538632, 501418463, 944602911}

Returns: 27
{381149, 141499, 703657, 900003, 218021, 20664, 102996, 56776, 403088, 517885, 216039, 688788, 707366, 554514, 704522, 603893, 165490, 663006, 734615, 385581, 60867, 584835, 779723, 190588, 921568, 576639, 249946, 504913, 812398, 502739, 447649, 59805, 736575, 521268, 727141, 737000, 913794, 722147, 812376, 912206, 245668, 537478, 604020, 340427, 534555, 230697, 407208, 777615, 478251, 142319, 671081, 178054, 180154, 921125, 207735, 843455, 348678, 1963, 620762, 548756, 771650, 209708, 575067, 890534, 469580, 171527, 305765, 547063, 673245, 455601, 686481, 495293, 581314, 457235, 905074, 719916, 22504, 174906, 610791, 449018, 418245, 998632, 33840, 584621, 51815, 63528, 635329, 723356, 106794, 217629, 505519, 197436}

{857634749, 592178308, 958688671, 34418160, 847690670, 572991025, 963159848, 826423977, 129017749, 17742397, 356236844, 277872450, 514973482, 298763156, 105827683, 978162831, 813553733, 793192425, 707831773, 125632139, 385260199, 518939843, 9716294, 298988002, 613584395, 494047373, 940803297, 987673639, 478896675, 199322698, 132361034, 277800699, 395851893, 500197734, 57880097, 528282647, 743310188, 35188300, 457263127, 688837328, 87950282, 739757411, 962318870, 816310107, 750686835, 225533884, 398039652, 210635570, 247461794, 777436845, 628517517, 153767820, 221121273, 532004562, 551951618, 799620536, 114532247, 312032390, 827297158, 650600549, 684791408, 793573403, 735932378, 580240074, 815785240, 924310292, 106770600, 851821594, 902928379, 526143481, 208486132, 40580457, 161287837, 790538422, 543532828, 811870055, 277548716, 159082739, 301181835, 400523951, 157695079, 911572039, 357240200, 980577724, 925069864, 853625940, 713391959, 896529440, 978911322, 571040946, 397614257, 965206460}

Returns: 63
{948454, 150345, 449051, 426489, 598522, 848584, 333041, 711141, 188542, 634295, 856241, 814929, 393316, 19867, 956490, 109689, 445103, 781408, 174903, 715642, 963855, 899654, 68168, 105690, 136152, 108272, 831255, 80157, 842170, 901977, 228546, 30049, 189696, 861504, 405499, 101193, 67168, 853913, 585542, 504917, 784822, 926147, 18299, 128662, 181237, 349975, 702417, 769905, 137257, 736166, 137982, 292264, 235025, 145415, 53935, 406683, 166472, 439499, 846742, 580660, 30611, 76147, 959739, 255944, 709594, 729410, 528346, 447377, 533046, 658406, 628006, 66382, 816074, 977480, 371359, 254588, 374016, 279326, 959539, 997794, 197462, 46370, 320429, 946060, 46706, 185871, 952439, 62027, 548883, 326397, 322708, 458161}

{770290504, 992164258, 365330558, 945698144, 985950063, 50577084, 394685690, 799010026, 842343878, 697276699, 645647088, 270204401, 684199672, 196558362, 558633716, 839300397, 851168912, 673923181, 175589869, 204563367, 664869283, 25891436, 571780890, 806471572, 848640199, 500003985, 246945116, 846880137, 278753558, 448365806, 515588646, 5752704, 810016246, 703632126, 56076457, 957917670, 366298957, 662790210, 436999492, 99641422, 81435419, 667150431, 367121134, 224108136, 278851272, 367238888, 744334620, 129607546, 668408721, 163207891, 639506701, 483867095, 958449884, 406535782, 624240572, 360740996, 217129348, 276786382, 991129955, 294585480, 721967341, 491354122, 268399390, 517757550, 190466592, 616585643, 439481773, 417095666, 212910191, 37795999, 347434841, 47746917, 915362141, 252600136, 72385971, 125070531, 293970754, 257113856, 517674451, 473753262, 811590956, 150119022, 664967026, 103078066, 752813265, 8879674, 629895715, 357689262, 304566468, 612363520, 42998396, 284345845}

Returns: 56
{852869, 390715, 382795, 165702, 954026, 990617, 92209, 784405, 269563, 94195, 505927, 562237, 530566, 489568, 699513, 357285, 634794, 405902, 170805, 965823, 309359, 126529, 466954, 443720, 612782, 708668, 277780, 261292, 756276, 252714, 847673, 798696, 48344, 164468, 34911, 802147, 966880, 319779, 678202, 863537, 439850, 518704, 259554, 921159, 222268, 975600, 59140, 727121, 285693, 834141, 608087, 870002, 609805, 222992, 540325, 40287, 337218, 287283, 139767, 436456, 125695, 121100, 239366, 556069, 951915, 188013, 730794, 761519, 640139, 788635, 190332, 632159, 116712, 410436, 339562, 281328, 7341, 992199, 937569, 722768, 835796, 925573, 975034, 725578, 524697, 560992, 286251, 755289, 185429, 535020, 900682, 8966, 660567, 540167, 616883}

{330010513, 932255272, 616271366, 319444605, 720848161, 439916697, 618354817, 626808371, 402208310, 355005167, 262388858, 302384349, 229755490, 730964528, 985398974, 741074732, 361716933, 433132623, 882582410, 849247768, 885370671, 750359833, 399340535, 735527425, 793830322, 891192891, 227214662, 146815374, 818624435, 381033068, 551813019, 31125319, 498497120, 159062300, 586203991, 377753679, 956513140, 424835480, 96050207, 92402514, 79149232, 596064679, 450618874, 924692028, 840066085, 849089340, 541471592, 919756490, 165476215, 718829401, 198863726, 875516600, 180766997, 486462816, 74426789, 229317622, 393470523, 724452966, 411093411, 206755840, 534360401, 751862505, 75680180, 674293821, 598657282, 533138315, 213153574, 60338392, 21506176, 346964754, 603604607, 208980917, 408664792, 13619272, 148780193, 597085466, 719790913, 422018054, 394850624, 249012896, 116816073, 268276783, 214271582, 415205170, 276678833, 632525025, 494954820, 871369031, 784096443, 838932445, 921740996, 425475305, 452013570, 519354032, 37056004}

Returns: 21
{162712, 203194, 372622, 986764, 958914, 624744, 817048, 757720, 558125, 919228, 367876, 900171, 154686, 727065, 49453, 899334, 677234, 870110, 38148, 133593, 664516, 192893, 188297, 52865, 12470, 733637, 374650, 955006, 221116, 925880, 24391, 530825, 916623, 139746, 31946, 766458, 360173, 782779, 265221, 316609, 434523, 888945, 851067, 779196, 865973, 150144, 469465, 836668, 758908, 465218, 169050, 696044, 167631, 556161, 911180, 447116, 13783, 134725, 967766, 190372, 515977, 939808, 851694, 132850, 938126, 437310, 388183, 26284, 8979, 610273, 481088, 213724, 317384, 869704, 175983, 292726, 541480, 759530, 808032, 320841, 688892, 640457, 435556, 192838, 893710, 336793, 949393, 106080, 613513, 386034, 920723, 846571}

{594290464, 707176747, 824584852, 239212159, 776016599, 978868013, 226191144, 661605763, 491246962, 476624804, 938200672, 200994255, 242278388, 850985548, 701122641, 295193954, 25807845, 885745750, 815633528, 677921921, 102797778, 424163403, 51500524, 391196853, 609761570, 679712758, 65880115, 470258132, 41822950, 114138777, 944837173, 274599070, 366565854, 707477856, 226505161, 394606608, 917242165, 10834424, 371853396, 238028912, 226828331, 210262236, 199074961, 961220052, 362528781, 251923221, 416804013, 939430919, 64354593, 713115710, 124537346, 138730495, 854283121, 654989799, 545752252, 665850732, 450052879, 350440484, 390406529, 481747371, 521850842, 495608910, 854145647, 532604883, 636610971, 181661923, 954827284, 813772704, 39036694, 447762948, 636558324, 942427785, 545065486, 875832630, 586057791, 498900932, 346312266, 397913057, 465135174, 183032966, 558214438, 696598388, 977213576, 594739213, 573994349, 246194914, 533071570, 441625819, 833246700, 802054357, 49849948, 377376562}

Returns: 15
{654603, 258099, 843966, 492105, 256494, 842383, 213954, 96380, 522840, 996849, 694728, 395475, 608848, 227669, 522077, 24746, 336221, 260645, 203039, 346542, 765865, 614996, 542304, 870314, 891179, 234939, 18252, 413977, 742793, 892443, 42564, 534984, 611177, 350575, 582307, 568793, 343040, 362357, 664031, 535708, 481827, 828662, 654577, 36665, 606027, 624375, 193620, 791058, 99097, 217055, 66250, 971821, 262596, 604778, 279054, 401006, 615028, 823354, 701405, 29245, 843480, 102811, 546372, 532634, 805230, 720292, 381234, 757412, 928564, 437710, 273572, 815391, 370447, 966324, 280564, 725300, 153267, 521282, 815422, 875333, 573499, 701916, 663853, 133561, 641735, 841641, 641785, 564803, 159711, 964145, 324493, 296529, 48503, 635382}

{467175411, 391251678, 586132455, 810818769, 662473526, 416345759, 756670185, 669749287, 821207729, 612306599, 677616341, 846757490, 723048381, 852952186, 472492748, 986091319, 592019790, 876973722, 670801582, 774488468, 896224, 278865714, 304090511, 515503228, 273238616, 828325873, 603552008, 784082685, 705255057, 903461130, 413340987, 170686111, 210220040, 997806214, 878963228, 898878542, 424687249, 440166965, 766637307, 686320033, 929011344, 503288736, 61799648, 953839294, 314774272, 531783065, 103544908, 561617135, 674725871, 859818146, 322643034, 764103377, 392993967, 891767217, 555486531, 594550079, 263940055, 925313467, 91438418, 620097292, 75206522, 34124861, 138022217, 285648583, 941636457, 751826411, 339246422, 437667634, 95849255, 231882571, 995142715, 666832692, 606394488, 307566913, 216363664, 364663892, 108384022, 579205779, 231347032, 863914828, 985153391, 829044725, 518430126, 836283622, 884482841, 197248525, 74760280, 528591933, 53839630, 217431792, 924658809, 67275077, 388071297, 37849204}

Returns: 70
{70278, 808246, 976047, 756699, 728517, 587729, 66551, 504677, 851568, 959524, 807285, 757641, 222057, 167622, 68438, 179223, 69651, 893167, 200477, 221235, 193028, 603633, 923630, 826661, 784331, 691288, 927423, 225746, 937416, 414400, 784595, 580117, 977483, 492268, 422629, 40073, 836492, 565774, 177912, 204767, 812489, 588107, 639418, 55964, 702730, 356998, 97130, 283775, 530775, 484637, 844857, 465520, 895538, 426358, 236058, 509308, 218811, 271927, 652543, 535900, 178826, 690510, 815240, 857565, 847212, 406398, 317805, 604278, 846813, 653980, 181955, 755823, 607563, 939565, 168029, 322789, 32580, 44247, 795891, 565074, 566471, 675132, 931421, 743454, 199972, 207569, 617297, 86534, 673652, 457583, 884189, 584414, 231033, 580618, 4868, 920158, 946109}

{549851588, 164340720, 262861545, 759451163, 503290173, 469453867, 95235704, 553183245, 815893512, 827924264, 980592314, 834591703, 565025590, 56155408, 871896094, 662957401, 647312045, 843837838, 180256975, 712798969, 788200891, 411067083, 309104502, 368518299, 322335023, 875825682, 429496452, 532967048, 95219402, 319035269, 305471190, 331954644, 529237251, 643055520, 876073207, 606816169, 128309768, 873688875, 797779191, 343450776, 867310662, 561695691, 352913883, 369006165, 478616841, 215531623, 43477473, 654561881, 4646453, 26595524, 788510380, 529673058, 546319294, 498307750, 711057926, 594799660, 967910399, 310331432, 457651019, 358871306, 681831998, 139680271, 693448450, 73669912, 731805257, 869232629, 109389119, 394775291, 227991412, 299560540, 971073063, 901278046, 521127888, 974930046, 784957744, 309365567, 644820898, 394607915, 773300462, 912038655, 966994848, 338836344, 225082584, 201893593, 230176522, 921265196, 968076581, 200899351, 917633102, 995650538, 175266566, 223593681, 515797199, 398621720, 640043114, 326198463, 169139982}

Returns: 25
{700072, 335346, 616201, 895988, 401609, 120709, 855233, 123854, 441252, 958376, 754829, 7370, 25451, 209418, 407740, 179046, 707772, 738029, 707657, 707666, 688392, 506451, 128888, 40765, 248727, 693479, 21200, 219220, 81909, 883834, 446785, 431181, 724580, 909939, 208431, 231931, 607892, 862922, 144125, 496418, 587972, 471184, 816636, 81205, 167364, 934016, 827268, 325104, 82507, 696122, 922170, 453580, 713344, 612125, 820151, 421123, 302197, 897503, 548186, 187014, 151521, 716525, 229281, 370955, 543246, 388618, 268009, 81082, 996130, 146291, 573166, 700411, 907409, 918198, 85692, 261566, 631363, 320846, 384983, 480611, 754771, 911519, 662989, 172096, 677204, 531699, 463170, 635749, 457513, 103049, 168015, 739292, 784037, 578100, 41812, 153441}

{511509549, 844022371, 961294017, 638278177, 332451308, 869913014, 904152782, 656783082, 730044928, 437591395, 496798370, 544179397, 440102364, 709100072, 560827327, 544245315, 444673836, 538522545, 977838708, 926752695, 984709622, 247071644, 545010690, 928833065, 289385849, 188454276, 457429111, 647939574, 120183439, 126223013, 779520120, 823463851, 813284629, 337575432, 404672486, 202796084, 239983108, 427979509, 745355947, 879353885, 846209598, 860171884, 44726746, 159750514, 70577740, 895750637, 826476099, 654132489, 193361552, 985608195, 396390736, 917536988, 379085800, 698980978, 462264146, 302131703, 921311426, 769312165, 646448217, 63708920, 486487471, 466645732, 939160948, 769285525, 24722282, 944906375, 767299466, 773617375, 830214588, 593531374, 39074178, 16910897, 750441716, 54763330, 650884673, 126634735, 43634182, 111687624, 586024446, 955696975, 120150272, 954435730, 929186867, 576096463, 958478561, 261685473, 15409549, 582492396, 153988913, 323890272, 939229418, 543169536, 514439136, 3019009, 88462094, 894128260}

Returns: 62
{627784, 570891, 649404, 838215, 601455, 278413, 973219, 899155, 985747, 811950, 497512, 195047, 950761, 225815, 229052, 846258, 945637, 349260, 888149, 729727, 807231, 88738, 916866, 703903, 624584, 611227, 522308, 116096, 21289, 489060, 717055, 466447, 29327, 44101, 523745, 481774, 217080, 786394, 806886, 122888, 608026, 420695, 339527, 445112, 378205, 835825, 953481, 772699, 907913, 815655, 166892, 914288, 308062, 434360, 809113, 703705, 506604, 596230, 260105, 310377, 962683, 476820, 351171, 847575, 404068, 553092, 977585, 327442, 857807, 455021, 642299, 791110, 345407, 464488, 3232, 156961, 767902, 258984, 926491, 643418, 375810, 232894, 896619, 124454, 321021, 828536, 84669, 793233, 728324, 506999, 342074, 104217, 340897, 3646, 416587, 210140, 805241, 552795}

{293101352, 579759864, 265100361, 149598064, 789279949, 853165280, 687801956, 34655700, 62836269, 330721440, 136069342, 653360220, 536221363, 848366090, 560935540, 321811273, 106910013, 533348814, 463082354, 209177002, 788342913, 449686969, 121068047, 390574757, 672385994, 420478089, 497776383, 856080697, 198226719, 298344805, 837313197, 307034373, 36252470, 633325145, 623543624, 735710271, 308319167, 260148323, 34636442, 947756497, 312782396, 364997333, 25968091, 526569485, 611663921, 412464207, 745880070, 990081899, 716187356, 297075184, 690385812, 451549862, 647645869, 189176530, 717398495, 119102727, 635962869, 6086131, 414274274, 953223067, 696790446, 576143705, 821065683, 598549868, 401016077, 786191965, 96652588, 597482186, 711240578, 740700327, 215668379, 608379129, 472784096, 546638646, 579628923, 826457311, 567560063, 911067249, 758805528, 796007964, 713288456, 166077273, 260102238, 647209620, 378278857, 856681769, 585743919, 513685017, 686046723, 833833505, 428171975, 399595350, 453037195, 958137310, 309441379, 423638985, 180714383, 194144106}

Returns: 50
{522043, 999019, 374473, 567332, 649037, 268583, 441013, 886028, 798119, 376097, 999318, 866705, 398494, 276238, 864417, 175959, 413717, 839670, 56704, 624224, 801260, 46560, 405354, 565086, 462191, 340605, 37898, 288952, 927835, 751446, 701529, 818858, 402171, 407214, 237237, 406376, 236585, 388133, 25890, 130899, 307692, 129959, 561425, 646800, 742337, 120476, 750161, 879692, 433088, 657291, 678294, 416032, 270028, 387269, 400387, 381473, 54656, 983453, 360177, 847911, 811327, 975653, 984765, 718230, 448243, 176714, 684067, 525481, 170721, 438373, 742415, 738658, 808538, 28754, 264642, 270895, 362904, 723553, 61524, 749543, 591772, 763048, 509389, 246743, 887941, 645948, 106313, 902731, 327092, 703041, 587694, 792791, 75158}

{459468839, 522334076, 591434011, 566568382, 990076617, 407958647, 379315460, 547831393, 884076272, 207979508, 682296325, 616877922, 494971671, 222012973, 407927848, 516062274, 366620520, 967099755, 265911524, 417497852, 300004213, 587475766, 769507663, 425919840, 407757707, 106656197, 396450164, 2392532, 757360037, 8041638, 251407901, 294996413, 47137019, 867346938, 123257328, 481224681, 357265603, 498571608, 782833775, 256712328, 461467567, 859008909, 957090707, 914721063, 895335625, 894822881, 609090650, 8181883, 301888433, 476954172, 419100247, 349333049, 948760486, 168560581, 389620199, 345843103, 904390912, 399841037, 887550614, 810500729, 377198659, 251598286, 357626038, 958614921, 782260933, 764053142, 277611819, 438423449, 34379575, 869075627, 780004310, 205586878, 307333890, 792212782, 839259204, 886075185, 591644352, 64538471, 639340143, 979257234, 184826110, 423858903, 86915495, 290549718, 508172444, 118016710, 59272105, 55677360, 161373862, 307684338, 628742989, 860856429, 183916799}

Returns: 17
{547171, 716489, 899678, 404142, 537102, 690242, 718365, 88636, 261870, 936579, 519759, 758821, 330147, 449692, 556987, 596129, 234247, 237143, 308404, 316084, 979728, 124044, 159317, 508925, 709125, 73689, 206319, 540969, 943828, 967540, 957262, 418795, 506089, 554699, 443868, 705221, 221509, 923597, 271074, 264572, 944942, 47489, 401401, 638027, 396777, 295762, 839498, 676249, 540750, 554879, 713403, 690977, 819787, 742530, 906105, 902698, 178789, 15338, 433511, 848732, 328296, 75674, 188705, 786905, 265548, 437272, 895604, 179966, 160290, 735826, 134764, 463688, 198873, 220367, 811866, 828923, 937064, 979504, 587140, 403780, 453163, 883714, 282461, 130568, 926207, 296342, 309155, 682217, 486086, 523610, 64149, 29016, 864127, 212808, 4268, 457386, 19372}

{111473886, 577079068, 449048027, 805627639, 703866433, 182464349, 475892902, 311041827, 492039618, 957201721, 785217042, 341649120, 444565304, 860850162, 491677659, 476785117, 815292292, 121421268, 652816204, 526058627, 942305866, 591471421, 236129505, 280454850, 63679758, 809511783, 2252101, 618467335, 429695557, 61593254, 694547491, 718191060, 549859699, 852799093, 30648417, 715820927, 538972607, 103449408, 816843133, 147389176, 647696316, 39056083, 612376494, 498082014, 264153336, 342863524, 501320587, 391783655, 789473241, 480685140, 399766518, 73683064, 713743555, 807978479, 958323734, 944648558, 446534435, 476709270, 581337030, 289532254, 132434146, 753299800, 351725680, 12318997, 527486805, 612300203, 557470326, 570357162, 732576191, 339556011, 589323562, 502527802, 119405363, 716935800, 889157515, 201632809, 473989367, 902122756, 890529841, 73863268, 265572467, 214796621, 617208572, 682158916, 301747884, 189359484, 823800684, 532375056, 741406693, 475356111, 231725461, 910136623, 947426268, 969729755, 488309545, 337391669, 292678419}

Returns: 50
{91304, 91302, 91300, 91297, 91305, 91297, 91301, 91299, 91304, 91299, 91304, 91301, 91305, 91299, 91305, 91304, 91302, 91304, 91300, 91298, 91300, 91303, 91305, 91298, 91300, 91302, 91297, 91297, 91305, 91305, 91302, 91298, 91297, 91306, 91297, 91304, 91302, 91305, 91304, 91302, 91299, 91298, 91300, 91299, 91297, 91298, 91300, 91301, 91306, 91299, 91299, 91300, 91298, 91302, 91302, 91303, 91303, 91306, 91303, 91303, 91300, 91300, 91303, 91303, 91301, 91306, 91299, 91303, 91299, 91304, 91300, 91299, 91304, 91297, 91299, 91297, 91297, 91297, 91300, 91302, 91299, 91302, 91303, 91302, 91300, 91298, 91303, 91302, 91299, 91298, 91302, 91303, 91298, 91305, 91300, 91298, 91301}

{588005042, 292964723, 577175449, 176497567, 663233064, 370603508, 690383175, 319649672, 287804319, 739439072, 404650072, 5668836, 298096689, 14336308, 648189665, 321912141, 437803023, 157150325, 294612853, 888963068, 99155082, 353987196, 454990157, 482977188, 518657901, 570056175, 817072230, 354396435, 136316880, 729411384, 371448662, 108258125, 126351014, 195863797, 797157035, 747622328, 797228081, 366303616, 313977452, 420969844, 682550505, 78438791, 915316487, 788537842, 721299552, 666227074, 128852938, 642654620, 784419664, 32978555, 642483985, 510764027, 563532805, 513305341, 395442765, 585710031, 165197415, 182713590, 420052166, 609089106, 786848169, 933310407, 823820535, 787090346, 644998627, 352720369, 198806069, 971180476, 432035024, 850257674, 572899639, 219732662, 264706349, 2981706, 485273346, 220025640, 601543627, 974932572, 95578435, 854240408, 954670179, 586937612, 348148138, 70697185, 622639878, 986346992, 895729487, 990611973, 8704940, 75868265, 246495326, 547224528, 108415624, 519205480, 406292813, 838294970, 596163940}

Returns: 508
{2, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 1, 1, 2, 2, 1, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 1, 2, 0, 0, 1, 1, 2, 1}

{375860125, 566837654, 300196776, 482324250, 272823566, 331459166, 272499848, 617787588, 714205336, 191036847, 691665289, 321149722, 249063624, 581129140, 637340452, 556037401, 817350226, 48731602, 768296167, 983260704, 295422506, 859273721, 162798889, 809322435, 588023668, 548965174, 950604648, 345355429, 840418471, 43723811, 479525611, 883835680, 776918113, 792459001, 89261702, 10158472, 988911869, 604666416, 71263942, 310581568, 259057185, 716268066, 797687542, 732936543, 221613870, 249601826, 122010157, 761957577, 91417786, 857216018, 361266163, 192505656, 550302677, 556206843, 705004125, 294666087, 928302446, 175899398, 968075807, 287035924, 448820770, 92151800, 423253253, 909573310, 451195897, 804096204, 315877768, 114648939, 81088451, 26977201, 214822281, 593634273, 654104186, 193826278, 929175779, 545864727, 524332418, 385046585, 603672295, 379222333, 347906692, 465317078, 1954413, 275276269, 65904514, 989555971, 364397845, 653176134, 951088073, 35536744, 970115889, 43567904, 110708822, 441515658, 325429078, 909194303, 536812831}

Returns: 1064
{6, 3, 2, 5, 4, 5, 2, 6, 4, 1, 2, 1, 1, 5, 3, 5, 2, 3, 3, 3, 6, 3, 2, 4, 6, 1, 2, 0, 6, 2, 0, 6, 4, 2, 6, 0, 0, 5, 6, 4, 3, 4, 3, 3, 4, 4, 2, 3, 3, 2, 5, 4, 4, 0, 5, 2, 3, 6, 6, 2, 0, 4, 6, 4, 4, 3, 1, 4, 3, 1, 5, 5, 6, 4, 2, 0, 2, 3, 6, 3, 1, 6, 4, 1, 3, 5, 6, 0, 1, 4, 5, 3, 4, 6, 2, 2, 0}

{480661562, 55444708, 300016713, 896925635, 110241397, 844670109, 583043399, 171468391, 722386051, 659441422, 594655150, 24097239, 368425047, 490149472, 989009434, 491291912, 219979588, 479920891, 42437754, 442484869, 461582349, 958946712, 22539727, 289600567, 247280770, 365102464, 337162760, 169225445, 647530871, 524532833, 962268263, 565513407, 453410374, 623051401, 727522654, 320830104, 344980723, 651283932, 373527041, 976835110, 873966450, 561282334, 629646421, 47915242, 518296953, 530628018, 304033971, 78500361, 924375051, 688837671, 478184916, 173949267, 217943299, 278231718, 61336795, 543520315, 552951205, 373013166, 374081512, 326870276, 187900850, 131372367, 224590378, 336525658, 826627842, 892593563, 147421582, 628012379, 430861329, 173931794, 411372868, 868447158, 458527939, 580344603, 521498820, 239879450, 329675722, 104687994, 171002567, 340099080, 119868509, 478094593, 282603114, 164499962, 745705417, 284347188, 274697167, 649707157, 990433297, 772275542, 807217182, 108846062, 462251109, 344200123, 197597952, 986672720, 872959309}

Returns: 440
{16474, 16474, 16474, 16474, 16475, 16474, 16474, 16474, 16475, 16474, 16474, 16475, 16474, 16475, 16475, 16474, 16474, 16475, 16474, 16474, 16475, 16475, 16475, 16474, 16474, 16474, 16475, 16474, 16474, 16475, 16474, 16474, 16475, 16474, 16475, 16475, 16474, 16475, 16475, 16475, 16475, 16474, 16474, 16475, 16475, 16474, 16474, 16474, 16474, 16475, 16475, 16474, 16474, 16474, 16474, 16475, 16475, 16474, 16475, 16474, 16475, 16474, 16475, 16474, 16474, 16475, 16474, 16475, 16475, 16475, 16475, 16474, 16475, 16474, 16474, 16474, 16475, 16475, 16474, 16474, 16474, 16475, 16475, 16474, 16475, 16475, 16474, 16475, 16474, 16474, 16475, 16475, 16474, 16474, 16474, 16475, 16474}

{814212556, 553363080, 51894789, 546692058, 383278023, 921973076, 737695496, 413841740, 54778052, 123309550, 590930790, 402695994, 325443462, 606217989, 876167254, 871201863, 520995873, 732147066, 343061596, 681112231, 880307863, 85896773, 274725424, 394152329, 185436332, 662183835, 96191779, 986752533, 337747167, 289532706, 197524112, 924933374, 864295855, 624963532, 476740861, 961825265, 32498229, 438230851, 723063100, 852659580, 434389781, 456603619, 525269250, 574914881, 441121265, 535452657, 227970213, 546792788, 467865300, 804803402, 906688863, 36299425, 682332456, 879497287, 456026537, 682554338, 228336424, 1234676, 412837567, 483442281, 847763158, 721708744, 317805379, 298378921, 380256475, 181543212, 679263918, 78279706, 308868105, 106543130, 881150022, 312115536, 862849440, 451556513, 698630479, 799351143, 65122511, 520467464, 875290523, 130911733, 980165858, 555930226, 449675742, 39021461, 26194312, 748678617, 909525251, 751559587, 168938109, 228674380, 124801841, 176275949, 586231636, 428848457, 116633428, 956095713, 363896617}

Returns: 1071
{25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217, 25217}

{639851273, 726419197, 904070038, 163436991, 794253164, 675669424, 59451751, 968084635, 491289163, 208923275, 307779227, 715106558, 883363086, 784675327, 557126572, 290356987, 135970605, 412581779, 77483223, 287853441, 131278984, 718046370, 265922841, 636243011, 310935795, 642379834, 990576554, 397827388, 231164918, 752458489, 363399259, 258710806, 225938558, 51176937, 809279886, 933754796, 788250131, 550469824, 902516915, 228762036, 619378475, 153181347, 281182103, 309427095, 236021617, 29004528, 622650410, 355930907, 504039929, 283133790, 936106005, 16457161, 836993938, 391421993, 533302069, 585196905, 702783898, 583941747, 264941694, 747596297, 297157756, 824209992, 121002753, 618673297, 517179605, 543451493, 790198433, 660596292, 182947542, 133138285, 500814293, 54207380, 232761426, 625746855, 559209681, 353022531, 546828482, 705712372, 747755528, 45173397, 356008119, 738120302, 409341341, 510919979, 89191644, 819562833, 469744447, 294199856, 604941753, 78118143, 367838535, 195206700, 686718273, 446338771, 104401786, 627183261, 565252647}

Returns: 37
{0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0}

{202574296, 670158905, 3231941, 62892258, 115455725, 659570984, 106695676, 729012490, 490281861, 611894348, 991193190, 12824764, 98001505, 933991377, 36546254, 826555185, 773952020, 73498468, 502235437, 961000284, 222654846, 231546618, 286034245, 264524095, 496003122, 765783286, 276892364, 218862989, 216978019, 898292080, 566148116, 678462292, 756309677, 238016664, 412630932, 210778348, 650136147, 977615985, 727166810, 871289979, 936386263, 732810018, 946968904, 710165315, 112536701, 769371289, 270911374, 463954061, 420233792, 191303662, 210885303, 149591052, 601667531, 469941836, 951348375, 844976514, 875048548, 104939757, 293503898, 663571515, 510329218, 565567673, 61953058, 900015990, 121130116, 548232395, 125159198, 255079870, 603106893, 801641502, 416724680, 607487421, 650333235, 575428333, 56698846, 168089255, 302042807, 617315214, 59444571, 660762339, 570792994, 756249067, 363647991, 432930686, 187721886, 188258372, 375954587, 86709476, 330781824, 533561403, 617369157, 1380680, 106217850, 692383675, 720224471, 547057793, 871491310}

Returns: 1218
{28707, 28705, 28705, 28707, 28704, 28702, 28703, 28706, 28704, 28704, 28701, 28701, 28705, 28706, 28707, 28703, 28704, 28701, 28707, 28703, 28702, 28706, 28702, 28701, 28703, 28705, 28707, 28704, 28704, 28704, 28703, 28706, 28702, 28707, 28704, 28703, 28707, 28702, 28701, 28703, 28707, 28703, 28706, 28701, 28705, 28703, 28704, 28705, 28706, 28703, 28707, 28702, 28701, 28705, 28704, 28705, 28707, 28704, 28705, 28703, 28703, 28707, 28703, 28706, 28705, 28705, 28702, 28705, 28703, 28702, 28704, 28703, 28707, 28704, 28707, 28704, 28705, 28702, 28702, 28701, 28702, 28703, 28703, 28702, 28706, 28702, 28703, 28703, 28706, 28705, 28705, 28703, 28707, 28704, 28707, 28702, 28701}

{832010014, 41137456, 322887604, 732239692, 550152127, 314084416, 805563680, 615603833, 127306021, 546037120, 259999836, 942569974, 998896208, 271072742, 952970474, 115530745, 664510116, 80442126, 309739370, 878291882, 536386635, 409190880, 218962549, 162641550, 835933621, 707933149, 210735947, 158047903, 112419968, 3295953, 252180668, 613555455, 642765115, 815522717, 727566335, 355731874, 248800272, 164243278, 371156015, 896336371, 930974286, 922716084, 863139035, 118161381, 140934397, 622346447, 767619179, 861289309, 459277475, 711753999, 365969287, 283106546, 541022091, 515773281, 811659720, 469950280, 664383583, 455304722, 470794054, 492644695, 548059349, 280944128, 609893733, 924006873, 180399584, 797448160, 825969011, 240061182, 146905657, 673167558, 881687130, 420862255, 662511493, 945148329, 902479681, 539743892, 142160119, 138660464, 637448328, 326404566, 82096880, 667570738, 192486641, 886921371, 131608315, 571956005, 724626690, 818551744, 837310041, 87322800, 50536205, 513008040, 485306322, 350512299, 965972849, 962810360, 411629486}

Returns: 501
{0, 1, 1, 1, 2, 2, 0, 2, 2, 2, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 2, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 1, 0, 1, 2, 1, 2, 0, 2, 0, 2, 0, 2, 2, 1, 0, 0, 1, 1, 0, 2, 0, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 2, 2, 0, 1, 1}

{952221865, 266279011, 803327617, 265323865, 500798695, 991880842, 427051013, 144920388, 84367371, 155875677, 403077688, 433336263, 501634748, 426100241, 134968074, 493353832, 889960673, 204681693, 555701577, 408110182, 718762577, 797533555, 434327515, 828253780, 727695025, 354165001, 473442440, 177743196, 140516340, 890047566, 590392837, 219230335, 138708643, 251571147, 871347929, 39672466, 404981418, 103485814, 212874775, 533445338, 571203552, 620355948, 392624284, 659243481, 87556258, 453071654, 192190150, 111583540, 797408648, 729322882, 883958518, 440124867, 787145379, 803795292, 194632109, 584107520, 614191826, 617677062, 364055286, 427716823, 339015479, 435968462, 623720240, 548739446, 892382570, 925455404, 407674483, 154157275, 893743333, 689989360, 492454837, 902432251, 131126654, 935705013, 589702519, 244396426, 806525748, 995452166, 676173149, 183824907, 820860581, 503475999, 902303751, 862125069, 375412105, 74777031, 702222271, 999366979, 270474158, 356594374, 959352749, 646913220, 627701348, 849460099, 356523333, 487277604, 733901661}

Returns: 700
{8874, 8873, 8873, 8876, 8873, 8875, 8874, 8876, 8877, 8874, 8877, 8877, 8875, 8877, 8875, 8875, 8874, 8875, 8877, 8875, 8873, 8876, 8875, 8875, 8875, 8875, 8875, 8874, 8875, 8877, 8874, 8877, 8877, 8877, 8876, 8875, 8875, 8873, 8875, 8874, 8873, 8873, 8874, 8875, 8875, 8873, 8873, 8876, 8877, 8877, 8873, 8875, 8873, 8874, 8876, 8877, 8873, 8876, 8874, 8876, 8877, 8875, 8876, 8873, 8877, 8873, 8877, 8874, 8874, 8877, 8875, 8874, 8873, 8877, 8875, 8874, 8877, 8875, 8877, 8877, 8877, 8874, 8876, 8874, 8874, 8874, 8876, 8874, 8875, 8873, 8876, 8874, 8876, 8877, 8876, 8877, 8875}

{591172051, 850730659, 845716911, 48218517, 374986149, 934642973, 352599646, 439350573, 927089333, 177696648, 388885847, 190529843, 913851868, 617109808, 433879051, 708195548, 253883460, 297740597, 671000696, 486111554, 882664884, 701138246, 426392259, 139147746, 656847911, 579927002, 187781780, 974112021, 174291076, 505455680, 442689535, 937148820, 327367316, 822522063, 173174765, 193551212, 667855727, 471693556, 929300870, 363582632, 265762818, 673525730, 961602050, 546521315, 82555669, 741219013, 303126804, 1935529, 358386439, 257234099, 169978915, 5332385, 417085790, 451893590, 260249761, 19191977, 211058456, 152231063, 240328784, 848914619, 839754504, 646944559, 784103083, 42102442, 65278865, 522392387, 570590088, 75614019, 888072689, 354775331, 444854828, 240996526, 613545450, 130822576, 973392291, 731284386, 40384778, 725019627, 152774931, 898083069, 77320035, 279198070, 139678848, 863322505, 307606073, 407761552, 457316638, 349667753, 445693604, 633986980, 164504667, 560705861, 767411986, 558671508, 907286427, 891607817, 384338871}

Returns: 752
{3, 6, 0, 3, 3, 1, 6, 7, 4, 3, 1, 6, 6, 2, 2, 4, 5, 3, 6, 7, 0, 3, 6, 1, 4, 7, 0, 7, 7, 1, 7, 2, 6, 3, 7, 4, 4, 0, 4, 2, 4, 2, 0, 2, 1, 3, 5, 2, 4, 0, 7, 7, 4, 4, 4, 0, 3, 4, 7, 3, 7, 0, 0, 0, 3, 6, 5, 3, 4, 0, 5, 5, 6, 3, 4, 3, 1, 3, 4, 0, 0, 5, 3, 0, 2, 7, 4, 2, 0, 4, 7, 2, 0, 7, 2, 4, 6}

{574484229, 961559742, 920702758, 216113266, 984555856, 191213550, 604709230, 165969143, 852610159, 27102966, 193004399, 123093902, 350764922, 939878147, 35444655, 790802043, 430596941, 682351058, 365158731, 258278783, 777771841, 558883703, 81795726, 934821595, 100020192, 866540952, 233020869, 626501032, 542589811, 325305688, 679388516, 475572268, 377166916, 497408656, 686785237, 849439807, 392729924, 66162003, 86384329, 248722347, 416601948, 252416402, 311353302, 972426552, 79513003, 529706090, 194457047, 5695114, 504967083, 785025394, 415959963, 648997878, 278653281, 972088612, 10128284, 316406116, 415224417, 799559715, 455547092, 350296063, 126811616, 829257780, 588717858, 105086422, 580142319, 355610749, 525156818, 97290932, 223068361, 200475691, 89954107, 842325069, 648376514, 203295294, 80587351, 413052747, 171465631, 715874852, 90667794, 256455770, 968595075, 254085439, 926295007, 787611059, 474185541, 804318130, 907825660, 527052836, 688449268, 823636717, 469377006, 39200768, 769352746, 274858994, 330183294, 912309445, 514276021}

Returns: 383
{36559, 36552, 36551, 36553, 36560, 36555, 36559, 36560, 36560, 36555, 36556, 36560, 36556, 36558, 36554, 36558, 36557, 36557, 36553, 36559, 36560, 36559, 36552, 36552, 36554, 36554, 36557, 36553, 36555, 36554, 36559, 36554, 36557, 36554, 36555, 36553, 36555, 36557, 36559, 36553, 36560, 36555, 36557, 36551, 36559, 36552, 36558, 36559, 36551, 36553, 36557, 36551, 36556, 36554, 36559, 36559, 36554, 36555, 36551, 36558, 36557, 36554, 36551, 36553, 36556, 36560, 36557, 36557, 36557, 36557, 36558, 36558, 36559, 36553, 36559, 36552, 36559, 36553, 36559, 36555, 36557, 36551, 36552, 36554, 36557, 36558, 36552, 36558, 36554, 36553, 36555, 36560, 36560, 36558, 36557, 36559, 36559}

{333746221, 358014182, 673365901, 947931681, 366475930, 46374677, 975136723, 877515171, 938738779, 790186213, 103025172, 863019392, 195158174, 18938630, 137626465, 952250572, 957115411, 925077013, 568256650, 808294262, 355216248, 293455235, 928548968, 392252885, 223824681, 325329791, 70948947, 5288606, 524112038, 573315505, 313578088, 149008374, 415839964, 396371564, 964250298, 245484104, 566069446, 569515674, 878157301, 118764661, 179922118, 487234237, 207143755, 531185914, 188135771, 871506578, 549702225, 588236581, 94875423, 4893494, 587860093, 795411599, 879128467, 217071465, 73262339, 731622903, 118060047, 777348935, 514864497, 759236677, 999040269, 291248215, 612079166, 11862788, 232127957, 759353628, 885612008, 27578903, 672523679, 279328164, 86331829, 839754669, 283705286, 560090862, 631479096, 427616474, 440213034, 348737652, 779155331, 315622440, 410425291, 287995108, 660347460, 622588792, 93644109, 111706642, 101008815, 914735333, 518918299, 978012424, 114596697, 813861906, 385579391, 384081447, 466707940, 161283384, 639474482}

Returns: 441
{3, 3, 3, 1, 2, 3, 3, 1, 2, 3, 1, 2, 1, 4, 4, 1, 3, 4, 3, 2, 0, 3, 1, 4, 3, 0, 4, 0, 2, 1, 2, 4, 4, 1, 0, 4, 2, 2, 1, 4, 4, 2, 0, 0, 3, 1, 2, 4, 0, 3, 3, 1, 3, 0, 3, 0, 3, 1, 0, 1, 4, 2, 2, 4, 1, 3, 2, 2, 2, 0, 3, 0, 2, 2, 0, 2, 0, 0, 1, 0, 3, 0, 3, 3, 2, 3, 3, 0, 1, 1, 4, 1, 0, 0, 1, 1, 2}

{643879810, 187567342, 3263795, 866006618, 616547101, 493272105, 414412882, 365714343, 908223236, 234918072, 851910870, 22412705, 952234154, 223806876, 434261213, 341032259, 964985025, 546902116, 130167004, 696387112, 131592512, 57850151, 719726183, 374527555, 222883137, 278961772, 513699969, 923601616, 413751801, 66680183, 40644075, 788759609, 731363337, 218380663, 495998210, 249171348, 989991894, 534605085, 478478018, 278225371, 733180410, 460443755, 809164418, 291190047, 855401601, 206475956, 141849552, 587737705, 668611735, 9643360, 313782180, 605180546, 414869176, 325301283, 519477763, 528130281, 743048468, 871638754, 226532703, 950852920, 877125908, 648042776, 321885096, 892143163, 744986876, 106567994, 694350699, 833494150, 439123736, 386242159, 274494368, 610853391, 258837489, 429525968, 363792281, 719993275, 668969310, 497392717, 179603432, 280359951, 556871647, 780704151, 17852751, 116933605, 872833841, 959288890, 506364412, 662183535, 783736738, 731850761, 850453599, 95287287, 63537839, 789070910, 987035206, 700939930, 107963391}

Returns: 720
{4, 2, 0, 7, 3, 4, 6, 0, 0, 0, 1, 2, 1, 2, 1, 2, 4, 0, 6, 4, 4, 0, 3, 1, 6, 2, 7, 2, 1, 0, 6, 4, 0, 0, 3, 7, 1, 3, 0, 6, 3, 0, 6, 2, 4, 0, 1, 3, 0, 6, 4, 1, 7, 6, 6, 3, 2, 0, 2, 6, 5, 6, 6, 4, 2, 7, 2, 5, 5, 0, 6, 4, 2, 1, 5, 6, 7, 4, 4, 2, 0, 6, 0, 1, 2, 3, 5, 4, 7, 2, 3, 2, 4, 1, 0, 6, 3}

{822166189, 60610680, 987269978, 255240063, 309519256, 784551313, 37670424, 655998443, 758411715, 420534427, 192322347, 884334732, 424231070, 113757114, 771627252, 523205207, 392193174, 182265311, 196991541, 639395815, 46939741, 163909746, 58346003, 981717823, 366462568, 506554877, 384172635, 476921647, 102588934, 698363488, 560872168, 669972551, 325203523, 697168237, 760048678, 638402344, 385326690, 144425869, 242222810, 16505255, 463789762, 686823545, 980315961, 837048657, 173328066, 912980088, 823022221, 121392380, 407347118, 69848276, 203836327, 206414731, 398950500, 556336026, 989884237, 943079232, 829233771, 452980930, 400055856, 969286101, 539700031, 412015991, 91046160, 478491640, 357955850, 198940824, 798983745, 457439296, 997514698, 404337181, 202493525, 22392108, 123173595, 293952164, 912734176, 457573430, 174595488, 55039640, 355469597, 922109060, 693764572, 631240573, 651766141, 77948902, 878005398, 890646070, 410513993, 27330364, 367935812, 315676014, 362756168, 531076788, 653016779, 507784944, 295081148, 560372678, 747601874}

Returns: 319
{0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1}

{370606387, 199709383, 609827175, 198365648, 724470509, 124540203, 186767588, 139096534, 614784166, 216121424, 85337213, 718934697, 234986389, 227808793, 730972091, 349654046, 30580680, 521185211, 920756674, 896349931, 798687811, 134294190, 640712972, 542385170, 693079792, 952641511, 18317295, 5513207, 512661206, 583754282, 709745950, 679906289, 566290519, 462145115, 411715000, 957773282, 497740569, 78257760, 593856893, 796288509, 517274459, 165246619, 382412742, 893201676, 436883959, 593942784, 198095720, 754329129, 701003273, 180437069, 269653162, 146529953, 957108839, 127862807, 460111484, 560364782, 773134783, 323582867, 73851536, 791707715, 46402621, 595306289, 923672974, 706279872, 468159199, 128305311, 289947055, 287698570, 534032102, 467224177, 673213428, 841829370, 630842633, 177088464, 228262151, 705242948, 50548795, 400833465, 490998538, 380672419, 545031516, 21119747, 202266069, 463799737, 721075325, 333255997, 8381407, 496324814, 694806084, 568227645, 587517298, 938595751, 921271049, 176504741, 913599853, 538993120, 214760308}

Returns: 950
{1, 2, 1, 0, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 1, 1, 2, 1, 0, 1, 0, 2, 2, 0, 1, 0, 1, 0, 2, 1, 2, 2, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 1, 1, 0, 1, 0, 2, 1, 1}

{908435537, 441396641, 816734394, 598251598, 894779133, 67863745, 556546434, 25295349, 815165268, 549319009, 486608297, 813348190, 966142663, 104269631, 888185926, 354281509, 43511514, 260222888, 658788783, 167338735, 803067266, 583509191, 630601648, 554715749, 535785631, 934176350, 415255401, 397338346, 51737906, 751193149, 332573953, 349921214, 509579566, 997087849, 819593125, 619442763, 958714315, 403335773, 655496455, 369307146, 243591648, 448858615, 28326943, 828585661, 360349995, 253386585, 377685087, 525244524, 18844961, 658997962, 683108119, 485592341, 732318900, 57158115, 181335675, 829935823, 789580809, 850788455, 642821708, 464518020, 984260427, 353052433, 722185601, 623881659, 803821989, 978012662, 577080671, 861223580, 502525724, 750077760, 648645523, 578416558, 48190176, 570226488, 138386736, 364000156, 514349168, 113125516, 698191792, 309593021, 551830270, 886615306, 585462240, 175015992, 881637552, 896421540, 237113789, 680087993, 11587759, 616171318, 41304814, 374416331, 85101561, 825119115, 482390627, 442178586, 484717456}

Returns: 902
{1, 0, 2, 1, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 2, 0, 1, 2, 1, 1, 0, 1, 0, 0, 2, 0, 1, 2, 0, 0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 0, 2, 1, 1, 2, 1, 2, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1}

{569033983, 25847480, 595770807, 989937083, 37897675, 673247059, 437459507, 254955252, 776956700, 16146759, 659553478, 540608099, 593581512, 413841886, 474093234, 97067116, 424800120, 401828936, 149015673, 221589982, 827781820, 951182792, 84176038, 823059331, 771619465, 713299972, 289806924, 244422484, 730784269, 3513058, 591446064, 179940913, 139659476, 291140772, 479464132, 647943978, 584339376, 170254052, 365771684, 872554662, 884052227, 364794834, 727232749, 74819222, 530455496, 554721097, 816546454, 70267218, 691999946, 752992490, 568588024, 589626854, 843397680, 717238203, 602742342, 253397311, 790413236, 30533210, 663489546, 1986025, 506063046, 47520588, 9105205, 530710967, 368093927, 308845983, 784393982, 583950527, 162077841, 927528290, 34512849, 884275441, 778347529, 788796434, 296653818, 248127757, 965544907, 502980368, 881122802, 924263738, 208071171, 323526149, 962030945, 982639348, 923745009, 122220903, 883690109, 472455950, 803870313, 164676744, 814444756, 841110259, 974706443, 866096581, 179206246, 475214427, 126862664}

Returns: 828
{88804, 88806, 88803, 88807, 88802, 88803, 88807, 88807, 88803, 88803, 88803, 88806, 88807, 88806, 88801, 88804, 88806, 88804, 88807, 88804, 88805, 88804, 88805, 88808, 88802, 88806, 88806, 88808, 88805, 88803, 88802, 88802, 88803, 88805, 88801, 88804, 88806, 88806, 88803, 88806, 88808, 88807, 88802, 88806, 88807, 88802, 88807, 88804, 88801, 88807, 88804, 88802, 88804, 88802, 88807, 88806, 88804, 88804, 88802, 88801, 88801, 88804, 88805, 88805, 88803, 88804, 88807, 88807, 88804, 88803, 88808, 88802, 88807, 88803, 88808, 88802, 88802, 88808, 88805, 88801, 88805, 88801, 88801, 88808, 88802, 88803, 88802, 88802, 88803, 88805, 88801, 88806, 88807, 88807, 88807, 88806, 88806}

{575881718, 59052294, 569209716, 277386188, 533447720, 291958453, 507263780, 774600826, 997127917, 535141760, 318251294, 148080930, 832675939, 459269045, 405614926, 214250276, 580792814, 53586381, 74123886, 32649856, 866878328, 311976021, 774939187, 298150603, 52971307, 745862134, 559493437, 336286986, 594573519, 861124048, 454575744, 786154313, 527110152, 988202157, 387705939, 220469167, 203626915, 187492256, 590956246, 297126269, 241085990, 69338912, 578793037, 96022088, 772916028, 762182607, 173304145, 965459088, 255019130, 395360414, 395324407, 793869869, 126052359, 517847253, 848083246, 178833218, 766998592, 104061284, 461193187, 618492268, 758161003, 973912346, 944085625, 687840194, 38780106, 648849367, 219640538, 49423509, 253367366, 885204179, 630934412, 450482735, 274174245, 762619214, 108593616, 99009126, 942139868, 37982646, 632488899, 730836525, 704391102, 103232872, 579608642, 887982835, 585627330, 404814551, 544532148, 706811902, 29003256, 946847302, 683040933, 571623168, 986415663, 91215389, 557541082, 240048855, 605710445}

Returns: 494
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{553793292, 789115381, 814029140, 973385329, 520921665, 130464473, 287370770, 159091986, 800786107, 332017936, 203536360, 740407477, 521306862, 450135505, 497651395, 63121605, 770569515, 893223774, 426401341, 438218154, 614847169, 614282228, 416046112, 571466347, 225389132, 646336387, 788897727, 540015496, 619862830, 415724907, 162729090, 437809200, 405532636, 699124086, 745035182, 24666834, 666080089, 88263149, 411617523, 973377969, 359842362, 862516263, 738668247, 182110303, 234879880, 642428666, 793243381, 578502994, 914370675, 120396879, 40626893, 478408304, 23431716, 198389221, 741077011, 775607148, 276781746, 486122604, 1779013, 500973877, 885510791, 868226980, 702185492, 684458193, 677441270, 360354953, 474662528, 22516362, 981726238, 85964384, 553928741, 51871389, 897759799, 530340831, 804014804, 753383136, 763799149, 605329944, 290579663, 644739931, 49840074, 251613276, 97549479, 938119080, 462242759, 252405458, 824171387, 767822643, 55030269, 661984107, 859431641, 677648109, 415930008, 597292754, 720498709, 788856668, 425919429}

Returns: 576
{5, 8, 0, 4, 7, 5, 1, 8, 1, 4, 1, 1, 6, 3, 3, 1, 6, 5, 4, 6, 2, 7, 8, 1, 2, 4, 6, 6, 9, 3, 0, 1, 7, 4, 8, 3, 4, 3, 0, 2, 8, 4, 0, 4, 5, 9, 2, 3, 5, 5, 5, 7, 1, 3, 9, 8, 4, 6, 0, 1, 4, 1, 0, 8, 3, 4, 2, 7, 4, 6, 0, 7, 0, 7, 8, 0, 0, 1, 9, 1, 6, 1, 2, 5, 2, 8, 5, 1, 5, 0, 5, 9, 2, 2, 6, 4, 8}

{193627622, 238908120, 255788600, 967840849, 81630258, 584417841, 892617132, 872419026, 616503236, 499743972, 309641880, 231369604, 162529527, 886496709, 474855213, 777353596, 976182433, 713750808, 534585628, 301824948, 109268917, 173175348, 747950308, 422285281, 587263640, 638297563, 723206513, 726840505, 846089073, 315587315, 206420631, 817759925, 658426310, 86995702, 65127668, 640813110, 708400109, 754753325, 494606189, 734883702, 605272343, 694277493, 385632183, 346180466, 532855218, 325633953, 1368511, 946112124, 766934497, 370573501, 813173902, 323746991, 924181875, 219520795, 687690511, 149729112, 307681638, 103663969, 822457203, 276386929, 556296941, 685091066, 961925001, 99864991, 844539242, 307218088, 929359409, 173485099, 223347435, 246724145, 901227154, 228000634, 2380579, 636917297, 499013614, 662000912, 422710926, 656635776, 207544055, 550632694, 116679281, 749005832, 655932155, 408760282, 670218454, 619727555, 322732265, 274555824, 395285504, 898453060, 63416355, 84554095, 667720686, 741484701, 420625304, 244961874, 116168853}

Returns: 431
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{756726467, 526350672, 539442013, 122544573, 810623579, 263195266, 378160093, 854968509, 355526282, 179226443, 496671191, 24260176, 631062847, 105426213, 720412489, 493352293, 494488688, 297197666, 685081510, 585103879, 736604807, 746550456, 739996156, 986463311, 25537872, 601508805, 203243638, 884873257, 729714785, 308222627, 43901204, 828718828, 282674978, 582239741, 518276963, 411998380, 73514839, 775694912, 843957082, 117075130, 944031162, 559272525, 761348628, 633503746, 643082352, 512516893, 576767594, 799221061, 849100513, 388654384, 621118348, 334682125, 442484490, 826768667, 733157854, 962200197, 964545184, 219977311, 786368717, 679160797, 98188880, 110252491, 550176499, 868789570, 327488404, 434950848, 357293696, 578737880, 897908492, 386678573, 913854418, 116822058, 876386674, 100051729, 917869313, 668324193, 798837167, 457550044, 387115370, 53950147, 375574709, 625812829, 928943729, 60640905, 993976202, 420753701, 680685374, 866619588, 287670032, 273090582, 226141679, 311090681, 224634686, 499291495, 971504919}

Returns: 0
{466873, 980465, 813383, 461847, 332872, 906811, 707258, 57431, 162819, 608474, 503001, 645, 28860, 443278, 908247, 479621, 545493, 459148, 643887, 854208, 901658, 270241, 308241, 107486, 317797, 129864, 978738, 177993, 443639, 353009, 521696, 446690, 245899, 527806, 597969, 538166, 275881, 328193, 581740, 24187, 963101, 638466, 705765, 915825, 397746, 897406, 958456, 623493, 617928, 730631, 623736, 723360, 654321, 962060, 484259, 646951, 585434, 188219, 715684, 735994, 395328, 854055, 44875, 190457, 642762, 974242, 190276, 654186, 81718, 508511, 430984, 63198, 235321, 484151, 184455, 975847, 626983, 417221, 4681, 654778, 145846, 779350, 76321, 587403, 408014, 791, 403040, 523582, 777893, 477231, 660368, 391328, 766115, 128434, 907491}

{548947956, 430015014, 109637007, 92381311, 847718053, 451283483, 442330297, 955753428, 591098776, 111951380, 914736691, 662807301, 187723308, 970209760, 714165865, 535330824, 510886849, 471638319, 640306371, 889758905, 100636319, 424668444, 563196277, 542924253, 351539984, 464477859, 804158885, 980750911, 211144145, 339716497, 426400949, 910274886, 80090327, 142284814, 765291446, 523577853, 357621017, 697865347, 697184248, 112574390, 271115612, 521260086, 849335197, 99546048, 383493615, 31925669, 423641320, 670770888, 87319694, 645911310, 240774618, 553833416, 691563365, 226325724, 545243636, 276680943, 765865032, 921223554, 820193933, 329181420, 536941529, 650205374, 122125672, 980661602, 603609902, 67053697, 308060350, 772702300, 190339682, 524279704, 746861205, 259106282, 434185123, 655650969, 509022208, 7600387, 632549436, 937244481, 429046082, 653966170, 252599355, 671430482, 595262025, 401686913, 860241464, 845548683, 114584280, 362763679, 69033215, 168657968, 633379556, 113697938, 256607957, 906858948, 462647075}

Returns: 0
{908049, 877011, 71071, 923963, 68634, 496148, 279766, 67482, 170143, 214671, 238478, 974009, 442602, 495600, 831854, 207044, 311126, 6227, 119733, 633878, 591832, 854131, 12439, 263303, 559312, 223345, 558160, 390772, 493890, 960974, 224666, 348571, 419917, 955572, 40197, 705701, 677871, 614964, 434865, 341259, 850335, 843437, 563714, 361470, 938607, 7845, 114596, 21555, 326077, 830212, 50948, 638554, 229296, 862915, 861087, 885506, 549703, 906440, 641637, 3523, 36609, 914223, 581598, 616711, 51650, 402072, 936445, 800139, 486578, 200245, 94133, 290723, 986754, 707910, 975551, 666704, 930246, 414638, 534998, 364761, 39646, 929735, 68437, 318811, 630652, 749012, 326305, 54558, 639849, 961335, 463207, 485921, 426527, 763911, 755322, 348771, 754434, 298991}

{96563433, 271881320, 915834029, 957372743, 451425245, 401042096, 105467296, 760537922, 405221553, 405306410, 189430593, 317497029, 31989629, 32726130, 617521431, 726017514, 619324220, 871948756, 951735768, 205501002, 135272467, 602537866, 239233695, 92667708, 8177954, 454128575, 459168225, 446959523, 759229788, 454231930, 620958490, 787641001, 136988491, 165344300, 830170090, 774867577, 794438710, 796228455, 914960510, 403416924, 578629391, 688684552, 973483088, 494006316, 282008120, 687581715, 886033332, 688680144, 158444828, 80619763, 42543235, 633350053, 259280605, 873094827, 784896456, 631112253, 137725855, 75703655, 974654824, 18824811, 147075428, 131683493, 556736525, 837370285, 136669035, 657283462, 917253377, 313656810, 611977491, 647129740, 945353534, 449164982, 587730181, 800411911, 524059222, 657631084, 916829794, 623784895, 934807900, 25189945, 179749844, 839551595, 864246082, 641872478, 581930458, 620904647, 884453280, 680032467, 777589860, 156614938, 998550954, 248279257, 911137235, 125931885, 162686523, 961925422, 975155806, 998922867}

Returns: 0
{507855, 941077, 846110, 681992, 513856, 482999, 864129, 895412, 634411, 324234, 429622, 790457, 970915, 471554, 634983, 192394, 13414, 448734, 847868, 826341, 979682, 914565, 511028, 513420, 767606, 427859, 360167, 393153, 582719, 316554, 838564, 940930, 322227, 413634, 872614, 867974, 394757, 37283, 654037, 800070, 551913, 281777, 148523, 490069, 411441, 106265, 876444, 924840, 808554, 691544, 112873, 621610, 35596, 385634, 983417, 669519, 860590, 934170, 356726, 696090, 710649, 599490, 787888, 154657, 1149, 273031, 368304, 167765, 650951, 900982, 41707, 835602, 844274, 432346, 504288, 752035, 339192, 154683, 278571, 988888, 268598, 346832, 428601, 689135, 116955, 215482, 946221, 701481, 980129, 185180, 651626, 921924, 241712, 966602, 295862, 696541, 257631, 483036, 729257, 341001}

{822514785, 566678280, 366068896, 992101255, 167581776, 566868633, 387564735, 119742496, 962856224, 157283769, 989045510, 190822316, 606252559, 993325838, 244278499, 579712237, 907283298, 613552594, 841249331, 566383530, 892819225, 833095612, 344020032, 685975530, 849986755, 686313606, 581779981, 221132853, 849113147, 683837377, 267547180, 43809682, 392440296, 408431883, 963287788, 809727135, 184616434, 526358252, 653678608, 787348667, 967600909, 779413612, 182842245, 994013395, 937637266, 207557985, 432322631, 864005186, 781877103, 718940261, 57626285, 503487332, 350884232, 589017925, 980174541, 579282472, 80153799, 277949394, 102260531, 148720049, 912658137, 718362961, 882190773, 553349043, 802872131, 622248952, 717226781, 223613533, 293876823, 641316025, 418215817, 933805531, 119174042, 274407612, 593674311, 384081636, 128444744, 403558185, 399695760, 697295742, 572360429, 241576537, 312392337, 269443405, 653481057, 726880980, 750581443, 698581539, 344474779, 611678994, 41154510, 815750641, 663889713, 222756081, 318072460, 478939337, 829775836, 991922160, 936906408, 376365986}

Returns: 0
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{490941912, 541236527, 236499459, 550743713, 548748658, 521132928, 304290806, 342001493, 468604459, 554339970, 267144961, 654921848, 730521680, 914819767, 754201963, 689727792, 944156015, 352830664, 612460485, 680788929, 225195980, 934987890, 613720296, 886058950, 190555654, 203371247, 256920390, 809231905, 44568549, 31547555, 746135705, 652946827, 914027477, 547139921, 923729021, 965378733, 872448898, 650364373, 279749953, 790175293, 653975628, 316428353, 963039860, 213199020, 368616927, 635579722, 928536538, 649265723, 676396199, 946956586, 600446389, 361553584, 541555156, 186630428, 802433617, 833335013, 910847219, 351951339, 400184363, 198432454, 168785932, 709487333, 780723746, 529817936, 81103306, 37782503, 419704491, 498449468, 998257390, 745713325, 483244204, 315973313, 667432713, 100871024, 848584237, 686573552, 747489349, 528621850, 869734476, 673666891, 921814484, 290424729, 358398436, 303088383, 746571564, 232994098, 880548957, 886913147, 973068820, 750897153, 912785634, 974258241}

Returns: 0
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{765183968, 480929298, 790133106, 766905042, 934188351, 834583516, 91022362, 348018471, 782066373, 588010766, 792594065, 693919127, 703996020, 231993630, 347371572, 672987831, 101020613, 850625277, 279436855, 556755569, 168658124, 298489062, 387453592, 149811814, 803695839, 176767640, 84539944, 936060169, 197845380, 873253680, 59908795, 915817695, 830211682, 546695398, 192797327, 648388737, 982778185, 984130081, 694548491, 869941946, 596447181, 657048495, 659111743, 110244359, 307193055, 45065367, 861668079, 344203211, 199147538, 92800142, 482794487, 296132580, 105909351, 320452293, 209762399, 636373934, 809649230, 809494948, 531432209, 670018416, 775254864, 154613846, 828429879, 928123569, 146306528, 261236478, 764189164, 578120340, 911521225, 258206410, 653448591, 335525631, 275785663, 722703084, 793874907, 964568269, 487871185, 869692514, 28229431, 331853798, 983452481, 202396398, 800223341, 981348322, 27309549, 462539401, 187131485, 288525764, 944663570, 750657729, 522820015, 202610552, 481592794, 13801158, 396785469, 682951183, 816560117}

Returns: 0
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{212617238, 272297391, 72661579, 728706102, 54359801, 260817298, 187496023, 655400073, 378584169, 371797147, 89760091, 734884755, 535993289, 280134610, 301299249, 825547802, 641592966, 395144936, 219442695, 873439308, 51486094, 885307929, 279650888, 523175053, 249946078, 713515653, 117424597, 567095307, 900685019, 328202785, 198192512, 426046960, 301908537, 795213017, 635367513, 981060515, 765388553, 216486917, 566987262, 300931477, 815929986, 172275959, 173352264, 343708249, 164534170, 298745039, 517629709, 105991854, 306762032, 745304563, 280681363, 162143874, 419878593, 724193896, 235521336, 238159964, 860849122, 808592009, 848136890, 191248812, 92590548, 987660076, 311456703, 554942739, 156493369, 876242436, 499431675, 834892399, 316968558, 33901619, 114449044, 952905551, 729813896, 595832881, 237159748, 222616950, 114139693, 211464672, 536220191, 411516943, 324732524, 769448532, 274169983, 13067810, 919717080, 360152609, 386949584, 450942183, 103822818, 94427180, 353892626, 995858021, 279236866, 572639174, 896214699, 248826998, 746349585}

Returns: 0
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{449470263, 383566399, 13877559, 747734428, 562817263, 364707773, 585987425, 798255605, 114938111, 821901445, 654620711, 388544003, 899541018, 547493939, 931847487, 414265721, 281294715, 164181215, 951306366, 56688851, 230979639, 56690751, 604562856, 281029826, 739067792, 277614974, 189250000, 401874114, 950060051, 658667778, 401158251, 248011407, 612564359, 621495514, 594568372, 872220175, 930006774, 994658876, 143127587, 253225510, 113920547, 952702929, 144266279, 385963701, 923636421, 55165533, 155823831, 786789267, 990476921, 187481096, 418898249, 826599392, 900571675, 825205549, 744611074, 713352710, 290524756, 560740182, 67494239, 669588349, 785950665, 571590226, 165324554, 965512135, 258641278, 345948915, 487992592, 919497848, 556632985, 792194210, 761415307, 282034524, 101148591, 376513443, 819631327, 275478583, 10155155, 677837919, 593916635, 299698976, 572832778, 287353557, 499217864, 563220040, 658538632, 501418463, 944602911, 161660825, 390297592, 144895587, 720544821, 921603226, 312521044}

Returns: 0
{102996, 56776, 403088, 517885, 216039, 688788, 707366, 554514, 704522, 603893, 165490, 663006, 734615, 385581, 60867, 584835, 779723, 190588, 921568, 576639, 249946, 504913, 812398, 502739, 447649, 59805, 736575, 521268, 727141, 737000, 913794, 722147, 812376, 912206, 245668, 537478, 604020, 340427, 534555, 230697, 407208, 777615, 478251, 142319, 671081, 178054, 180154, 921125, 207735, 843455, 348678, 1963, 620762, 548756, 771650, 209708, 575067, 890534, 469580, 171527, 305765, 547063, 673245, 455601, 686481, 495293, 581314, 457235, 905074, 719916, 22504, 174906, 610791, 449018, 418245, 998632, 33840, 584621, 51815, 63528, 635329, 723356, 106794, 217629, 505519, 197436, 837533, 578299, 936219, 33611, 150345}

{847690670, 572991025, 963159848, 826423977, 129017749, 17742397, 356236844, 277872450, 514973482, 298763156, 105827683, 978162831, 813553733, 793192425, 707831773, 125632139, 385260199, 518939843, 9716294, 298988002, 613584395, 494047373, 940803297, 987673639, 478896675, 199322698, 132361034, 277800699, 395851893, 500197734, 57880097, 528282647, 743310188, 35188300, 457263127, 688837328, 87950282, 739757411, 962318870, 816310107, 750686835, 225533884, 398039652, 210635570, 247461794, 777436845, 628517517, 153767820, 221121273, 532004562, 551951618, 799620536, 114532247, 312032390, 827297158, 650600549, 684791408, 793573403, 735932378, 580240074, 815785240, 924310292, 106770600, 851821594, 902928379, 526143481, 208486132, 40580457, 161287837, 790538422, 543532828, 811870055, 277548716, 159082739, 301181835, 400523951, 157695079, 911572039, 357240200, 980577724, 925069864, 853625940, 713391959, 896529440, 978911322, 571040946, 397614257, 965206460, 136452757, 971217701, 814859501}

Returns: 0
{426489, 598522, 848584, 333041, 711141, 188542, 634295, 856241, 814929, 393316, 19867, 956490, 109689, 445103, 781408, 174903, 715642, 963855, 899654, 68168, 105690, 136152, 108272, 831255, 80157, 842170, 901977, 228546, 30049, 189696, 861504, 405499, 101193, 67168, 853913, 585542, 504917, 784822, 926147, 18299, 128662, 181237, 349975, 702417, 769905, 137257, 736166, 137982, 292264, 235025, 145415, 53935, 406683, 166472, 439499, 846742, 580660, 30611, 76147, 959739, 255944, 709594, 729410, 528346, 447377, 533046, 658406, 628006, 66382, 816074, 977480, 371359, 254588, 374016, 279326, 959539, 997794, 197462, 46370, 320429, 946060, 46706, 185871, 952439, 62027, 548883, 326397, 322708, 458161, 752236, 968910, 356768, 923533, 962841, 49391, 385435, 562237}

{799010026, 842343878, 697276699, 645647088, 270204401, 684199672, 196558362, 558633716, 839300397, 851168912, 673923181, 175589869, 204563367, 664869283, 25891436, 571780890, 806471572, 848640199, 500003985, 246945116, 846880137, 278753558, 448365806, 515588646, 5752704, 810016246, 703632126, 56076457, 957917670, 366298957, 662790210, 436999492, 99641422, 81435419, 667150431, 367121134, 224108136, 278851272, 367238888, 744334620, 129607546, 668408721, 163207891, 639506701, 483867095, 958449884, 406535782, 624240572, 360740996, 217129348, 276786382, 991129955, 294585480, 721967341, 491354122, 268399390, 517757550, 190466592, 616585643, 439481773, 417095666, 212910191, 37795999, 347434841, 47746917, 915362141, 252600136, 72385971, 125070531, 293970754, 257113856, 517674451, 473753262, 811590956, 150119022, 664967026, 103078066, 752813265, 8879674, 629895715, 357689262, 304566468, 612363520, 42998396, 284345845, 401900571, 873338537, 400092317, 391982935, 169679835, 976923235, 94422492, 803231122, 276033386, 96455715, 518070107, 466548521}

Returns: 0
{6, 2, 4, 1, 7, 6, 4, 3, 3, 0, 2, 0, 4, 6, 7, 3, 3, 0, 4, 3, 0, 5, 4, 2, 6, 1, 1, 3, 2, 2, 1, 6, 5, 4, 0, 4, 2, 0, 4, 4, 6, 5, 5, 3, 4, 3, 5, 6, 5, 3, 2, 5, 0, 7, 2, 5, 6, 1, 1, 1, 6, 2, 2, 2, 7, 1, 3, 5, 6, 3, 7, 1, 7, 3, 0, 0, 5, 3, 6, 0, 2, 6, 5, 3, 1, 3, 3, 6, 4, 7, 6, 6, 7, 0, 2, 2, 3, 5, 3}

{981927962, 639738851, 836657775, 775905725, 571520333, 941289530, 376705807, 921776062, 158398834, 744514680, 50639981, 920918424, 693488424, 890993518, 39063557, 136799443, 680465334, 197523246, 192816984, 54134030, 12769697, 751244489, 383642516, 977926534, 226423338, 948101814, 24977080, 543565394, 938622442, 143100002, 32713167, 784853898, 368817927, 801566119, 271586749, 324208623, 444951927, 910279856, 871493484, 797897210, 886757080, 153748332, 480732219, 856748457, 777122240, 476383678, 173107502, 712749601, 171654841, 569509367, 933048785, 457846969, 14114772, 137958470, 990992757, 194941837, 528360720, 962364201, 872134791, 136039138, 960641926, 447806318, 397499609, 26915741, 9194590, 624920394, 492634658, 218853653, 325001962, 890577758, 180207121, 299751650, 554475641, 777759503, 827424773, 328541461, 705425726, 655828451, 446010366, 197466387, 915159570, 344876994, 972179165, 108626094, 628237463, 395299420, 942820730, 866888797, 594290464, 707176747, 824584852, 239212159, 776016599, 978868013, 226191144, 661605763, 491246962, 476624804, 467150300}

Returns: 0
{3, 3, 0, 1, 1, 0, 2, 0, 2, 3, 3, 3, 1, 3, 1, 2, 1, 3, 2, 1, 1, 2, 0, 0, 1, 1, 0, 3, 1, 0, 1, 1, 3, 3, 0, 0, 1, 3, 2, 2, 2, 3, 3, 0, 2, 2, 2, 3, 0, 2, 2, 2, 3, 1, 0, 0, 0, 3, 3, 2, 3, 2, 1, 0, 0, 2, 1, 2, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 3, 2, 3, 0, 0, 3, 0, 0, 1, 3, 1, 3, 0, 0, 1, 0, 1, 3}

{83874939, 905046545, 457508385, 441529446, 741970685, 931777654, 213433768, 237498020, 622481562, 883632702, 147584380, 508332504, 602084158, 482493412, 836235658, 83153984, 171381249, 956432548, 847122973, 332907089, 84487818, 712829592, 944302175, 464466265, 730464617, 626816456, 839835238, 431230802, 309449793, 919043423, 561343424, 191502885, 155158180, 733722386, 234783913, 379858329, 556284200, 397945240, 274441803, 83028451, 149802542, 586922842, 717221266, 929187650, 940235698, 87749104, 267844394, 646516058, 328546435, 394222771, 492145981, 772885939, 933396107, 678900761, 176227196, 693457804, 544460187, 474286647, 651007614, 468493487, 105522536, 172047865, 757035968, 802854716, 591975214, 42815917, 157124251, 511509549, 844022371, 961294017, 638278177, 332451308, 869913014, 904152782, 656783082, 730044928, 437591395, 496798370, 544179397, 440102364, 709100072, 560827327, 544245315, 444673836, 538522545, 977838708, 926752695, 984709622, 247071644, 545010690, 928833065, 289385849, 188454276, 457429111, 647939574, 120183439, 126223013, 779520120, 823463851, 416884109}

Returns: 0
{0, 1, 0, 1, 2, 2, 3, 2, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 0, 0, 2, 3, 1, 1, 1, 2, 0, 3, 0, 0, 3, 3, 0, 0, 3, 3, 1, 0, 3, 2, 3, 2, 1, 2, 3, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 0, 1, 1, 2, 1, 0, 2, 0, 3, 2, 0, 2, 0, 3, 1, 2, 1, 1, 0, 0, 2, 1, 3, 2, 0, 3, 3, 1, 3, 0, 2, 3, 3}

{497776383, 856080697, 198226719, 298344805, 837313197, 307034373, 36252470, 633325145, 623543624, 735710271, 308319167, 260148323, 34636442, 947756497, 312782396, 364997333, 25968091, 526569485, 611663921, 412464207, 745880070, 990081899, 716187356, 297075184, 690385812, 451549862, 647645869, 189176530, 717398495, 119102727, 635962869, 6086131, 414274274, 953223067, 696790446, 576143705, 821065683, 598549868, 401016077, 786191965, 96652588, 597482186, 711240578, 740700327, 215668379, 608379129, 472784096, 546638646, 579628923, 826457311, 567560063, 911067249, 758805528, 796007964, 713288456, 166077273, 260102238, 647209620, 378278857, 856681769, 585743919, 513685017, 686046723, 833833505, 428171975, 399595350, 453037195, 958137310, 309441379, 423638985, 180714383, 194144106, 221039829, 534572122, 383460640, 580947998, 664614523, 275029901, 451597666, 907293492, 817274316, 385123536, 887506635, 408058387, 282867949, 885163795, 180182443, 423646482, 859822497, 58065639, 639205876, 820490767, 47678233, 853811061}

Returns: 0
{0, 4, 6, 6, 3, 6, 3, 5, 0, 1, 4, 1, 1, 6, 6, 4, 5, 6, 5, 0, 5, 6, 2, 2, 6, 0, 4, 4, 5, 0, 7, 3, 1, 4, 1, 6, 7, 6, 5, 3, 7, 3, 6, 7, 5, 3, 6, 4, 6, 6, 1, 5, 0, 0, 3, 4, 0, 1, 7, 5, 7, 3, 6, 0, 4, 7, 6, 5, 2, 5, 5, 5, 5, 3, 5, 4, 6, 0, 3, 4, 0, 2, 6, 1, 4, 7, 1, 0, 0, 2, 4, 2, 7, 6, 1, 3, 7, 5, 1}

{460485298, 570354759, 610437100, 239869943, 242834563, 315805714, 323670119, 127021351, 163140833, 521139631, 726144294, 75457832, 211270960, 553952571, 966480543, 990761781, 980236850, 428846153, 518235817, 568012238, 454521590, 722146915, 226825969, 945763456, 277580767, 270922436, 967621443, 48629266, 411035380, 653339999, 406300369, 302861081, 859646207, 692479712, 553728402, 568196438, 730525216, 707560991, 839462048, 760350830, 927851694, 924363195, 183080888, 15706439, 443915489, 869102117, 336175447, 77490478, 193234444, 805791553, 271922126, 447767337, 917099413, 184285563, 164137487, 753486684, 137998446, 474817499, 203646746, 225655915, 831351748, 848817666, 959554085, 601232103, 413471447, 464039112, 904923452, 289241062, 133702003, 948436911, 303454344, 316575275, 698590864, 497752770, 536177336, 65689112, 29713092, 884866863, 217915573, 4371134, 468363949, 19836955, 111473886, 577079068, 449048027, 805627639, 703866433, 182464349, 475892902, 311041827, 492039618, 957201721, 785217042, 341649120, 444565304, 860850162, 491677659, 476785117, 447281341}

Returns: 0
{34236, 34236, 34242, 34236, 34236, 34237, 34238, 34236, 34243, 34239, 34241, 34243, 34241, 34243, 34241, 34237, 34242, 34243, 34240, 34237, 34241, 34236, 34243, 34241, 34243, 34237, 34239, 34243, 34237, 34239, 34239, 34240, 34238, 34243, 34243, 34239, 34243, 34241, 34240, 34238, 34243, 34241, 34239, 34236, 34236, 34240, 34238, 34243, 34238, 34243, 34240, 34238, 34243, 34241, 34243, 34239, 34237, 34239, 34242, 34237, 34239, 34241, 34236, 34236, 34241, 34237, 34236, 34236, 34243, 34241, 34243, 34241, 34238, 34237, 34239, 34238, 34236, 34237, 34239, 34240, 34238, 34238, 34239, 34237, 34241, 34241, 34242, 34242, 34242, 34242, 34239, 34239, 34242, 34242, 34240, 34238, 34242, 34238, 34243, 34243}

{249060479, 855814891, 186809152, 472493274, 755362478, 827999454, 26261579, 848743614, 148577839, 763894385, 697634511, 733091279, 22642952, 38270125, 703466708, 677092595, 55685177, 962646822, 202508146, 336499256, 935216397, 691288423, 741495228, 863268798, 793033462, 190303011, 384914079, 747671450, 428722393, 366247841, 867725441, 225387205, 120554925, 460110932, 370722898, 169923288, 95562494, 336148724, 408715779, 109697828, 885080917, 930980453, 762302369, 930743715, 814601406, 543322333, 784982537, 210706919, 112307224, 802609064, 330649022, 588005042, 292964723, 577175449, 176497567, 663233064, 370603508, 690383175, 319649672, 287804319, 739439072, 404650072, 5668836, 298096689, 14336308, 648189665, 321912141, 437803023, 157150325, 294612853, 888963068, 99155082, 353987196, 454990157, 482977188, 518657901, 570056175, 817072230, 354396435, 136316880, 729411384, 371448662, 108258125, 126351014, 195863797, 797157035, 747622328, 797228081, 366303616, 313977452, 420969844, 682550505, 78438791, 915316487, 788537842, 721299552, 666227074, 128852938, 642654620, 805982066}

Returns: 0
{2, 2, 6, 5, 2, 6, 3, 3, 0, 7, 3, 1, 5, 1, 0, 1, 3, 1, 7, 6, 2, 5, 4, 0, 5, 6, 7, 2, 0, 1, 4, 4, 1, 0, 6, 1, 1, 0, 1, 4, 1, 7, 7, 5, 3, 7, 5, 3, 2, 5, 0, 1, 2, 0, 1, 4, 7, 3, 7, 4, 6, 2, 4, 5, 6, 4, 1, 7, 5, 2, 5, 0, 5, 3, 0, 0, 0, 3, 4, 4, 1, 0, 3, 7, 3, 3, 6, 6, 5, 5, 4, 7, 4, 4, 4, 2, 4, 3, 3}

{581129140, 637340452, 556037401, 817350226, 48731602, 768296167, 983260704, 295422506, 859273721, 162798889, 809322435, 588023668, 548965174, 950604648, 345355429, 840418471, 43723811, 479525611, 883835680, 776918113, 792459001, 89261702, 10158472, 988911869, 604666416, 71263942, 310581568, 259057185, 716268066, 797687542, 732936543, 221613870, 249601826, 122010157, 761957577, 91417786, 857216018, 361266163, 192505656, 550302677, 556206843, 705004125, 294666087, 928302446, 175899398, 968075807, 287035924, 448820770, 92151800, 423253253, 909573310, 451195897, 804096204, 315877768, 114648939, 81088451, 26977201, 214822281, 593634273, 654104186, 193826278, 929175779, 545864727, 524332418, 385046585, 603672295, 379222333, 347906692, 465317078, 1954413, 275276269, 65904514, 989555971, 364397845, 653176134, 951088073, 35536744, 970115889, 43567904, 110708822, 441515658, 325429078, 909194303, 536812831, 438569036, 424442653, 845146587, 415821282, 273391490, 725180990, 593063329, 786683766, 303056683, 876042880, 667079571, 165998439, 315973496, 244836529, 992522252}

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

{344980723, 651283932, 373527041, 976835110, 873966450, 561282334, 629646421, 47915242, 518296953, 530628018, 304033971, 78500361, 924375051, 688837671, 478184916, 173949267, 217943299, 278231718, 61336795, 543520315, 552951205, 373013166, 374081512, 326870276, 187900850, 131372367, 224590378, 336525658, 826627842, 892593563, 147421582, 628012379, 430861329, 173931794, 411372868, 868447158, 458527939, 580344603, 521498820, 239879450, 329675722, 104687994, 171002567, 340099080, 119868509, 478094593, 282603114, 164499962, 745705417, 284347188, 274697167, 649707157, 990433297, 772275542, 807217182, 108846062, 462251109, 344200123, 197597952, 986672720, 872959309, 967585652, 80739850, 248922044, 134947084, 969558037, 170787427, 786034586, 246576626, 34169095, 563107169, 806370146, 4927514, 354352193, 618490305, 826727244, 59864824, 901061173, 138995017, 94196418, 293667984, 33272228, 678289287, 57732319, 392266616, 6978977, 781817945, 620196168, 286928868, 314975043, 4005216, 953154697, 186269401, 493102156, 224957620, 257632723, 898435431}

Returns: 0
{10454, 10453, 10453, 10454, 10453, 10453, 10454, 10453, 10454, 10454, 10453, 10454, 10454, 10454, 10454, 10453, 10453, 10454, 10454, 10453, 10453, 10453, 10453, 10454, 10454, 10453, 10453, 10453, 10453, 10454, 10454, 10453, 10454, 10453, 10454, 10453, 10454, 10453, 10453, 10454, 10453, 10454, 10454, 10454, 10454, 10453, 10454, 10453, 10453, 10453, 10454, 10454, 10453, 10453, 10453, 10454, 10454, 10453, 10454, 10454, 10453, 10454, 10453, 10453, 10454, 10454, 10453, 10453, 10453, 10454, 10453, 10453, 10454, 10454, 10453, 10453, 10454, 10454, 10454, 10454, 10453, 10454, 10454, 10453, 10453, 10454, 10454, 10453, 10454, 10453, 10454, 10454, 10454, 10454, 10453}

{574914881, 441121265, 535452657, 227970213, 546792788, 467865300, 804803402, 906688863, 36299425, 682332456, 879497287, 456026537, 682554338, 228336424, 1234676, 412837567, 483442281, 847763158, 721708744, 317805379, 298378921, 380256475, 181543212, 679263918, 78279706, 308868105, 106543130, 881150022, 312115536, 862849440, 451556513, 698630479, 799351143, 65122511, 520467464, 875290523, 130911733, 980165858, 555930226, 449675742, 39021461, 26194312, 748678617, 909525251, 751559587, 168938109, 228674380, 124801841, 176275949, 586231636, 428848457, 116633428, 956095713, 363896617, 18051010, 888480753, 254718396, 206573155, 720761588, 504025746, 175753643, 514477376, 198826451, 919884929, 275833948, 58088808, 42410836, 198491022, 800600745, 587587023, 178039528, 170467273, 555359996, 213458466, 177755414, 542079272, 506178478, 815948527, 155423066, 780598543, 445179457, 211126065, 592647605, 249138084, 579035143, 138325807, 563182764, 240567205, 823451850, 296124973, 142247627, 139853641, 217523046, 993757292, 86275115}

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

{161069602, 728045721, 602781633, 895927329, 689426037, 939551938, 387334255, 478087408, 172025160, 497092301, 448283302, 637641310, 218680511, 172232501, 430315245, 561249095, 835553708, 228925263, 451178361, 720094335, 681313475, 459761018, 236550568, 409548641, 639851273, 726419197, 904070038, 163436991, 794253164, 675669424, 59451751, 968084635, 491289163, 208923275, 307779227, 715106558, 883363086, 784675327, 557126572, 290356987, 135970605, 412581779, 77483223, 287853441, 131278984, 718046370, 265922841, 636243011, 310935795, 642379834, 990576554, 397827388, 231164918, 752458489, 363399259, 258710806, 225938558, 51176937, 809279886, 933754796, 788250131, 550469824, 902516915, 228762036, 619378475, 153181347, 281182103, 309427095, 236021617, 29004528, 622650410, 355930907, 504039929, 283133790, 936106005, 16457161, 836993938, 391421993, 533302069, 585196905, 702783898, 583941747, 264941694, 747596297, 297157756, 824209992, 121002753, 618673297, 517179605, 543451493, 790198433, 687226680}

Returns: 0
{28419, 28414, 28419, 28420, 28421, 28415, 28420, 28418, 28415, 28419, 28416, 28420, 28415, 28415, 28421, 28416, 28420, 28419, 28420, 28414, 28421, 28420, 28416, 28417, 28420, 28419, 28417, 28414, 28414, 28415, 28420, 28417, 28418, 28420, 28419, 28419, 28418, 28418, 28418, 28420, 28415, 28421, 28417, 28421, 28418, 28417, 28419, 28421, 28417, 28414, 28420, 28415, 28421, 28420, 28417, 28414, 28418, 28415, 28417, 28414, 28420, 28417, 28417, 28417, 28417, 28415, 28415, 28417, 28415, 28415, 28419, 28418, 28418, 28421, 28416, 28420, 28421, 28419, 28421, 28414, 28419, 28418, 28421, 28415, 28419, 28421, 28418, 28418, 28421, 28420, 28418, 28417}

{622216541, 55969642, 500439992, 898394286, 373019420, 404929754, 683620283, 607622305, 710969189, 14589105, 441211947, 900900532, 638022937, 607091260, 525244091, 71857956, 977854859, 309939594, 993242937, 800876375, 952817401, 784852619, 785947173, 366858027, 566517748, 876909418, 939184565, 200848857, 733913078, 202752618, 321634805, 420704573, 795029222, 107827100, 968016124, 119146669, 872429272, 140543119, 373951263, 742675856, 884426167, 359292501, 360777650, 729508953, 978057151, 198047691, 202574296, 670158905, 3231941, 62892258, 115455725, 659570984, 106695676, 729012490, 490281861, 611894348, 991193190, 12824764, 98001505, 933991377, 36546254, 826555185, 773952020, 73498468, 502235437, 961000284, 222654846, 231546618, 286034245, 264524095, 496003122, 765783286, 276892364, 218862989, 216978019, 898292080, 566148116, 678462292, 756309677, 238016664, 412630932, 210778348, 650136147, 977615985, 727166810, 871289979, 936386263, 732810018, 946968904, 710165315, 112536701, 555562945}

Returns: 0
{18,10,18,9,20,26,0,12,10,16,3,1,8}

{3,29,18,29,22,7,24,28,4,23,9,26,6}

Returns: 11
{0, 0, 0, 0, 1, 0}

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

Returns: 6
{4, 7, 3, 8, 0 }

{75, 54, 99, 45, 48 }

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

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

Returns: 122

Statistics

Problem Statement for "Colonists"

Problem Statement

Definition

Notes

Constraints

Examples