diff --git "a/maximum_score_from_grid_operations/haskell_tests/Main.hs" "b/maximum_score_from_grid_operations/haskell_tests/Main.hs" new file mode 100644--- /dev/null +++ "b/maximum_score_from_grid_operations/haskell_tests/Main.hs" @@ -0,0 +1,41 @@ + +module Main where +import Test.HUnit + +--Program start +maximumScore :: [[Int]] -> Int +maximumScore grid = undefined + +--Program end + +-- Test cases + +test1 :: Test +test1 = TestCase (assertEqual "for (maximumScore [[0,0,0,0,0],[0,0,3,0,0],[0,1,0,0,0],[5,0,0,3,0],[0,0,0,0,2]])," 11 (maximumScore [[0,0,0,0,0],[0,0,3,0,0],[0,1,0,0,0],[5,0,0,3,0],[0,0,0,0,2]])) + +test2 :: Test +test2 = TestCase (assertEqual "for (maximumScore [[10,9,0,0,15],[7,1,0,8,0],[5,20,0,11,0],[0,0,0,1,2],[8,12,1,10,3]])," 94 (maximumScore [[10,9,0,0,15],[7,1,0,8,0],[5,20,0,11,0],[0,0,0,1,2],[8,12,1,10,3]])) + +test3 :: Test +test3 = TestCase (assertEqual "for (maximumScore [[160176171, 271287409, 907227201, 415450117, 645524004, 407724588, 359360510, 704979947, 815129016, 332654706, 52283921, 288357506, 265995658, 532751756, 230235803, 714348779, 246925507, 133531074, 540914818, 806561820, 538574923, 736117330, 711985474, 696187396, 766291403, 228125453, 174221018, 343799712, 920615448, 58144918, 727884816, 133496823, 610606320, 504922730, 363206565, 204086586, 574474107, 157669989, 333380872, 786600138, 487335535, 351264905, 12688339, 126691539, 458593816, 362943059, 923005599, 268794188, 252462189, 194870183, 997488097, 270290845, 697000864, 622336726, 683869495, 667950721, 185182737, 91784609, 236426890, 4613408, 321016364], [535000256, 692039387, 851217958, 51481309, 140433707, 756150324, 954783973, 856313544, 142575204, 330143992, 313102765, 397585533, 594301028, 943582286, 619761732, 550045411, 267708102, 223856657, 240840940, 496035849, 427084027, 992211797, 429540385, 312433405, 204722625, 487599202, 823143102, 97174094, 457048325, 668458896, 524871230, 327235614, 331550249, 758987264, 405233669, 705402373, 194164817, 700955146, 334371365, 841714850, 311005463, 713795272, 828528149, 508105953, 2518438, 398186020, 515541013, 980380700, 306926790, 867563280, 986508708, 651387296, 852521686, 702005811, 376766368, 523898079, 560231504, 863051948, 582310935, 530309107, 169008060], [446902430, 796135345, 352384311, 899883, 120780521, 704104750, 664781882, 425962513, 367828069, 295714977, 366116930, 335449677, 939332707, 12439738, 721265607, 502071618, 241083593, 699184521, 251974346, 40608827, 440008261, 239290285, 949556341, 522397838, 615077833, 650906469, 506970523, 581052127, 686701247, 840483431, 387874229, 164226388, 614140673, 298415997, 801960345, 445041961, 185189166, 452523999, 379045623, 178300582, 641220545, 212619614, 905686131, 775246198, 996541056, 756283054, 374966216, 290806270, 379854770, 5487435, 42000103, 790204882, 441779752, 654628824, 290895363, 40408430, 214208757, 336475982, 202720325, 771794890, 15483363], [366045039, 334460733, 313352552, 246388205, 193812026, 564129944, 325875158, 243145556, 488596017, 188306665, 311799549, 718861909, 314646727, 50507671, 153048907, 818402137, 324893765, 562666340, 114586961, 565213623, 604242523, 764299190, 754905240, 11631559, 154190951, 905560362, 742322142, 476790698, 239337669, 450519971, 25295964, 445215697, 54414133, 398490485, 226649902, 382602139, 958303699, 626866952, 86202589, 285384250, 30949631, 549398064, 788792474, 431827147, 464048131, 179137008, 188693252, 817009276, 93681778, 92756853, 241703573, 470355412, 294421371, 253901015, 47455569, 111061953, 137844217, 841077163, 700355073, 269780977, 721632848], [169345595, 222566416, 793738244, 1839342, 447418124, 478950226, 580191521, 2964121, 453851922, 3313300, 194226320, 241818276, 139521203, 107328948, 147451194, 846783080, 384889720, 859967679, 764222220, 80399639, 14927675, 944853968, 676388989, 575036402, 720119428, 768426194, 2230200, 962967782, 426785525, 221992697, 662157542, 736633922, 102620362, 284564396, 866030721, 111511529, 780339164, 451897987, 660553053, 680492406, 390183712, 20373152, 585927024, 587630827, 634774974, 219507254, 367511164, 748050323, 893625332, 41941240, 112279255, 149509702, 212782919, 372114356, 633030912, 484667847, 351397552, 194076328, 441682158, 772061264, 929560118], [496669481, 430533585, 622976876, 664615668, 288242450, 855654959, 952605964, 843858023, 743055564, 195297578, 691438697, 879281981, 692287297, 816608101, 106215685, 110814117, 822719762, 224119836, 765030009, 253148035, 256457906, 405550523, 822267972, 327066277, 189237048, 452078307, 5196840, 322685502, 426043104, 5783406, 722890931, 33711566, 761772595, 233394668, 862922788, 242990486, 534009528, 306935055, 106307665, 222878954, 830830676, 441528397, 351691142, 286663894, 13356386, 976314151, 665608052, 968594335, 572722786, 858210969, 960708837, 342362967, 877649886, 248752962, 36267651, 530337024, 6313015, 526673320, 702511676, 860108639, 921077334], [93861975, 737128306, 777212714, 373594276, 364231422, 667462334, 915881314, 340262001, 64394173, 262515228, 403216043, 870470409, 518372587, 255017572, 453882796, 407699511, 871572357, 735065490, 614570259, 277871779, 913401148, 670711513, 160872831, 469608729, 786869485, 999250016, 433544092, 90822939, 559900489, 20748218, 698672011, 860765453, 837979105, 187759537, 999388439, 496330542, 83328743, 617339160, 245482026, 752245119, 302577752, 749567765, 827055675, 105414389, 633961055, 653573839, 12324129, 733410546, 427784985, 2457796, 323345768, 49783333, 634161550, 768295317, 710919102, 759724695, 727681259, 973085705, 819240904, 305719903, 601464042], [212799396, 26434151, 829543706, 109798124, 221214813, 19727630, 740289993, 127838673, 861633171, 408383973, 863182500, 93273692, 632322244, 4495735, 305732553, 548214323, 267216203, 525134395, 538542118, 77228785, 441870123, 473257274, 444981065, 740491095, 698599120, 478106056, 899327920, 300502832, 242596660, 836744770, 927030301, 621945504, 594766608, 602423294, 382106225, 78479933, 236592963, 763397072, 610787365, 587556061, 235626136, 467481074, 573739971, 394971709, 39242904, 610282317, 232212006, 142103927, 277809049, 279282692, 973144371, 655758204, 219195126, 924477215, 47861006, 721229374, 384726585, 119230694, 729043010, 30770636, 655963701], [792930147, 997932473, 283047403, 596543748, 784494840, 617311968, 819626834, 881681244, 177277372, 851284772, 677530992, 58905309, 410554468, 69009132, 589423104, 621242434, 559332395, 722948135, 342055531, 602143917, 793106075, 209935258, 593396187, 757819893, 498425183, 318202412, 599013435, 266406413, 183039783, 996590818, 702953966, 149128911, 213934485, 800835026, 452913803, 844090357, 788070435, 699722700, 722926885, 962366236, 475285423, 563577986, 652059673, 864836502, 486058579, 62215441, 479644450, 709128644, 952821669, 454950935, 696576574, 395980757, 236145808, 899484733, 955368018, 508903609, 892879488, 506165902, 604828268, 141091872, 330607651], [76808752, 527819793, 544334154, 802574641, 789305096, 815435549, 834852015, 549107768, 733354667, 301929961, 285946976, 262079596, 511240552, 856292290, 725242242, 414107666, 974925110, 126638156, 836988338, 922341684, 12942783, 738961830, 279652322, 422965387, 429024113, 992192157, 182444072, 70427888, 572338974, 597032510, 703539179, 216426481, 442972835, 88713817, 315639119, 226317381, 969234429, 641030889, 799294068, 707125309, 911554610, 384281378, 934225772, 466449454, 304180982, 210675413, 6801936, 363876423, 706704514, 370094229, 905561615, 581432361, 214019336, 885762253, 574785219, 457078267, 867370135, 321853659, 926979087, 503864872, 9758438], [168385003, 907717970, 368531603, 769896460, 382050619, 910167693, 46850865, 255759080, 386840488, 547744342, 674198795, 536089659, 648845011, 410986146, 302083978, 70885980, 748552999, 945995558, 429617234, 668030594, 769348311, 371333689, 502805800, 654931961, 539184686, 49204597, 608354097, 313262087, 774665740, 893172151, 771227011, 423145658, 773574368, 438316727, 346657554, 30149430, 468950798, 980713106, 960579684, 590630641, 866282646, 198666025, 260965509, 174220476, 471582660, 349698262, 64028925, 139767030, 558069740, 175148965, 558692327, 679995353, 598551680, 46730302, 986088516, 677264222, 137426706, 189129056, 415412638, 969613480, 461185050], [759803089, 759563859, 986572272, 119867314, 973143291, 496967218, 725890326, 407990700, 559805203, 88667552, 27221596, 982233916, 585784477, 448113333, 434248576, 505118131, 885733359, 410422532, 249926085, 800707993, 375133089, 269601997, 322852902, 50420172, 147910607, 871567931, 641409814, 899440855, 961842120, 622781500, 578075356, 295731084, 349053097, 23910985, 637144080, 321033976, 22834023, 717512667, 608686592, 555335769, 542157251, 459248490, 308520715, 890615378, 883878071, 462695529, 830785595, 766567255, 335924607, 172597604, 792655471, 247742465, 903029399, 705849691, 35675306, 29497923, 464952600, 474895515, 169618898, 766345487, 341708931], [956014907, 230126640, 2682997, 808510385, 368291519, 113939118, 444071244, 645663493, 257033005, 579406832, 338342643, 212581259, 335895466, 66811346, 905170026, 423467887, 887139335, 56172838, 941621728, 646214152, 317696231, 632338242, 103459403, 779198891, 511119921, 926089951, 405976717, 637144449, 397659520, 191444651, 808171054, 824338573, 245325688, 440912077, 673111141, 88893463, 768765689, 366955970, 448097066, 902365911, 173621523, 606615622, 586394632, 315855268, 818237542, 814810513, 947759717, 5217772, 755004638, 915581733, 544645934, 874107198, 829498926, 135106962, 330518523, 670781337, 288475812, 542732596, 886384289, 844467119, 487169596], [334394700, 192912685, 621397859, 423416781, 971026170, 777276250, 549686236, 543388432, 190601854, 915733351, 415564986, 147827847, 182195276, 111223307, 605785872, 298118402, 657070179, 439802782, 119098482, 811190739, 100638583, 501002062, 696223920, 74525053, 387497388, 428879166, 644396297, 76011292, 664960316, 678018332, 573074469, 970356393, 316339135, 3749703, 860028637, 629292897, 535715936, 953780946, 346761246, 173593022, 188112739, 815996034, 102011033, 931404438, 939173816, 147972428, 355736480, 30997033, 887955211, 862276177, 339079390, 524935190, 52554201, 331832712, 807821790, 882210617, 982130663, 436597724, 798697262, 366271517, 605785410], [108766037, 704669360, 630537091, 555747469, 545036806, 856563943, 273082964, 701503320, 966135444, 632562781, 927139131, 450992742, 963652384, 865694109, 361748228, 556709773, 28594451, 382223240, 70560545, 972202014, 603542650, 932922733, 855677988, 745716414, 471532951, 989269705, 500413503, 566522525, 662949032, 963864786, 784104519, 69411635, 581426814, 492961132, 654861513, 757026779, 789312985, 15562454, 228253931, 878757142, 736130293, 745923424, 971937590, 76190503, 949875470, 404742423, 164027635, 541163659, 322867059, 703630359, 714446951, 381215319, 726432303, 145495200, 770803334, 296329809, 425163246, 16702453, 834751278, 169597739, 234579630], [78225209, 695635504, 326831092, 473991841, 581650846, 588370255, 855943478, 560547633, 493917977, 12879364, 692145371, 799692179, 197682143, 973910414, 780160989, 321475163, 532914099, 346365850, 899970613, 993006414, 19567120, 608574922, 748683168, 225476170, 374615472, 710649178, 347582030, 387475065, 206626871, 168363820, 874397815, 571271465, 725981563, 116309758, 32258876, 987480983, 813235205, 66708623, 175781267, 241843385, 351231586, 176659686, 562506242, 568494642, 736740630, 725079668, 415978311, 823724444, 693030260, 933483093, 89010480, 925017867, 430763342, 128725958, 46584847, 800062857, 668286674, 545742398, 132725885, 323551220, 980789173], [813485642, 838182592, 818358494, 627382769, 90785577, 893594732, 524677313, 659583844, 282058521, 135441284, 307942683, 842919516, 917106935, 336913501, 538849990, 250330193, 487134505, 538551088, 724821202, 74855053, 121998352, 7078028, 834149733, 325001299, 391314823, 757429099, 947708039, 723506583, 344935106, 476579430, 129151206, 431484976, 712184570, 187939343, 736845803, 175084929, 34583508, 633272806, 900131652, 166069227, 381065485, 340383027, 528004678, 401325756, 329102199, 875917346, 971628009, 604065173, 192010349, 984313897, 209938852, 208546044, 550985810, 167792123, 256974985, 706593204, 324537897, 797801614, 537416504, 113185285, 960605059], [679426994, 639743692, 854147867, 477085444, 8424164, 89809799, 136050136, 861625364, 509071064, 827779244, 666047140, 994067717, 701845082, 712273413, 923641676, 690419871, 445287536, 318374844, 420864538, 173085281, 862824253, 867049240, 207608190, 819616464, 654129945, 70643897, 849694461, 656926609, 222679025, 201683482, 286681871, 742681756, 256481054, 280797833, 883264153, 194637558, 200764212, 877069229, 195685004, 721860770, 961275544, 888204664, 159877154, 997978203, 433534373, 456344516, 214619881, 411465600, 566330458, 367766116, 736409717, 690628521, 523792498, 422649597, 713795841, 905159949, 162845121, 150590690, 43595452, 271859481, 558261524], [96692320, 770275527, 635402134, 968408442, 277478878, 833313755, 329472087, 447979400, 265414783, 108266298, 354612631, 613868527, 207005756, 617383104, 15688269, 430527597, 593000134, 537932284, 622486598, 839280243, 2860756, 939414827, 178456587, 892417728, 372245481, 654315471, 843629260, 268599320, 308926036, 402440683, 885001956, 187071893, 18241711, 158334757, 122202175, 55960582, 902210145, 766972948, 206201624, 264947312, 891653977, 70196403, 481592767, 671796633, 928891901, 655255537, 298046958, 85135295, 990433169, 867658415, 228318389, 252235698, 302509032, 221767887, 100573640, 872350979, 414672790, 827356626, 691637363, 93540466, 360067097], [742955386, 357674203, 354478093, 325882255, 219284898, 702301127, 70381280, 820708839, 889236357, 687322770, 804654255, 459532261, 27968974, 180311415, 612878120, 608970486, 284853458, 614922720, 987651585, 27317481, 842631172, 707176239, 782439324, 696255074, 455251345, 617732772, 536650017, 372359010, 732985753, 696337936, 487525737, 429372876, 469186394, 292644922, 621065924, 640929508, 892664640, 801542605, 328428792, 222174766, 128017381, 522785652, 359467140, 111356284, 898927245, 333258010, 715056649, 304761756, 599371922, 188149574, 779896123, 112649825, 658781771, 850619772, 496293639, 948580657, 239942971, 40672130, 598969206, 395539344, 424624788], [731914330, 785635538, 874524498, 703908348, 722737019, 833969840, 813377728, 282850695, 86717497, 441858552, 675826828, 502039636, 445998630, 930724821, 666071676, 147508743, 707121979, 48671871, 292904164, 788810822, 808788168, 44968788, 539967443, 221966661, 606709046, 208174, 228298716, 356508725, 750469237, 708290851, 144118514, 378184343, 966013417, 806920679, 348488745, 996015211, 192469995, 111683576, 809708391, 774167725, 12906630, 511014141, 372072828, 740140171, 958852325, 497968668, 454670801, 186783314, 609510504, 60619573, 285640726, 886611161, 718059070, 95565580, 6022187, 750088357, 900960889, 173823749, 687512911, 445859831, 643554098], [648424139, 152791547, 618280851, 506287640, 706234576, 377869666, 494340620, 270458969, 379379958, 815109309, 501968322, 799871175, 833309300, 252784072, 259564040, 17544924, 83661745, 493069867, 513148080, 696602994, 251976069, 389654428, 262847396, 411991313, 416093414, 939441899, 374304063, 157416326, 229258856, 89617682, 280531311, 74374881, 183161865, 407953707, 112351410, 995544278, 762016754, 697803942, 33739607, 275715528, 698813706, 598087194, 528782442, 729216405, 112756227, 643764991, 593834963, 953113617, 180341026, 811527100, 23623373, 835262998, 406473094, 533315587, 534431016, 257858268, 457639761, 469191307, 345109694, 113664655, 666348637], [418408339, 574923234, 76037081, 73936258, 617588104, 88669736, 38275458, 361920638, 850363807, 86369514, 475271079, 214592297, 945165873, 839503428, 50485308, 203010711, 270574803, 745735241, 595468054, 650816701, 550935648, 66063422, 817284035, 459425572, 815104430, 72529329, 5253490, 575816570, 841741902, 423112696, 471920728, 654080480, 315662442, 835464387, 338289523, 764692450, 66661141, 580692791, 424262347, 673419028, 881621148, 177758055, 313568756, 506597681, 714146734, 215246341, 699264361, 63584831, 188850440, 795550513, 629708790, 833007819, 886462622, 316455826, 415303768, 968999341, 467080918, 955095532, 917181287, 12832402, 753013324], [766854308, 176377339, 176366424, 857776348, 447072440, 75195340, 614022024, 846206797, 79685460, 448853713, 483986107, 759539776, 441924800, 385781386, 208788684, 673059726, 293149672, 16917864, 364163211, 758545846, 280145071, 565346243, 658984231, 157470892, 716366757, 754995396, 444703570, 880478484, 402668518, 982917395, 537636830, 426275750, 34831961, 826243596, 60477351, 640247287, 279765967, 276382854, 400862641, 3013152, 320574617, 45438555, 85805732, 385224571, 632743776, 798755356, 824083160, 107904095, 310939445, 509985395, 519152966, 388660864, 52376001, 110372686, 657990402, 297658611, 609841706, 669470940, 549652865, 412409259, 120073095], [940398580, 259467195, 353315077, 941673929, 759058222, 708666169, 917614750, 61791995, 512449611, 203911055, 807004291, 924915376, 481324906, 819885939, 461978584, 306500325, 160759389, 806441973, 272117237, 712750111, 731543422, 313421460, 704782781, 850050590, 136617881, 677212952, 663005803, 698939470, 250136433, 758597991, 734904609, 845338397, 102696592, 503826870, 400727528, 684481547, 905065215, 294569458, 728271345, 173765279, 411243021, 275836738, 655816587, 415601969, 354614687, 538263857, 436334887, 752141927, 948040416, 551423443, 120753634, 725794677, 987689160, 134215616, 247574901, 38341122, 309209551, 662374563, 439303950, 352419009, 460918300], [203051453, 277391645, 822174820, 729781872, 108814608, 529992653, 253954772, 952116610, 307662834, 984690222, 880127286, 360513437, 632309598, 728878874, 902816302, 347514651, 755381704, 16245951, 369074856, 912656426, 188722437, 5766067, 720019500, 891055611, 483765675, 121651066, 474309326, 297626360, 540536902, 665536802, 516549418, 512264513, 159750007, 961889192, 761630942, 941274416, 57026232, 945250480, 965137097, 880827072, 37994554, 468559783, 426508540, 328585697, 797756592, 626787070, 130886804, 861343885, 567335072, 495359484, 170820546, 88072523, 721887241, 356428032, 825452190, 474224100, 811011242, 148078291, 910835709, 465087866, 327112895], [10135671, 966889833, 392957175, 811812366, 213556033, 995617911, 549489633, 317483588, 454974716, 339279815, 231396204, 104587183, 213752125, 731138448, 32724670, 273650932, 573295153, 205136811, 611614351, 797303364, 978940676, 320752015, 469661001, 330295280, 568278647, 325472820, 228177240, 683621295, 281716595, 543122696, 340978407, 464375723, 279614448, 885785151, 27924398, 609069234, 535035493, 825532648, 953665942, 124518379, 77766054, 591874127, 573106479, 156767295, 522425177, 918017925, 78980277, 93968849, 428869573, 68762903, 274163850, 558497064, 741667763, 88365611, 139510826, 570107221, 117793271, 801250082, 568567408, 195641613, 510285714], [688901937, 480161471, 467455745, 887656241, 643137478, 196158678, 918586181, 107670239, 16073537, 303706483, 792587089, 429001390, 727332119, 86632631, 579104194, 930169707, 258743356, 449285414, 37292262, 676029147, 545941166, 652064563, 351241028, 411801150, 908108509, 226960505, 15777619, 104240502, 968755120, 753755990, 954621547, 858409644, 643188993, 46958938, 395364814, 166941791, 438125149, 666023200, 255281225, 705395147, 432616589, 650383111, 908300658, 866072889, 183878542, 709522041, 187376605, 143840187, 279073071, 883972455, 115923941, 163495613, 387509079, 523334694, 137186211, 973802283, 386038404, 428650382, 20217707, 146865371, 734150382], [235126508, 199959196, 38728013, 571822034, 679763633, 627547158, 245518693, 10208714, 430873444, 382807802, 738970933, 182309575, 819373988, 494254046, 119396508, 278108331, 811848224, 855058030, 789930256, 233223682, 444032594, 290954672, 927970062, 131571542, 220908028, 231549743, 567573365, 904908182, 174053521, 767471288, 692251508, 616322582, 99580677, 805843251, 899458800, 803339806, 52652926, 347294391, 88605480, 294638315, 638820976, 140723851, 672486648, 572017858, 79786677, 394360112, 944449653, 864575117, 262101876, 566806918, 494860664, 245577500, 640654732, 917787496, 277559415, 514486361, 194129440, 130048787, 654065376, 734734694, 139221695], [184702708, 756745073, 32156290, 720060884, 571824613, 425202096, 137479077, 5020176, 833116723, 345984819, 405687226, 404173203, 842193487, 657922129, 768780733, 768278972, 620923091, 557821286, 640557527, 415900022, 683995185, 622664687, 850274137, 656660400, 426905601, 832731934, 358447901, 141775673, 192089610, 564401309, 540887949, 229517131, 877536926, 936817314, 592200890, 233374775, 772023724, 136257417, 559426055, 850224011, 929092751, 766214558, 56058995, 99301291, 646307354, 544383914, 345257933, 702745991, 908154590, 685916788, 543377054, 657322524, 39923095, 607431319, 103982125, 291778700, 911790341, 874616055, 811298999, 119551412, 969468692], [298217055, 488031450, 52339042, 678996219, 449190498, 436973048, 298680463, 180790954, 141451500, 431581490, 895776265, 431069607, 692927968, 921376306, 827431047, 415178449, 68015168, 264054199, 32651301, 916258761, 588474611, 682052504, 185059506, 725896740, 4617356, 669299782, 963661981, 704420614, 941866296, 911570259, 142898857, 529483598, 744426484, 768809577, 900143829, 155636749, 845958557, 383985817, 591236041, 22224085, 579399860, 398076356, 521911, 840971509, 302260075, 382280450, 240276579, 192501518, 229721628, 31217493, 658075830, 80252727, 909581759, 10800412, 869071877, 790909675, 399247004, 30274178, 834193788, 91724109, 812746389], [692585644, 277786178, 839694673, 103912710, 585750838, 926554504, 303011046, 96506807, 611220679, 108242858, 509604367, 26833080, 341044823, 565225028, 682001117, 916325838, 280573494, 648815024, 534281384, 669279867, 629857643, 285806686, 969178856, 675027095, 932970798, 49752962, 487725514, 432727265, 781534881, 701147277, 12096404, 224537623, 173965602, 558654337, 322277660, 856156492, 424890577, 574054071, 689079480, 224186850, 331188236, 380914616, 114309016, 506686929, 961836753, 15076895, 742775135, 545416446, 516109922, 484809896, 836800643, 713360955, 833524682, 363913972, 430325195, 284527857, 191267816, 727644692, 241585146, 99712797, 545773059], [117202671, 484164926, 586945278, 305879047, 782566496, 93232206, 780941671, 623531042, 704623386, 977218964, 54935083, 382114923, 840380889, 453174452, 385749411, 95840070, 164885326, 532475463, 935975141, 467438940, 669823526, 140419142, 36461808, 744864405, 173283925, 702668906, 219573270, 353317452, 458224202, 89664141, 362279669, 868550788, 155146301, 219987687, 839400460, 546494374, 701028620, 199926173, 328560343, 718931479, 782030707, 374758445, 679823405, 417401518, 534182046, 657486051, 402520215, 492363950, 950576434, 387865877, 395823134, 972406662, 206798505, 267227223, 785914176, 847048004, 833679819, 887036341, 946000543, 800869352, 721158787], [495238994, 540003568, 552894368, 989713880, 879814806, 101526545, 298190040, 892032818, 351335670, 446277204, 379295903, 823442431, 430359255, 594745491, 108530134, 102363820, 220497912, 790500155, 664482072, 463953479, 273560554, 204730249, 63281115, 483556222, 893584227, 768743984, 216166974, 503288237, 316758993, 894025961, 304327654, 156525269, 455008038, 960763582, 480008576, 482549297, 50565744, 799171027, 839739086, 843344527, 394649998, 466290627, 325509088, 130960400, 752047141, 805877514, 701158146, 306419384, 25649729, 316578301, 207213969, 369875679, 555992317, 897045569, 116375728, 336579752, 727840943, 569748162, 43422714, 462393479, 954558423], [647219878, 146453876, 524787869, 679148239, 63381961, 214420202, 174411902, 473752219, 764321227, 684827497, 548905414, 721791625, 776992824, 633415180, 765019532, 661905474, 197520647, 188856200, 476857230, 189856630, 679709035, 402445597, 190631552, 387597362, 126153522, 456656350, 922035736, 54181167, 630306470, 136664139, 608552847, 207560737, 877891, 249724171, 166072077, 149845892, 402100463, 468545233, 267432771, 949487663, 247104036, 461578533, 408488863, 515057647, 233539476, 410650668, 579241817, 312491587, 283120829, 45182962, 539613043, 351178249, 667456978, 469783680, 348324909, 961713319, 716105086, 186567061, 672976839, 323662012, 722116700], [669594221, 22273465, 170254496, 631424657, 783937539, 662191708, 677906150, 350107090, 681717149, 968607706, 794914571, 746028127, 44837839, 176510697, 995330961, 15759272, 563680313, 143321984, 325892365, 922730710, 968644701, 148571317, 200116154, 747776006, 737264066, 475750260, 712540280, 50155079, 375846441, 910401125, 571341840, 15419181, 174522544, 230061381, 645858440, 128385529, 832410265, 690038825, 769318185, 550453687, 865972850, 958650263, 186651657, 299071387, 19036722, 397563978, 557907833, 298714688, 340053022, 643853007, 624833221, 9553322, 234144255, 927907750, 524444578, 747975455, 78602968, 652648704, 725018021, 338593670, 939215774], [232974709, 156732510, 524079010, 107239071, 220717766, 357337985, 864269726, 453107199, 448886375, 317566494, 637451209, 629478055, 668768132, 415910470, 603527082, 210477918, 82980363, 206688007, 571882701, 981379578, 374222507, 124419870, 267312009, 618316674, 42029447, 555869642, 522637190, 741952218, 703334189, 267887810, 250690324, 482843619, 273564742, 453009368, 214001597, 912064475, 835648784, 275573338, 64981723, 617050211, 690743764, 214775330, 231283447, 712477609, 506102926, 331410400, 466939786, 660195358, 852700075, 329154298, 868854597, 967539989, 207109204, 961577351, 34180302, 621828373, 914095559, 390249432, 288482566, 957198836, 69582135], [247511235, 944518444, 329857133, 182527582, 411493045, 912049326, 232752963, 923012079, 598346182, 827119152, 511026820, 994126595, 902318333, 275451846, 430757633, 95396006, 85278644, 21491990, 988003195, 183759780, 714063389, 859418638, 439512527, 172655040, 886606583, 423485405, 857153127, 674916405, 668744730, 936075634, 567878233, 746651595, 247099803, 364335738, 764583148, 294548881, 868138842, 759122205, 596208731, 274281096, 320473993, 216179985, 159863388, 834118114, 728694743, 463141539, 137119163, 71533668, 736397436, 265222420, 655804519, 476603110, 757254410, 324815197, 122274152, 982098848, 639635532, 248173899, 935182095, 438721260, 70009456], [469257070, 861432610, 429927788, 950541466, 281413342, 409862694, 507807245, 836453987, 124971947, 921541401, 266114300, 425826078, 60538776, 94726328, 345291394, 844683843, 878187226, 705987830, 890031106, 413439292, 458077514, 299092503, 578308738, 500433644, 45980027, 184629168, 764675535, 163491066, 804082517, 380512847, 387180964, 501086628, 579594269, 698736366, 283704003, 458767380, 566623073, 995321011, 589003398, 206528563, 678947775, 737380578, 753926258, 310743963, 575467358, 26711160, 548712307, 919955052, 211272815, 600685532, 76433734, 101318378, 731125616, 162520869, 16301296, 468203196, 338720215, 33012629, 785714723, 203678822, 647328072], [161768562, 746464700, 153462523, 603434674, 923656454, 529243305, 424707040, 476906651, 505398264, 194504431, 472529191, 847264563, 373458073, 341062368, 142346597, 760842387, 692490943, 270741971, 406503572, 824139888, 659476951, 107118696, 485234034, 779341807, 442352408, 620231902, 979327554, 838721029, 719861803, 943105029, 860593535, 23989668, 609683627, 928632280, 451557233, 843717389, 871002724, 51829304, 611675157, 474622984, 234114344, 109235830, 883969251, 734487750, 553589560, 579361899, 461665267, 232310094, 661727700, 843257974, 589820758, 800055284, 158573459, 314202797, 32996992, 831815403, 709669673, 185445206, 20191838, 559250390, 333429282], [691009272, 930932231, 164872781, 221210797, 561350685, 270666084, 731573625, 516799562, 768596302, 708359930, 227999391, 429997575, 594200942, 655296951, 430624285, 279408899, 142368218, 272679074, 555375832, 989983866, 147431748, 354852355, 146684478, 801284967, 95588839, 464352268, 27686541, 689235084, 212510096, 689706739, 788500610, 151925670, 878307117, 59041142, 790341448, 774833100, 30196562, 841555433, 603447920, 757206336, 398899887, 701900316, 116556902, 627632480, 894513743, 316669616, 341821835, 127856538, 547336043, 428194364, 824597006, 509384424, 254973802, 753519697, 615000398, 520658703, 605061049, 474451832, 275395052, 916490132, 12207306], [978883832, 224561151, 729283494, 676905386, 528865726, 8635056, 57081778, 473379140, 96093325, 637061596, 22833801, 292564361, 918484123, 918000475, 214021009, 446944856, 758472310, 117723946, 260920590, 343300782, 308511502, 178084035, 258855293, 426308530, 493298792, 207710443, 99661489, 562343731, 38555305, 85702732, 830394185, 786709755, 811295564, 133283625, 799393295, 477953146, 731566984, 649067638, 989494938, 65458321, 360968527, 612354881, 867072409, 7217043, 801578703, 394147383, 565825369, 128875953, 64512773, 218355710, 786663700, 391506460, 968577517, 118372348, 529549791, 279841357, 785771669, 114334511, 852657563, 965795629, 891998348], [341586577, 318107166, 162817673, 858012583, 563436329, 286491274, 164657792, 625998265, 609566781, 528949800, 987617913, 8462236, 560822628, 797114030, 677782964, 258142037, 622853892, 169673434, 608358221, 960156634, 812697309, 443393532, 279254306, 238109725, 253586122, 982035908, 995239360, 255509118, 175748936, 465688662, 774284183, 190666715, 998971193, 250376981, 133843274, 115979165, 638748789, 365686286, 641694132, 385404367, 473180407, 150943515, 139605005, 877447112, 572388279, 628882971, 846824995, 657704914, 203661633, 349093858, 235692908, 307284784, 443046628, 499444939, 945677792, 357185844, 990331501, 108659953, 833509498, 10138315, 550729186], [776328056, 413437278, 83894585, 534238379, 163765989, 517821916, 183093023, 614437832, 223507793, 614855247, 753723569, 847547541, 424335797, 938508017, 274747700, 769562464, 729891363, 419969301, 110651781, 766727344, 888453459, 110983164, 787557655, 703477682, 996194340, 433318747, 475432099, 413389223, 445524840, 429218574, 996692108, 903920967, 394322338, 456177130, 761225338, 879715290, 273108190, 589293979, 42271730, 478403317, 231132772, 832340444, 522153053, 692751818, 291316840, 953087639, 958386471, 812415028, 615737438, 483414665, 822028303, 193721076, 701782333, 757461273, 784353465, 35712004, 91186721, 9289068, 797468455, 144138017, 121630898], [161697098, 371999275, 365709572, 28748403, 698921102, 917438681, 776835053, 674761034, 320904508, 725876705, 555571697, 267801147, 342010011, 53988976, 977274071, 65799110, 821476559, 245528804, 844616510, 861561803, 755097134, 585187355, 591635969, 515863684, 394983499, 926196988, 182042034, 471843150, 76113990, 94431634, 689604972, 995954064, 13250063, 591923232, 466986110, 926511639, 85784613, 152005930, 479267353, 892603504, 439485898, 232591114, 147798664, 526467772, 69419364, 556900143, 144885344, 286242641, 381845912, 286187068, 314777157, 573379823, 639307850, 389023285, 718113690, 145648337, 860956305, 782242668, 549186653, 553331110, 331492443], [351249570, 545082948, 416662345, 63377996, 327261925, 68131365, 721747390, 627363691, 240818104, 342770509, 931995902, 972576902, 319663506, 917815994, 3739131, 140042027, 932891155, 69946507, 942649362, 163831427, 618937441, 158985225, 410516827, 651255880, 151249149, 256146228, 841973735, 822764588, 133671308, 617345757, 579809365, 953111564, 136388896, 289837051, 50081591, 96871785, 853981527, 626948862, 876252669, 570345443, 851543201, 681872723, 843486874, 595840037, 270122678, 769270149, 129446482, 874102914, 689891575, 451698925, 347926648, 818006798, 124252500, 372541795, 128992841, 74454929, 709545770, 161313379, 937338153, 78629644, 506422752], [753095291, 882457789, 888056678, 597335544, 466781854, 628663052, 192889478, 874645598, 838153501, 95428625, 451680707, 567761941, 657438888, 763767125, 559528119, 322471213, 905935372, 171521297, 744859971, 336856859, 984180516, 191623098, 491663253, 602485648, 898916210, 516921697, 851257981, 254926794, 439660157, 664450593, 557774688, 88442740, 580783853, 485896477, 841501786, 677254845, 801526345, 980167390, 93151658, 315428495, 869988845, 722479405, 123471759, 71063461, 284413976, 754327648, 253950518, 52360225, 581087432, 807012700, 902801534, 692158963, 133045988, 428630509, 98994449, 247531888, 373887819, 453295691, 888770289, 846081796, 614330622], [125156282, 618752026, 883154717, 703132917, 565362551, 765534238, 478750365, 903392936, 396575159, 789840311, 245648506, 360384777, 447494907, 15978781, 177882290, 913348317, 350618782, 872144295, 959115370, 675501566, 621579649, 915505828, 51701727, 4555852, 174701932, 285850974, 24133740, 304628385, 683748844, 607411149, 600668528, 675541851, 703403079, 815215841, 723908710, 909484843, 181905179, 579793063, 89092378, 440430707, 903485918, 427027505, 248229221, 567976538, 141705840, 143640182, 828145588, 234092566, 518135850, 715260092, 651844863, 592787606, 146972221, 355844695, 696092091, 688764306, 288786391, 925094483, 30726195, 131335024, 867008499], [27581125, 700324574, 553082424, 842797142, 492544923, 337829502, 331395810, 91509882, 751543923, 510636609, 370853912, 208198231, 125911745, 94372338, 992196713, 81445649, 918993931, 971723026, 200586767, 973107056, 952355174, 489678286, 498525008, 208127721, 223187895, 949850080, 69231402, 958454628, 568005082, 258640298, 29171753, 22724619, 163203273, 906005224, 261652213, 332489359, 815321370, 955769604, 493448785, 761622253, 97210577, 940207301, 113794714, 965535503, 140560504, 745394872, 136443342, 841626841, 804615604, 976936568, 869187746, 622566939, 249831747, 493478931, 829973435, 305165905, 63909086, 453237270, 220022047, 608297562, 871474150], [308765628, 830626855, 528821803, 105182518, 30472900, 285608511, 464271491, 117694084, 273171569, 585864958, 910048530, 762336744, 528315205, 869069071, 606037506, 59643095, 220119730, 535769252, 816867401, 197664511, 897888501, 35799760, 494651770, 329280810, 720164511, 119463169, 538455092, 152302963, 114172346, 117125205, 517612799, 536093339, 507628579, 425403160, 959516130, 794252934, 76449834, 746154344, 242301407, 480097275, 306780149, 217197209, 597169364, 867710997, 152742289, 906058364, 751985003, 363553860, 617817194, 82792383, 230878347, 401057644, 215715847, 500415951, 174287062, 168981711, 280828986, 808343440, 724794129, 419108771, 858046187], [453560424, 86455984, 523489071, 244981299, 705146011, 498794300, 562547149, 17560690, 221499881, 902821217, 63738754, 612175215, 965458920, 106406489, 224646112, 586276913, 115378010, 412676095, 579432363, 982989204, 780247995, 116707280, 187340236, 631885073, 892779644, 760143324, 998920539, 117445218, 821458470, 606821536, 898462412, 583873546, 120466920, 682793383, 87942182, 780743485, 45312400, 22730081, 655396486, 137624846, 759517314, 483393033, 306224856, 632808267, 872303084, 261929028, 41138636, 121628084, 575134314, 71011441, 468611211, 831362817, 613312796, 479951635, 224105594, 258108460, 12579074, 987270056, 657271208, 940170671, 524779703], [684258103, 36517497, 41175774, 807592569, 453569924, 41865450, 26442021, 407630876, 356000269, 828346890, 719892539, 16487489, 430218583, 484083526, 572649478, 566305009, 112615081, 777817132, 644481229, 386543457, 475930457, 495813509, 563814963, 85080468, 479173974, 18747710, 380046957, 236206734, 466233944, 807304450, 785518275, 186832819, 186963565, 842073267, 433833274, 774432221, 465841699, 605462210, 999811960, 447355946, 178259933, 739418720, 469063057, 205157675, 783730111, 656259203, 995798641, 810209639, 186527508, 145216906, 702953543, 657331013, 67710360, 899805045, 308990904, 434232199, 599533284, 249753184, 7266219, 521859690, 542691899], [572777240, 278773487, 585758192, 376474511, 210259885, 887598760, 640250195, 193949783, 813527727, 746534690, 832311550, 775650725, 490033614, 420652353, 699031937, 669301792, 253476441, 692246470, 69369644, 283549162, 185338948, 503534842, 536298862, 123511117, 253439201, 924099648, 421248170, 852516699, 843602892, 120912489, 883535806, 174347568, 85633350, 906366537, 859115496, 497548468, 440168574, 158212704, 10134260, 248477800, 620938695, 9303922, 979907853, 150973585, 684419264, 714124993, 97018115, 158190587, 706562755, 217111651, 416034548, 563474092, 918190986, 665054317, 291533956, 678148444, 644710586, 176781527, 12262524, 653244386, 501638019], [871480861, 570672428, 532255085, 560299363, 604676753, 80605205, 404197811, 732452410, 695317054, 677757149, 700329353, 848495152, 854505440, 149154167, 59862238, 875277957, 719260034, 819640583, 356519545, 767398296, 416228559, 871289247, 554335329, 420424281, 928105239, 421235259, 697387021, 948251958, 397242973, 441438252, 907897753, 762665107, 807210065, 614901641, 343139622, 246163606, 403540633, 784058281, 904661228, 440172160, 383638207, 186490579, 20885775, 758341046, 541137454, 53650518, 589465834, 319811078, 43645836, 417158178, 123094091, 8027872, 972879681, 706211871, 307215098, 140715609, 907237073, 361961475, 607469348, 901674761, 976156049], [718011065, 704551252, 244454113, 7786272, 155317740, 850859141, 584743225, 683148081, 594223401, 136199938, 639893887, 651179849, 981808789, 843608435, 229518731, 339922420, 584372388, 565824194, 469133522, 50598409, 661519924, 121023942, 434331153, 668109709, 269344836, 944019130, 288375130, 470171647, 21819709, 313982751, 171145368, 121790637, 254712292, 731313367, 276548060, 302747079, 585724901, 4088884, 848513553, 197983164, 179772839, 806483477, 956540412, 525989583, 851429034, 869883728, 577476510, 943076644, 701335722, 644401098, 982016309, 929030657, 221978473, 508829812, 600115183, 383365035, 459376556, 806159522, 253996063, 217234986, 892492884], [206823984, 457383868, 657308963, 475277683, 418730183, 547832142, 523175309, 970132185, 25485695, 538488875, 349977958, 530170032, 273002628, 714996868, 613382883, 86404429, 397899815, 547124342, 62976712, 204663288, 573990063, 657759808, 690751134, 399758573, 256802973, 24828646, 73354832, 471953924, 371323151, 209710462, 231802203, 887630239, 65797614, 618010290, 518743610, 178245812, 241963554, 190252316, 876099664, 645248371, 419362827, 554076419, 783641283, 660863823, 210432974, 458563648, 273063153, 56799935, 332454940, 909925123, 866078665, 469826321, 306558732, 425788040, 854154227, 815874875, 747355632, 98988445, 364822327, 497122283, 900840530], [983906171, 845856331, 155596737, 588448364, 321186000, 752019160, 476347021, 692607307, 144522749, 427861429, 360929772, 739107330, 291649557, 484249692, 804488954, 465834886, 48714878, 620420900, 822173433, 692420021, 927846750, 67500749, 271529717, 512206864, 948202483, 617071063, 417045737, 466081035, 428931873, 511123594, 736720203, 658906228, 346545604, 846384867, 777520829, 390516106, 574506683, 480367029, 470940183, 609135687, 576073145, 783501783, 545442239, 680768824, 482778102, 472266932, 939054836, 422181982, 231612429, 717812281, 774364435, 937619525, 183121879, 939916914, 901021508, 597317590, 99763496, 14529450, 986916247, 95221185, 82510440], [211112177, 778218080, 773084365, 620134221, 439200152, 54810207, 97912483, 772437198, 575524011, 807759591, 478556265, 396691085, 722902634, 991116906, 484653054, 330644998, 514345415, 993702464, 948306838, 339675529, 896445410, 807895584, 562582483, 754072341, 419651509, 596116147, 764443939, 677358999, 543529255, 256999298, 407971152, 881477410, 352566917, 404504414, 682253608, 758510045, 93590900, 767304642, 150067656, 823431223, 181634152, 141887591, 15476845, 537148961, 16484682, 640508112, 621767764, 780894003, 370997757, 323053950, 471673783, 730992058, 435034847, 313426324, 839857453, 576089056, 272415974, 126424150, 127756282, 528889432, 801605195], [511584524, 15380014, 6679591, 445234204, 323834495, 99787142, 734306823, 118495787, 20844397, 189942950, 648758361, 962298977, 539866180, 921256233, 383021506, 716961332, 624704876, 298919356, 368755246, 504742445, 773892150, 695602361, 467957247, 868574567, 158221861, 32709512, 329699525, 785408352, 844368288, 769798835, 532872022, 485693779, 639867305, 83924636, 260821485, 587952183, 198411064, 828857663, 90352785, 292238788, 689963118, 355425376, 935665314, 69171502, 518714231, 4870875, 388119699, 140203790, 631913241, 293527253, 463556989, 819617593, 948716451, 279948423, 471396259, 797955237, 926783817, 971885395, 624641594, 999764727, 418403256], [981567806, 343919466, 24717869, 127071215, 109737481, 794122631, 636666287, 537795564, 855117048, 567817710, 822691831, 441392929, 92948785, 310271341, 851326752, 357866139, 584704275, 720902219, 173534975, 968623244, 496617850, 878947703, 83877315, 597088706, 809380729, 608430560, 639208709, 892501688, 874489974, 935992333, 743627426, 797382402, 459112746, 579377807, 293737105, 304518996, 705635631, 348461298, 461238068, 575542053, 299370569, 735173927, 887344491, 423526704, 670645519, 254677223, 169856912, 293257380, 819782271, 467702122, 49698523, 169389620, 285332261, 891143117, 731419863, 713364071, 559994610, 20035478, 970732026, 870326504, 735125715], [173354624, 217008334, 301475526, 419458305, 101355778, 600473843, 937691361, 337666287, 719681888, 854468172, 652976329, 518385962, 303458299, 841459372, 256148810, 908763223, 241695608, 615137420, 367778616, 331410193, 740462820, 342966324, 694934119, 453097829, 205090812, 746567837, 668637968, 788470990, 538309600, 19297904, 156592389, 563803205, 699157220, 339502657, 686145394, 653604946, 10594705, 833033214, 972611296, 854879441, 140313521, 864485678, 895549087, 622571134, 462111179, 620220897, 621591541, 172473864, 615976707, 233125349, 1264483, 466708253, 788240899, 272361398, 638585122, 781434031, 1891331, 322819741, 701323851, 654945539, 48951283]])," 1219373567348 (maximumScore [[160176171, 271287409, 907227201, 415450117, 645524004, 407724588, 359360510, 704979947, 815129016, 332654706, 52283921, 288357506, 265995658, 532751756, 230235803, 714348779, 246925507, 133531074, 540914818, 806561820, 538574923, 736117330, 711985474, 696187396, 766291403, 228125453, 174221018, 343799712, 920615448, 58144918, 727884816, 133496823, 610606320, 504922730, 363206565, 204086586, 574474107, 157669989, 333380872, 786600138, 487335535, 351264905, 12688339, 126691539, 458593816, 362943059, 923005599, 268794188, 252462189, 194870183, 997488097, 270290845, 697000864, 622336726, 683869495, 667950721, 185182737, 91784609, 236426890, 4613408, 321016364], [535000256, 692039387, 851217958, 51481309, 140433707, 756150324, 954783973, 856313544, 142575204, 330143992, 313102765, 397585533, 594301028, 943582286, 619761732, 550045411, 267708102, 223856657, 240840940, 496035849, 427084027, 992211797, 429540385, 312433405, 204722625, 487599202, 823143102, 97174094, 457048325, 668458896, 524871230, 327235614, 331550249, 758987264, 405233669, 705402373, 194164817, 700955146, 334371365, 841714850, 311005463, 713795272, 828528149, 508105953, 2518438, 398186020, 515541013, 980380700, 306926790, 867563280, 986508708, 651387296, 852521686, 702005811, 376766368, 523898079, 560231504, 863051948, 582310935, 530309107, 169008060], [446902430, 796135345, 352384311, 899883, 120780521, 704104750, 664781882, 425962513, 367828069, 295714977, 366116930, 335449677, 939332707, 12439738, 721265607, 502071618, 241083593, 699184521, 251974346, 40608827, 440008261, 239290285, 949556341, 522397838, 615077833, 650906469, 506970523, 581052127, 686701247, 840483431, 387874229, 164226388, 614140673, 298415997, 801960345, 445041961, 185189166, 452523999, 379045623, 178300582, 641220545, 212619614, 905686131, 775246198, 996541056, 756283054, 374966216, 290806270, 379854770, 5487435, 42000103, 790204882, 441779752, 654628824, 290895363, 40408430, 214208757, 336475982, 202720325, 771794890, 15483363], [366045039, 334460733, 313352552, 246388205, 193812026, 564129944, 325875158, 243145556, 488596017, 188306665, 311799549, 718861909, 314646727, 50507671, 153048907, 818402137, 324893765, 562666340, 114586961, 565213623, 604242523, 764299190, 754905240, 11631559, 154190951, 905560362, 742322142, 476790698, 239337669, 450519971, 25295964, 445215697, 54414133, 398490485, 226649902, 382602139, 958303699, 626866952, 86202589, 285384250, 30949631, 549398064, 788792474, 431827147, 464048131, 179137008, 188693252, 817009276, 93681778, 92756853, 241703573, 470355412, 294421371, 253901015, 47455569, 111061953, 137844217, 841077163, 700355073, 269780977, 721632848], [169345595, 222566416, 793738244, 1839342, 447418124, 478950226, 580191521, 2964121, 453851922, 3313300, 194226320, 241818276, 139521203, 107328948, 147451194, 846783080, 384889720, 859967679, 764222220, 80399639, 14927675, 944853968, 676388989, 575036402, 720119428, 768426194, 2230200, 962967782, 426785525, 221992697, 662157542, 736633922, 102620362, 284564396, 866030721, 111511529, 780339164, 451897987, 660553053, 680492406, 390183712, 20373152, 585927024, 587630827, 634774974, 219507254, 367511164, 748050323, 893625332, 41941240, 112279255, 149509702, 212782919, 372114356, 633030912, 484667847, 351397552, 194076328, 441682158, 772061264, 929560118], [496669481, 430533585, 622976876, 664615668, 288242450, 855654959, 952605964, 843858023, 743055564, 195297578, 691438697, 879281981, 692287297, 816608101, 106215685, 110814117, 822719762, 224119836, 765030009, 253148035, 256457906, 405550523, 822267972, 327066277, 189237048, 452078307, 5196840, 322685502, 426043104, 5783406, 722890931, 33711566, 761772595, 233394668, 862922788, 242990486, 534009528, 306935055, 106307665, 222878954, 830830676, 441528397, 351691142, 286663894, 13356386, 976314151, 665608052, 968594335, 572722786, 858210969, 960708837, 342362967, 877649886, 248752962, 36267651, 530337024, 6313015, 526673320, 702511676, 860108639, 921077334], [93861975, 737128306, 777212714, 373594276, 364231422, 667462334, 915881314, 340262001, 64394173, 262515228, 403216043, 870470409, 518372587, 255017572, 453882796, 407699511, 871572357, 735065490, 614570259, 277871779, 913401148, 670711513, 160872831, 469608729, 786869485, 999250016, 433544092, 90822939, 559900489, 20748218, 698672011, 860765453, 837979105, 187759537, 999388439, 496330542, 83328743, 617339160, 245482026, 752245119, 302577752, 749567765, 827055675, 105414389, 633961055, 653573839, 12324129, 733410546, 427784985, 2457796, 323345768, 49783333, 634161550, 768295317, 710919102, 759724695, 727681259, 973085705, 819240904, 305719903, 601464042], [212799396, 26434151, 829543706, 109798124, 221214813, 19727630, 740289993, 127838673, 861633171, 408383973, 863182500, 93273692, 632322244, 4495735, 305732553, 548214323, 267216203, 525134395, 538542118, 77228785, 441870123, 473257274, 444981065, 740491095, 698599120, 478106056, 899327920, 300502832, 242596660, 836744770, 927030301, 621945504, 594766608, 602423294, 382106225, 78479933, 236592963, 763397072, 610787365, 587556061, 235626136, 467481074, 573739971, 394971709, 39242904, 610282317, 232212006, 142103927, 277809049, 279282692, 973144371, 655758204, 219195126, 924477215, 47861006, 721229374, 384726585, 119230694, 729043010, 30770636, 655963701], [792930147, 997932473, 283047403, 596543748, 784494840, 617311968, 819626834, 881681244, 177277372, 851284772, 677530992, 58905309, 410554468, 69009132, 589423104, 621242434, 559332395, 722948135, 342055531, 602143917, 793106075, 209935258, 593396187, 757819893, 498425183, 318202412, 599013435, 266406413, 183039783, 996590818, 702953966, 149128911, 213934485, 800835026, 452913803, 844090357, 788070435, 699722700, 722926885, 962366236, 475285423, 563577986, 652059673, 864836502, 486058579, 62215441, 479644450, 709128644, 952821669, 454950935, 696576574, 395980757, 236145808, 899484733, 955368018, 508903609, 892879488, 506165902, 604828268, 141091872, 330607651], [76808752, 527819793, 544334154, 802574641, 789305096, 815435549, 834852015, 549107768, 733354667, 301929961, 285946976, 262079596, 511240552, 856292290, 725242242, 414107666, 974925110, 126638156, 836988338, 922341684, 12942783, 738961830, 279652322, 422965387, 429024113, 992192157, 182444072, 70427888, 572338974, 597032510, 703539179, 216426481, 442972835, 88713817, 315639119, 226317381, 969234429, 641030889, 799294068, 707125309, 911554610, 384281378, 934225772, 466449454, 304180982, 210675413, 6801936, 363876423, 706704514, 370094229, 905561615, 581432361, 214019336, 885762253, 574785219, 457078267, 867370135, 321853659, 926979087, 503864872, 9758438], [168385003, 907717970, 368531603, 769896460, 382050619, 910167693, 46850865, 255759080, 386840488, 547744342, 674198795, 536089659, 648845011, 410986146, 302083978, 70885980, 748552999, 945995558, 429617234, 668030594, 769348311, 371333689, 502805800, 654931961, 539184686, 49204597, 608354097, 313262087, 774665740, 893172151, 771227011, 423145658, 773574368, 438316727, 346657554, 30149430, 468950798, 980713106, 960579684, 590630641, 866282646, 198666025, 260965509, 174220476, 471582660, 349698262, 64028925, 139767030, 558069740, 175148965, 558692327, 679995353, 598551680, 46730302, 986088516, 677264222, 137426706, 189129056, 415412638, 969613480, 461185050], [759803089, 759563859, 986572272, 119867314, 973143291, 496967218, 725890326, 407990700, 559805203, 88667552, 27221596, 982233916, 585784477, 448113333, 434248576, 505118131, 885733359, 410422532, 249926085, 800707993, 375133089, 269601997, 322852902, 50420172, 147910607, 871567931, 641409814, 899440855, 961842120, 622781500, 578075356, 295731084, 349053097, 23910985, 637144080, 321033976, 22834023, 717512667, 608686592, 555335769, 542157251, 459248490, 308520715, 890615378, 883878071, 462695529, 830785595, 766567255, 335924607, 172597604, 792655471, 247742465, 903029399, 705849691, 35675306, 29497923, 464952600, 474895515, 169618898, 766345487, 341708931], [956014907, 230126640, 2682997, 808510385, 368291519, 113939118, 444071244, 645663493, 257033005, 579406832, 338342643, 212581259, 335895466, 66811346, 905170026, 423467887, 887139335, 56172838, 941621728, 646214152, 317696231, 632338242, 103459403, 779198891, 511119921, 926089951, 405976717, 637144449, 397659520, 191444651, 808171054, 824338573, 245325688, 440912077, 673111141, 88893463, 768765689, 366955970, 448097066, 902365911, 173621523, 606615622, 586394632, 315855268, 818237542, 814810513, 947759717, 5217772, 755004638, 915581733, 544645934, 874107198, 829498926, 135106962, 330518523, 670781337, 288475812, 542732596, 886384289, 844467119, 487169596], [334394700, 192912685, 621397859, 423416781, 971026170, 777276250, 549686236, 543388432, 190601854, 915733351, 415564986, 147827847, 182195276, 111223307, 605785872, 298118402, 657070179, 439802782, 119098482, 811190739, 100638583, 501002062, 696223920, 74525053, 387497388, 428879166, 644396297, 76011292, 664960316, 678018332, 573074469, 970356393, 316339135, 3749703, 860028637, 629292897, 535715936, 953780946, 346761246, 173593022, 188112739, 815996034, 102011033, 931404438, 939173816, 147972428, 355736480, 30997033, 887955211, 862276177, 339079390, 524935190, 52554201, 331832712, 807821790, 882210617, 982130663, 436597724, 798697262, 366271517, 605785410], [108766037, 704669360, 630537091, 555747469, 545036806, 856563943, 273082964, 701503320, 966135444, 632562781, 927139131, 450992742, 963652384, 865694109, 361748228, 556709773, 28594451, 382223240, 70560545, 972202014, 603542650, 932922733, 855677988, 745716414, 471532951, 989269705, 500413503, 566522525, 662949032, 963864786, 784104519, 69411635, 581426814, 492961132, 654861513, 757026779, 789312985, 15562454, 228253931, 878757142, 736130293, 745923424, 971937590, 76190503, 949875470, 404742423, 164027635, 541163659, 322867059, 703630359, 714446951, 381215319, 726432303, 145495200, 770803334, 296329809, 425163246, 16702453, 834751278, 169597739, 234579630], [78225209, 695635504, 326831092, 473991841, 581650846, 588370255, 855943478, 560547633, 493917977, 12879364, 692145371, 799692179, 197682143, 973910414, 780160989, 321475163, 532914099, 346365850, 899970613, 993006414, 19567120, 608574922, 748683168, 225476170, 374615472, 710649178, 347582030, 387475065, 206626871, 168363820, 874397815, 571271465, 725981563, 116309758, 32258876, 987480983, 813235205, 66708623, 175781267, 241843385, 351231586, 176659686, 562506242, 568494642, 736740630, 725079668, 415978311, 823724444, 693030260, 933483093, 89010480, 925017867, 430763342, 128725958, 46584847, 800062857, 668286674, 545742398, 132725885, 323551220, 980789173], [813485642, 838182592, 818358494, 627382769, 90785577, 893594732, 524677313, 659583844, 282058521, 135441284, 307942683, 842919516, 917106935, 336913501, 538849990, 250330193, 487134505, 538551088, 724821202, 74855053, 121998352, 7078028, 834149733, 325001299, 391314823, 757429099, 947708039, 723506583, 344935106, 476579430, 129151206, 431484976, 712184570, 187939343, 736845803, 175084929, 34583508, 633272806, 900131652, 166069227, 381065485, 340383027, 528004678, 401325756, 329102199, 875917346, 971628009, 604065173, 192010349, 984313897, 209938852, 208546044, 550985810, 167792123, 256974985, 706593204, 324537897, 797801614, 537416504, 113185285, 960605059], [679426994, 639743692, 854147867, 477085444, 8424164, 89809799, 136050136, 861625364, 509071064, 827779244, 666047140, 994067717, 701845082, 712273413, 923641676, 690419871, 445287536, 318374844, 420864538, 173085281, 862824253, 867049240, 207608190, 819616464, 654129945, 70643897, 849694461, 656926609, 222679025, 201683482, 286681871, 742681756, 256481054, 280797833, 883264153, 194637558, 200764212, 877069229, 195685004, 721860770, 961275544, 888204664, 159877154, 997978203, 433534373, 456344516, 214619881, 411465600, 566330458, 367766116, 736409717, 690628521, 523792498, 422649597, 713795841, 905159949, 162845121, 150590690, 43595452, 271859481, 558261524], [96692320, 770275527, 635402134, 968408442, 277478878, 833313755, 329472087, 447979400, 265414783, 108266298, 354612631, 613868527, 207005756, 617383104, 15688269, 430527597, 593000134, 537932284, 622486598, 839280243, 2860756, 939414827, 178456587, 892417728, 372245481, 654315471, 843629260, 268599320, 308926036, 402440683, 885001956, 187071893, 18241711, 158334757, 122202175, 55960582, 902210145, 766972948, 206201624, 264947312, 891653977, 70196403, 481592767, 671796633, 928891901, 655255537, 298046958, 85135295, 990433169, 867658415, 228318389, 252235698, 302509032, 221767887, 100573640, 872350979, 414672790, 827356626, 691637363, 93540466, 360067097], [742955386, 357674203, 354478093, 325882255, 219284898, 702301127, 70381280, 820708839, 889236357, 687322770, 804654255, 459532261, 27968974, 180311415, 612878120, 608970486, 284853458, 614922720, 987651585, 27317481, 842631172, 707176239, 782439324, 696255074, 455251345, 617732772, 536650017, 372359010, 732985753, 696337936, 487525737, 429372876, 469186394, 292644922, 621065924, 640929508, 892664640, 801542605, 328428792, 222174766, 128017381, 522785652, 359467140, 111356284, 898927245, 333258010, 715056649, 304761756, 599371922, 188149574, 779896123, 112649825, 658781771, 850619772, 496293639, 948580657, 239942971, 40672130, 598969206, 395539344, 424624788], [731914330, 785635538, 874524498, 703908348, 722737019, 833969840, 813377728, 282850695, 86717497, 441858552, 675826828, 502039636, 445998630, 930724821, 666071676, 147508743, 707121979, 48671871, 292904164, 788810822, 808788168, 44968788, 539967443, 221966661, 606709046, 208174, 228298716, 356508725, 750469237, 708290851, 144118514, 378184343, 966013417, 806920679, 348488745, 996015211, 192469995, 111683576, 809708391, 774167725, 12906630, 511014141, 372072828, 740140171, 958852325, 497968668, 454670801, 186783314, 609510504, 60619573, 285640726, 886611161, 718059070, 95565580, 6022187, 750088357, 900960889, 173823749, 687512911, 445859831, 643554098], [648424139, 152791547, 618280851, 506287640, 706234576, 377869666, 494340620, 270458969, 379379958, 815109309, 501968322, 799871175, 833309300, 252784072, 259564040, 17544924, 83661745, 493069867, 513148080, 696602994, 251976069, 389654428, 262847396, 411991313, 416093414, 939441899, 374304063, 157416326, 229258856, 89617682, 280531311, 74374881, 183161865, 407953707, 112351410, 995544278, 762016754, 697803942, 33739607, 275715528, 698813706, 598087194, 528782442, 729216405, 112756227, 643764991, 593834963, 953113617, 180341026, 811527100, 23623373, 835262998, 406473094, 533315587, 534431016, 257858268, 457639761, 469191307, 345109694, 113664655, 666348637], [418408339, 574923234, 76037081, 73936258, 617588104, 88669736, 38275458, 361920638, 850363807, 86369514, 475271079, 214592297, 945165873, 839503428, 50485308, 203010711, 270574803, 745735241, 595468054, 650816701, 550935648, 66063422, 817284035, 459425572, 815104430, 72529329, 5253490, 575816570, 841741902, 423112696, 471920728, 654080480, 315662442, 835464387, 338289523, 764692450, 66661141, 580692791, 424262347, 673419028, 881621148, 177758055, 313568756, 506597681, 714146734, 215246341, 699264361, 63584831, 188850440, 795550513, 629708790, 833007819, 886462622, 316455826, 415303768, 968999341, 467080918, 955095532, 917181287, 12832402, 753013324], [766854308, 176377339, 176366424, 857776348, 447072440, 75195340, 614022024, 846206797, 79685460, 448853713, 483986107, 759539776, 441924800, 385781386, 208788684, 673059726, 293149672, 16917864, 364163211, 758545846, 280145071, 565346243, 658984231, 157470892, 716366757, 754995396, 444703570, 880478484, 402668518, 982917395, 537636830, 426275750, 34831961, 826243596, 60477351, 640247287, 279765967, 276382854, 400862641, 3013152, 320574617, 45438555, 85805732, 385224571, 632743776, 798755356, 824083160, 107904095, 310939445, 509985395, 519152966, 388660864, 52376001, 110372686, 657990402, 297658611, 609841706, 669470940, 549652865, 412409259, 120073095], [940398580, 259467195, 353315077, 941673929, 759058222, 708666169, 917614750, 61791995, 512449611, 203911055, 807004291, 924915376, 481324906, 819885939, 461978584, 306500325, 160759389, 806441973, 272117237, 712750111, 731543422, 313421460, 704782781, 850050590, 136617881, 677212952, 663005803, 698939470, 250136433, 758597991, 734904609, 845338397, 102696592, 503826870, 400727528, 684481547, 905065215, 294569458, 728271345, 173765279, 411243021, 275836738, 655816587, 415601969, 354614687, 538263857, 436334887, 752141927, 948040416, 551423443, 120753634, 725794677, 987689160, 134215616, 247574901, 38341122, 309209551, 662374563, 439303950, 352419009, 460918300], [203051453, 277391645, 822174820, 729781872, 108814608, 529992653, 253954772, 952116610, 307662834, 984690222, 880127286, 360513437, 632309598, 728878874, 902816302, 347514651, 755381704, 16245951, 369074856, 912656426, 188722437, 5766067, 720019500, 891055611, 483765675, 121651066, 474309326, 297626360, 540536902, 665536802, 516549418, 512264513, 159750007, 961889192, 761630942, 941274416, 57026232, 945250480, 965137097, 880827072, 37994554, 468559783, 426508540, 328585697, 797756592, 626787070, 130886804, 861343885, 567335072, 495359484, 170820546, 88072523, 721887241, 356428032, 825452190, 474224100, 811011242, 148078291, 910835709, 465087866, 327112895], [10135671, 966889833, 392957175, 811812366, 213556033, 995617911, 549489633, 317483588, 454974716, 339279815, 231396204, 104587183, 213752125, 731138448, 32724670, 273650932, 573295153, 205136811, 611614351, 797303364, 978940676, 320752015, 469661001, 330295280, 568278647, 325472820, 228177240, 683621295, 281716595, 543122696, 340978407, 464375723, 279614448, 885785151, 27924398, 609069234, 535035493, 825532648, 953665942, 124518379, 77766054, 591874127, 573106479, 156767295, 522425177, 918017925, 78980277, 93968849, 428869573, 68762903, 274163850, 558497064, 741667763, 88365611, 139510826, 570107221, 117793271, 801250082, 568567408, 195641613, 510285714], [688901937, 480161471, 467455745, 887656241, 643137478, 196158678, 918586181, 107670239, 16073537, 303706483, 792587089, 429001390, 727332119, 86632631, 579104194, 930169707, 258743356, 449285414, 37292262, 676029147, 545941166, 652064563, 351241028, 411801150, 908108509, 226960505, 15777619, 104240502, 968755120, 753755990, 954621547, 858409644, 643188993, 46958938, 395364814, 166941791, 438125149, 666023200, 255281225, 705395147, 432616589, 650383111, 908300658, 866072889, 183878542, 709522041, 187376605, 143840187, 279073071, 883972455, 115923941, 163495613, 387509079, 523334694, 137186211, 973802283, 386038404, 428650382, 20217707, 146865371, 734150382], [235126508, 199959196, 38728013, 571822034, 679763633, 627547158, 245518693, 10208714, 430873444, 382807802, 738970933, 182309575, 819373988, 494254046, 119396508, 278108331, 811848224, 855058030, 789930256, 233223682, 444032594, 290954672, 927970062, 131571542, 220908028, 231549743, 567573365, 904908182, 174053521, 767471288, 692251508, 616322582, 99580677, 805843251, 899458800, 803339806, 52652926, 347294391, 88605480, 294638315, 638820976, 140723851, 672486648, 572017858, 79786677, 394360112, 944449653, 864575117, 262101876, 566806918, 494860664, 245577500, 640654732, 917787496, 277559415, 514486361, 194129440, 130048787, 654065376, 734734694, 139221695], [184702708, 756745073, 32156290, 720060884, 571824613, 425202096, 137479077, 5020176, 833116723, 345984819, 405687226, 404173203, 842193487, 657922129, 768780733, 768278972, 620923091, 557821286, 640557527, 415900022, 683995185, 622664687, 850274137, 656660400, 426905601, 832731934, 358447901, 141775673, 192089610, 564401309, 540887949, 229517131, 877536926, 936817314, 592200890, 233374775, 772023724, 136257417, 559426055, 850224011, 929092751, 766214558, 56058995, 99301291, 646307354, 544383914, 345257933, 702745991, 908154590, 685916788, 543377054, 657322524, 39923095, 607431319, 103982125, 291778700, 911790341, 874616055, 811298999, 119551412, 969468692], [298217055, 488031450, 52339042, 678996219, 449190498, 436973048, 298680463, 180790954, 141451500, 431581490, 895776265, 431069607, 692927968, 921376306, 827431047, 415178449, 68015168, 264054199, 32651301, 916258761, 588474611, 682052504, 185059506, 725896740, 4617356, 669299782, 963661981, 704420614, 941866296, 911570259, 142898857, 529483598, 744426484, 768809577, 900143829, 155636749, 845958557, 383985817, 591236041, 22224085, 579399860, 398076356, 521911, 840971509, 302260075, 382280450, 240276579, 192501518, 229721628, 31217493, 658075830, 80252727, 909581759, 10800412, 869071877, 790909675, 399247004, 30274178, 834193788, 91724109, 812746389], [692585644, 277786178, 839694673, 103912710, 585750838, 926554504, 303011046, 96506807, 611220679, 108242858, 509604367, 26833080, 341044823, 565225028, 682001117, 916325838, 280573494, 648815024, 534281384, 669279867, 629857643, 285806686, 969178856, 675027095, 932970798, 49752962, 487725514, 432727265, 781534881, 701147277, 12096404, 224537623, 173965602, 558654337, 322277660, 856156492, 424890577, 574054071, 689079480, 224186850, 331188236, 380914616, 114309016, 506686929, 961836753, 15076895, 742775135, 545416446, 516109922, 484809896, 836800643, 713360955, 833524682, 363913972, 430325195, 284527857, 191267816, 727644692, 241585146, 99712797, 545773059], [117202671, 484164926, 586945278, 305879047, 782566496, 93232206, 780941671, 623531042, 704623386, 977218964, 54935083, 382114923, 840380889, 453174452, 385749411, 95840070, 164885326, 532475463, 935975141, 467438940, 669823526, 140419142, 36461808, 744864405, 173283925, 702668906, 219573270, 353317452, 458224202, 89664141, 362279669, 868550788, 155146301, 219987687, 839400460, 546494374, 701028620, 199926173, 328560343, 718931479, 782030707, 374758445, 679823405, 417401518, 534182046, 657486051, 402520215, 492363950, 950576434, 387865877, 395823134, 972406662, 206798505, 267227223, 785914176, 847048004, 833679819, 887036341, 946000543, 800869352, 721158787], [495238994, 540003568, 552894368, 989713880, 879814806, 101526545, 298190040, 892032818, 351335670, 446277204, 379295903, 823442431, 430359255, 594745491, 108530134, 102363820, 220497912, 790500155, 664482072, 463953479, 273560554, 204730249, 63281115, 483556222, 893584227, 768743984, 216166974, 503288237, 316758993, 894025961, 304327654, 156525269, 455008038, 960763582, 480008576, 482549297, 50565744, 799171027, 839739086, 843344527, 394649998, 466290627, 325509088, 130960400, 752047141, 805877514, 701158146, 306419384, 25649729, 316578301, 207213969, 369875679, 555992317, 897045569, 116375728, 336579752, 727840943, 569748162, 43422714, 462393479, 954558423], [647219878, 146453876, 524787869, 679148239, 63381961, 214420202, 174411902, 473752219, 764321227, 684827497, 548905414, 721791625, 776992824, 633415180, 765019532, 661905474, 197520647, 188856200, 476857230, 189856630, 679709035, 402445597, 190631552, 387597362, 126153522, 456656350, 922035736, 54181167, 630306470, 136664139, 608552847, 207560737, 877891, 249724171, 166072077, 149845892, 402100463, 468545233, 267432771, 949487663, 247104036, 461578533, 408488863, 515057647, 233539476, 410650668, 579241817, 312491587, 283120829, 45182962, 539613043, 351178249, 667456978, 469783680, 348324909, 961713319, 716105086, 186567061, 672976839, 323662012, 722116700], [669594221, 22273465, 170254496, 631424657, 783937539, 662191708, 677906150, 350107090, 681717149, 968607706, 794914571, 746028127, 44837839, 176510697, 995330961, 15759272, 563680313, 143321984, 325892365, 922730710, 968644701, 148571317, 200116154, 747776006, 737264066, 475750260, 712540280, 50155079, 375846441, 910401125, 571341840, 15419181, 174522544, 230061381, 645858440, 128385529, 832410265, 690038825, 769318185, 550453687, 865972850, 958650263, 186651657, 299071387, 19036722, 397563978, 557907833, 298714688, 340053022, 643853007, 624833221, 9553322, 234144255, 927907750, 524444578, 747975455, 78602968, 652648704, 725018021, 338593670, 939215774], [232974709, 156732510, 524079010, 107239071, 220717766, 357337985, 864269726, 453107199, 448886375, 317566494, 637451209, 629478055, 668768132, 415910470, 603527082, 210477918, 82980363, 206688007, 571882701, 981379578, 374222507, 124419870, 267312009, 618316674, 42029447, 555869642, 522637190, 741952218, 703334189, 267887810, 250690324, 482843619, 273564742, 453009368, 214001597, 912064475, 835648784, 275573338, 64981723, 617050211, 690743764, 214775330, 231283447, 712477609, 506102926, 331410400, 466939786, 660195358, 852700075, 329154298, 868854597, 967539989, 207109204, 961577351, 34180302, 621828373, 914095559, 390249432, 288482566, 957198836, 69582135], [247511235, 944518444, 329857133, 182527582, 411493045, 912049326, 232752963, 923012079, 598346182, 827119152, 511026820, 994126595, 902318333, 275451846, 430757633, 95396006, 85278644, 21491990, 988003195, 183759780, 714063389, 859418638, 439512527, 172655040, 886606583, 423485405, 857153127, 674916405, 668744730, 936075634, 567878233, 746651595, 247099803, 364335738, 764583148, 294548881, 868138842, 759122205, 596208731, 274281096, 320473993, 216179985, 159863388, 834118114, 728694743, 463141539, 137119163, 71533668, 736397436, 265222420, 655804519, 476603110, 757254410, 324815197, 122274152, 982098848, 639635532, 248173899, 935182095, 438721260, 70009456], [469257070, 861432610, 429927788, 950541466, 281413342, 409862694, 507807245, 836453987, 124971947, 921541401, 266114300, 425826078, 60538776, 94726328, 345291394, 844683843, 878187226, 705987830, 890031106, 413439292, 458077514, 299092503, 578308738, 500433644, 45980027, 184629168, 764675535, 163491066, 804082517, 380512847, 387180964, 501086628, 579594269, 698736366, 283704003, 458767380, 566623073, 995321011, 589003398, 206528563, 678947775, 737380578, 753926258, 310743963, 575467358, 26711160, 548712307, 919955052, 211272815, 600685532, 76433734, 101318378, 731125616, 162520869, 16301296, 468203196, 338720215, 33012629, 785714723, 203678822, 647328072], [161768562, 746464700, 153462523, 603434674, 923656454, 529243305, 424707040, 476906651, 505398264, 194504431, 472529191, 847264563, 373458073, 341062368, 142346597, 760842387, 692490943, 270741971, 406503572, 824139888, 659476951, 107118696, 485234034, 779341807, 442352408, 620231902, 979327554, 838721029, 719861803, 943105029, 860593535, 23989668, 609683627, 928632280, 451557233, 843717389, 871002724, 51829304, 611675157, 474622984, 234114344, 109235830, 883969251, 734487750, 553589560, 579361899, 461665267, 232310094, 661727700, 843257974, 589820758, 800055284, 158573459, 314202797, 32996992, 831815403, 709669673, 185445206, 20191838, 559250390, 333429282], [691009272, 930932231, 164872781, 221210797, 561350685, 270666084, 731573625, 516799562, 768596302, 708359930, 227999391, 429997575, 594200942, 655296951, 430624285, 279408899, 142368218, 272679074, 555375832, 989983866, 147431748, 354852355, 146684478, 801284967, 95588839, 464352268, 27686541, 689235084, 212510096, 689706739, 788500610, 151925670, 878307117, 59041142, 790341448, 774833100, 30196562, 841555433, 603447920, 757206336, 398899887, 701900316, 116556902, 627632480, 894513743, 316669616, 341821835, 127856538, 547336043, 428194364, 824597006, 509384424, 254973802, 753519697, 615000398, 520658703, 605061049, 474451832, 275395052, 916490132, 12207306], [978883832, 224561151, 729283494, 676905386, 528865726, 8635056, 57081778, 473379140, 96093325, 637061596, 22833801, 292564361, 918484123, 918000475, 214021009, 446944856, 758472310, 117723946, 260920590, 343300782, 308511502, 178084035, 258855293, 426308530, 493298792, 207710443, 99661489, 562343731, 38555305, 85702732, 830394185, 786709755, 811295564, 133283625, 799393295, 477953146, 731566984, 649067638, 989494938, 65458321, 360968527, 612354881, 867072409, 7217043, 801578703, 394147383, 565825369, 128875953, 64512773, 218355710, 786663700, 391506460, 968577517, 118372348, 529549791, 279841357, 785771669, 114334511, 852657563, 965795629, 891998348], [341586577, 318107166, 162817673, 858012583, 563436329, 286491274, 164657792, 625998265, 609566781, 528949800, 987617913, 8462236, 560822628, 797114030, 677782964, 258142037, 622853892, 169673434, 608358221, 960156634, 812697309, 443393532, 279254306, 238109725, 253586122, 982035908, 995239360, 255509118, 175748936, 465688662, 774284183, 190666715, 998971193, 250376981, 133843274, 115979165, 638748789, 365686286, 641694132, 385404367, 473180407, 150943515, 139605005, 877447112, 572388279, 628882971, 846824995, 657704914, 203661633, 349093858, 235692908, 307284784, 443046628, 499444939, 945677792, 357185844, 990331501, 108659953, 833509498, 10138315, 550729186], [776328056, 413437278, 83894585, 534238379, 163765989, 517821916, 183093023, 614437832, 223507793, 614855247, 753723569, 847547541, 424335797, 938508017, 274747700, 769562464, 729891363, 419969301, 110651781, 766727344, 888453459, 110983164, 787557655, 703477682, 996194340, 433318747, 475432099, 413389223, 445524840, 429218574, 996692108, 903920967, 394322338, 456177130, 761225338, 879715290, 273108190, 589293979, 42271730, 478403317, 231132772, 832340444, 522153053, 692751818, 291316840, 953087639, 958386471, 812415028, 615737438, 483414665, 822028303, 193721076, 701782333, 757461273, 784353465, 35712004, 91186721, 9289068, 797468455, 144138017, 121630898], [161697098, 371999275, 365709572, 28748403, 698921102, 917438681, 776835053, 674761034, 320904508, 725876705, 555571697, 267801147, 342010011, 53988976, 977274071, 65799110, 821476559, 245528804, 844616510, 861561803, 755097134, 585187355, 591635969, 515863684, 394983499, 926196988, 182042034, 471843150, 76113990, 94431634, 689604972, 995954064, 13250063, 591923232, 466986110, 926511639, 85784613, 152005930, 479267353, 892603504, 439485898, 232591114, 147798664, 526467772, 69419364, 556900143, 144885344, 286242641, 381845912, 286187068, 314777157, 573379823, 639307850, 389023285, 718113690, 145648337, 860956305, 782242668, 549186653, 553331110, 331492443], [351249570, 545082948, 416662345, 63377996, 327261925, 68131365, 721747390, 627363691, 240818104, 342770509, 931995902, 972576902, 319663506, 917815994, 3739131, 140042027, 932891155, 69946507, 942649362, 163831427, 618937441, 158985225, 410516827, 651255880, 151249149, 256146228, 841973735, 822764588, 133671308, 617345757, 579809365, 953111564, 136388896, 289837051, 50081591, 96871785, 853981527, 626948862, 876252669, 570345443, 851543201, 681872723, 843486874, 595840037, 270122678, 769270149, 129446482, 874102914, 689891575, 451698925, 347926648, 818006798, 124252500, 372541795, 128992841, 74454929, 709545770, 161313379, 937338153, 78629644, 506422752], [753095291, 882457789, 888056678, 597335544, 466781854, 628663052, 192889478, 874645598, 838153501, 95428625, 451680707, 567761941, 657438888, 763767125, 559528119, 322471213, 905935372, 171521297, 744859971, 336856859, 984180516, 191623098, 491663253, 602485648, 898916210, 516921697, 851257981, 254926794, 439660157, 664450593, 557774688, 88442740, 580783853, 485896477, 841501786, 677254845, 801526345, 980167390, 93151658, 315428495, 869988845, 722479405, 123471759, 71063461, 284413976, 754327648, 253950518, 52360225, 581087432, 807012700, 902801534, 692158963, 133045988, 428630509, 98994449, 247531888, 373887819, 453295691, 888770289, 846081796, 614330622], [125156282, 618752026, 883154717, 703132917, 565362551, 765534238, 478750365, 903392936, 396575159, 789840311, 245648506, 360384777, 447494907, 15978781, 177882290, 913348317, 350618782, 872144295, 959115370, 675501566, 621579649, 915505828, 51701727, 4555852, 174701932, 285850974, 24133740, 304628385, 683748844, 607411149, 600668528, 675541851, 703403079, 815215841, 723908710, 909484843, 181905179, 579793063, 89092378, 440430707, 903485918, 427027505, 248229221, 567976538, 141705840, 143640182, 828145588, 234092566, 518135850, 715260092, 651844863, 592787606, 146972221, 355844695, 696092091, 688764306, 288786391, 925094483, 30726195, 131335024, 867008499], [27581125, 700324574, 553082424, 842797142, 492544923, 337829502, 331395810, 91509882, 751543923, 510636609, 370853912, 208198231, 125911745, 94372338, 992196713, 81445649, 918993931, 971723026, 200586767, 973107056, 952355174, 489678286, 498525008, 208127721, 223187895, 949850080, 69231402, 958454628, 568005082, 258640298, 29171753, 22724619, 163203273, 906005224, 261652213, 332489359, 815321370, 955769604, 493448785, 761622253, 97210577, 940207301, 113794714, 965535503, 140560504, 745394872, 136443342, 841626841, 804615604, 976936568, 869187746, 622566939, 249831747, 493478931, 829973435, 305165905, 63909086, 453237270, 220022047, 608297562, 871474150], [308765628, 830626855, 528821803, 105182518, 30472900, 285608511, 464271491, 117694084, 273171569, 585864958, 910048530, 762336744, 528315205, 869069071, 606037506, 59643095, 220119730, 535769252, 816867401, 197664511, 897888501, 35799760, 494651770, 329280810, 720164511, 119463169, 538455092, 152302963, 114172346, 117125205, 517612799, 536093339, 507628579, 425403160, 959516130, 794252934, 76449834, 746154344, 242301407, 480097275, 306780149, 217197209, 597169364, 867710997, 152742289, 906058364, 751985003, 363553860, 617817194, 82792383, 230878347, 401057644, 215715847, 500415951, 174287062, 168981711, 280828986, 808343440, 724794129, 419108771, 858046187], [453560424, 86455984, 523489071, 244981299, 705146011, 498794300, 562547149, 17560690, 221499881, 902821217, 63738754, 612175215, 965458920, 106406489, 224646112, 586276913, 115378010, 412676095, 579432363, 982989204, 780247995, 116707280, 187340236, 631885073, 892779644, 760143324, 998920539, 117445218, 821458470, 606821536, 898462412, 583873546, 120466920, 682793383, 87942182, 780743485, 45312400, 22730081, 655396486, 137624846, 759517314, 483393033, 306224856, 632808267, 872303084, 261929028, 41138636, 121628084, 575134314, 71011441, 468611211, 831362817, 613312796, 479951635, 224105594, 258108460, 12579074, 987270056, 657271208, 940170671, 524779703], [684258103, 36517497, 41175774, 807592569, 453569924, 41865450, 26442021, 407630876, 356000269, 828346890, 719892539, 16487489, 430218583, 484083526, 572649478, 566305009, 112615081, 777817132, 644481229, 386543457, 475930457, 495813509, 563814963, 85080468, 479173974, 18747710, 380046957, 236206734, 466233944, 807304450, 785518275, 186832819, 186963565, 842073267, 433833274, 774432221, 465841699, 605462210, 999811960, 447355946, 178259933, 739418720, 469063057, 205157675, 783730111, 656259203, 995798641, 810209639, 186527508, 145216906, 702953543, 657331013, 67710360, 899805045, 308990904, 434232199, 599533284, 249753184, 7266219, 521859690, 542691899], [572777240, 278773487, 585758192, 376474511, 210259885, 887598760, 640250195, 193949783, 813527727, 746534690, 832311550, 775650725, 490033614, 420652353, 699031937, 669301792, 253476441, 692246470, 69369644, 283549162, 185338948, 503534842, 536298862, 123511117, 253439201, 924099648, 421248170, 852516699, 843602892, 120912489, 883535806, 174347568, 85633350, 906366537, 859115496, 497548468, 440168574, 158212704, 10134260, 248477800, 620938695, 9303922, 979907853, 150973585, 684419264, 714124993, 97018115, 158190587, 706562755, 217111651, 416034548, 563474092, 918190986, 665054317, 291533956, 678148444, 644710586, 176781527, 12262524, 653244386, 501638019], [871480861, 570672428, 532255085, 560299363, 604676753, 80605205, 404197811, 732452410, 695317054, 677757149, 700329353, 848495152, 854505440, 149154167, 59862238, 875277957, 719260034, 819640583, 356519545, 767398296, 416228559, 871289247, 554335329, 420424281, 928105239, 421235259, 697387021, 948251958, 397242973, 441438252, 907897753, 762665107, 807210065, 614901641, 343139622, 246163606, 403540633, 784058281, 904661228, 440172160, 383638207, 186490579, 20885775, 758341046, 541137454, 53650518, 589465834, 319811078, 43645836, 417158178, 123094091, 8027872, 972879681, 706211871, 307215098, 140715609, 907237073, 361961475, 607469348, 901674761, 976156049], [718011065, 704551252, 244454113, 7786272, 155317740, 850859141, 584743225, 683148081, 594223401, 136199938, 639893887, 651179849, 981808789, 843608435, 229518731, 339922420, 584372388, 565824194, 469133522, 50598409, 661519924, 121023942, 434331153, 668109709, 269344836, 944019130, 288375130, 470171647, 21819709, 313982751, 171145368, 121790637, 254712292, 731313367, 276548060, 302747079, 585724901, 4088884, 848513553, 197983164, 179772839, 806483477, 956540412, 525989583, 851429034, 869883728, 577476510, 943076644, 701335722, 644401098, 982016309, 929030657, 221978473, 508829812, 600115183, 383365035, 459376556, 806159522, 253996063, 217234986, 892492884], [206823984, 457383868, 657308963, 475277683, 418730183, 547832142, 523175309, 970132185, 25485695, 538488875, 349977958, 530170032, 273002628, 714996868, 613382883, 86404429, 397899815, 547124342, 62976712, 204663288, 573990063, 657759808, 690751134, 399758573, 256802973, 24828646, 73354832, 471953924, 371323151, 209710462, 231802203, 887630239, 65797614, 618010290, 518743610, 178245812, 241963554, 190252316, 876099664, 645248371, 419362827, 554076419, 783641283, 660863823, 210432974, 458563648, 273063153, 56799935, 332454940, 909925123, 866078665, 469826321, 306558732, 425788040, 854154227, 815874875, 747355632, 98988445, 364822327, 497122283, 900840530], [983906171, 845856331, 155596737, 588448364, 321186000, 752019160, 476347021, 692607307, 144522749, 427861429, 360929772, 739107330, 291649557, 484249692, 804488954, 465834886, 48714878, 620420900, 822173433, 692420021, 927846750, 67500749, 271529717, 512206864, 948202483, 617071063, 417045737, 466081035, 428931873, 511123594, 736720203, 658906228, 346545604, 846384867, 777520829, 390516106, 574506683, 480367029, 470940183, 609135687, 576073145, 783501783, 545442239, 680768824, 482778102, 472266932, 939054836, 422181982, 231612429, 717812281, 774364435, 937619525, 183121879, 939916914, 901021508, 597317590, 99763496, 14529450, 986916247, 95221185, 82510440], [211112177, 778218080, 773084365, 620134221, 439200152, 54810207, 97912483, 772437198, 575524011, 807759591, 478556265, 396691085, 722902634, 991116906, 484653054, 330644998, 514345415, 993702464, 948306838, 339675529, 896445410, 807895584, 562582483, 754072341, 419651509, 596116147, 764443939, 677358999, 543529255, 256999298, 407971152, 881477410, 352566917, 404504414, 682253608, 758510045, 93590900, 767304642, 150067656, 823431223, 181634152, 141887591, 15476845, 537148961, 16484682, 640508112, 621767764, 780894003, 370997757, 323053950, 471673783, 730992058, 435034847, 313426324, 839857453, 576089056, 272415974, 126424150, 127756282, 528889432, 801605195], [511584524, 15380014, 6679591, 445234204, 323834495, 99787142, 734306823, 118495787, 20844397, 189942950, 648758361, 962298977, 539866180, 921256233, 383021506, 716961332, 624704876, 298919356, 368755246, 504742445, 773892150, 695602361, 467957247, 868574567, 158221861, 32709512, 329699525, 785408352, 844368288, 769798835, 532872022, 485693779, 639867305, 83924636, 260821485, 587952183, 198411064, 828857663, 90352785, 292238788, 689963118, 355425376, 935665314, 69171502, 518714231, 4870875, 388119699, 140203790, 631913241, 293527253, 463556989, 819617593, 948716451, 279948423, 471396259, 797955237, 926783817, 971885395, 624641594, 999764727, 418403256], [981567806, 343919466, 24717869, 127071215, 109737481, 794122631, 636666287, 537795564, 855117048, 567817710, 822691831, 441392929, 92948785, 310271341, 851326752, 357866139, 584704275, 720902219, 173534975, 968623244, 496617850, 878947703, 83877315, 597088706, 809380729, 608430560, 639208709, 892501688, 874489974, 935992333, 743627426, 797382402, 459112746, 579377807, 293737105, 304518996, 705635631, 348461298, 461238068, 575542053, 299370569, 735173927, 887344491, 423526704, 670645519, 254677223, 169856912, 293257380, 819782271, 467702122, 49698523, 169389620, 285332261, 891143117, 731419863, 713364071, 559994610, 20035478, 970732026, 870326504, 735125715], [173354624, 217008334, 301475526, 419458305, 101355778, 600473843, 937691361, 337666287, 719681888, 854468172, 652976329, 518385962, 303458299, 841459372, 256148810, 908763223, 241695608, 615137420, 367778616, 331410193, 740462820, 342966324, 694934119, 453097829, 205090812, 746567837, 668637968, 788470990, 538309600, 19297904, 156592389, 563803205, 699157220, 339502657, 686145394, 653604946, 10594705, 833033214, 972611296, 854879441, 140313521, 864485678, 895549087, 622571134, 462111179, 620220897, 621591541, 172473864, 615976707, 233125349, 1264483, 466708253, 788240899, 272361398, 638585122, 781434031, 1891331, 322819741, 701323851, 654945539, 48951283]])) + +test4 :: Test +test4 = TestCase (assertEqual "for (maximumScore [[790082025, 991879404, 543562661, 952595112, 128097644, 229094593, 41808791, 714078277, 49893556, 22167314, 190745832, 652435941, 657814917, 370192542, 446969592, 277988661, 969376969, 212193662, 632332464, 288512293, 957399085, 790777808, 135407362, 412838914, 508469612, 825461694, 473884649, 152949748, 385845299, 124609369, 253779789, 349616424, 810347225, 533343540, 908850987, 221917639, 275187623, 643412021, 816485639, 888824599, 766920739, 172771889, 897855382, 918067450, 294067301, 77331302, 901291971, 625132278, 457212603, 283795184, 313256518, 772162467, 208564297, 470742175, 342930915, 68637737, 232642268, 449084078], [793508211, 47286047, 858563711, 358553331, 860164490, 671785374, 856217899, 292622805, 984185105, 267811243, 622876418, 970441976, 411420439, 702594022, 867807094, 627288308, 616692017, 27644942, 724230019, 905292974, 383512706, 653603182, 611162106, 396216663, 47299906, 786760189, 805068254, 628065521, 350326171, 723049289, 97327637, 299020198, 934537823, 940411443, 300393558, 220752606, 266338092, 433700153, 513268887, 156962197, 931386180, 280720103, 698640389, 102848400, 730998001, 769957357, 605162661, 836605211, 38465161, 12946285, 477857719, 695150506, 251951455, 949115500, 136931094, 965823882, 995386762, 778280270], [571990780, 393565386, 907323014, 616717026, 202823360, 409138458, 957343965, 120019550, 39854261, 584736162, 347821141, 358769796, 402693073, 828203577, 195838014, 216667492, 48852954, 167570727, 152403602, 62195833, 443056318, 328451217, 592720842, 611276506, 234924941, 795602386, 641690542, 445431237, 56730435, 452415966, 335200766, 508597137, 731274319, 26003249, 45114500, 962315072, 951579360, 692524840, 902714774, 65264873, 196298886, 861818865, 852542679, 279869143, 560978817, 699638960, 845135135, 415891607, 77720718, 314231822, 81247220, 523265890, 12029190, 137015183, 571726665, 76949713, 504856618, 592702], [960576389, 142907052, 374804855, 983439754, 100361749, 858088353, 756062445, 819167255, 291541515, 306636470, 248199239, 617214287, 197253452, 766716012, 578217740, 813346172, 771306855, 430711820, 861592747, 978416990, 860735869, 594791357, 793137880, 871680942, 303283697, 980904463, 774248868, 651165420, 420733684, 523183851, 723757203, 73607928, 531875922, 575314261, 382954750, 421468828, 220695025, 970435658, 918170259, 333275364, 567532303, 792493439, 560988910, 208763901, 617637112, 217224501, 512694581, 888621410, 665896260, 629324035, 623215165, 748260747, 341806652, 942055958, 854476076, 704512901, 268292857, 44501065], [801289250, 214706329, 315454300, 515638774, 733935083, 532295053, 271315415, 86736178, 308402079, 671323697, 826584244, 745986641, 392629365, 503311046, 26862355, 502273423, 800131911, 630442105, 752119657, 975094880, 118107749, 884490091, 970375550, 194460858, 851300123, 777879846, 876996655, 313874163, 288356243, 50031798, 593974724, 423419895, 236409806, 626320634, 318610178, 848497245, 449933328, 409752910, 65466954, 571248801, 546549881, 256424293, 757931574, 828538748, 447799232, 970698900, 120170577, 262464819, 545418479, 324279983, 668746645, 418281409, 562979450, 117314659, 510292353, 987044744, 997564303, 903600702], [534667122, 501886160, 234693211, 538130944, 723620509, 541100793, 245752298, 474498424, 793510085, 524923536, 247218098, 388153094, 986479926, 298049561, 792570838, 153198574, 217371775, 447577936, 209705035, 303831556, 28457279, 865886421, 822209542, 262974837, 662310122, 171728582, 918699733, 249948512, 25485107, 227891183, 694173217, 223614474, 532038940, 679158286, 871798159, 371917859, 193666971, 556815931, 153659549, 644012418, 570073825, 709424301, 895434991, 838074329, 292439893, 530427185, 255918402, 693998998, 363781960, 983485306, 496610855, 587347854, 531375144, 341518506, 435377851, 131790319, 481430236, 477228340], [755839316, 247812608, 557634005, 547123842, 949676124, 205442574, 637797428, 182342448, 140165124, 972588604, 597914795, 659254396, 585798627, 4352469, 34077467, 462764135, 389292825, 129864202, 235111941, 398369708, 531037560, 707178066, 274915625, 129362919, 790679686, 396528477, 235716107, 280195946, 701585713, 415561567, 991682570, 505254117, 599380498, 538041709, 510595272, 317865398, 77373158, 327954339, 772193682, 986484884, 111611009, 685289481, 845156633, 354570404, 799292226, 551625041, 280608810, 343128141, 128360366, 807783903, 86730851, 425701490, 197897864, 695831970, 401596003, 692344396, 805346313, 489233010], [857017572, 638571923, 478626365, 151969569, 599710742, 165195854, 385626454, 556841393, 599855484, 241248399, 109867928, 928886633, 1555443, 331955480, 209466624, 7436020, 708278187, 626404213, 443787389, 201446911, 348103054, 451302534, 807354792, 759432991, 133996133, 937370097, 327039231, 133388154, 189427005, 235306938, 939181458, 791357863, 19064274, 24804702, 544365301, 943224337, 5905318, 336717871, 565953741, 198558164, 130388713, 120083679, 320473484, 285790557, 924176339, 406693789, 339070657, 767006609, 678947760, 80744252, 532547603, 701648679, 510253129, 383146699, 297160857, 225768035, 400295041, 63528087], [847385808, 202426578, 878456718, 887073446, 329522983, 236341496, 199951680, 399799374, 174931400, 592004280, 811204077, 74068351, 997908797, 98689259, 956189971, 286229521, 589979875, 632274518, 146358701, 632560510, 357372388, 470240723, 540024531, 125634194, 830430033, 430428390, 472856297, 953352455, 535297079, 787645555, 44651187, 943142883, 936548595, 971689084, 633938886, 178661266, 58671960, 316840453, 669633594, 759204641, 799954610, 146155599, 47369793, 900969758, 502309470, 650536608, 770931652, 14205790, 957910537, 232059990, 710695158, 719837835, 677070686, 526023829, 860482030, 410631026, 208901943, 734960071], [827004593, 156254123, 460256264, 609907630, 466509942, 387743096, 849635321, 341348604, 298971903, 732014053, 386462223, 410301634, 282848677, 412322512, 506063390, 924233461, 425412485, 314339895, 861783270, 142937732, 349337877, 202668939, 933234745, 709500797, 986179952, 142693638, 514759878, 938277061, 508417249, 883792628, 755953864, 865075754, 136235105, 715549218, 133212890, 92344873, 492029247, 74140378, 747543758, 413971951, 756518771, 103250080, 565258053, 379861974, 224325833, 936089675, 393193753, 941873220, 598406251, 675176858, 48265053, 745937279, 761799606, 311780371, 974197177, 119252244, 876749620, 878175225], [943400359, 230696755, 982295716, 947610707, 154815232, 247238854, 184285079, 940619490, 81213713, 245498169, 156534975, 925860692, 786513615, 143480412, 882202627, 712377314, 903048801, 224278658, 977840464, 913764147, 697489451, 144417782, 690197196, 67938972, 747858611, 804425195, 652235781, 955941404, 6461765, 661818408, 259651114, 339468344, 621614541, 766627429, 182264274, 88402557, 717123555, 295172974, 433649522, 303033847, 170500860, 18551812, 608504819, 785321461, 206625042, 768880092, 219560010, 697126618, 948675881, 598670079, 761939992, 534216903, 561701938, 745101191, 187323904, 600683754, 709651914, 6655166], [613169990, 44426367, 214626764, 330430614, 469086479, 420003412, 833368647, 196637503, 465781695, 31745999, 190475420, 496031575, 139117212, 713945123, 729401592, 580292497, 14314107, 509690449, 285054832, 737497053, 674863807, 373781381, 39996740, 814177956, 308960434, 954987905, 1800784, 819074789, 44502723, 678632057, 100341577, 554908439, 152281814, 725553705, 724070656, 580832070, 99923299, 722102193, 556694900, 495114467, 468995595, 963652263, 974655419, 262203225, 413086417, 883500814, 249566618, 601488585, 364135521, 437594744, 198146669, 933971776, 621781590, 879564325, 625728949, 734729631, 72930765, 116828830], [259757892, 277232942, 175058956, 358597948, 925740455, 546581638, 912093460, 641174746, 563346516, 784161465, 385322141, 514744010, 177292588, 559792139, 929657732, 333502460, 903113552, 805501340, 862478584, 926351555, 786552926, 809529253, 494486351, 686696465, 294411639, 521952230, 835891721, 203612749, 848603161, 828459617, 333177533, 364429284, 822402920, 803008274, 177997882, 689816681, 415311121, 486675393, 615818906, 795806585, 556890786, 953240904, 328582345, 5822066, 761027762, 109469335, 613937120, 865721905, 220552988, 853001807, 914684336, 165511751, 161364256, 781758466, 99345999, 54801139, 547112148, 208752371], [252295780, 791220429, 308315626, 454670764, 307099130, 338169954, 830413922, 903702681, 32141139, 510434710, 670088974, 842008576, 85733930, 907976654, 797502512, 164817243, 302439572, 43222164, 290946669, 364835703, 126696800, 644241179, 468690079, 155465199, 550693640, 533437736, 389141262, 115865493, 888878236, 272612979, 175263673, 288547808, 571316934, 154732851, 149967717, 195225714, 261703599, 351069310, 911414250, 943372298, 814756324, 454759097, 465971168, 640702093, 419544229, 725286140, 137656388, 975991973, 564229842, 529372283, 717793755, 141475336, 857299650, 820618339, 86087969, 558210631, 309422035, 497918127], [562040937, 190528692, 504248986, 187923959, 591610620, 319484213, 356204704, 413219074, 140373634, 438711836, 232830626, 16599519, 263236289, 289926751, 462941565, 130238568, 410176418, 627870054, 686696750, 534402984, 698080380, 192179448, 970257999, 807797286, 868674957, 605022823, 922379810, 728516753, 324433512, 308795098, 343393086, 748413944, 145749855, 270235603, 670177989, 875835519, 33433273, 859192980, 1833590, 274902382, 729257054, 420627820, 979043225, 63337180, 588839529, 232183297, 857623517, 219750652, 181505403, 161573445, 663168698, 355278394, 100462623, 137629575, 399423569, 711767239, 249854900, 803768467], [965706721, 709455509, 762174776, 808963157, 674157816, 910759251, 939232925, 756211790, 246773696, 664172964, 831318787, 995278097, 696625554, 201977939, 562430209, 841929634, 325895572, 335984233, 446616788, 682148704, 494109635, 81355573, 403516753, 417477677, 802698813, 16281270, 423837006, 51706962, 229566701, 88434094, 550542017, 70231460, 902864764, 124327375, 984008602, 691678508, 826017593, 510403119, 218066927, 220016457, 273428816, 296557944, 748619440, 6953855, 619008052, 179338672, 34177483, 200949189, 218293549, 985166055, 192679424, 374176409, 668898910, 200130956, 698689910, 629116312, 668902520, 823287288], [423000817, 109620102, 162669281, 62336694, 511219636, 408502511, 474533483, 129649114, 538782947, 89266973, 56057714, 780929848, 211241522, 220310741, 938711968, 172719522, 762055897, 614767408, 929579517, 310843633, 586886752, 117355086, 1805992, 366387656, 522963212, 622665826, 812896331, 537895580, 47393580, 858023540, 701384735, 348636222, 906727147, 418896585, 800140988, 618744509, 445503104, 642747072, 28600782, 315412332, 822210939, 836706154, 604505264, 180886624, 908247600, 767922179, 366373676, 172452714, 723978250, 239870490, 307321405, 551871694, 227721516, 931539164, 358553030, 335181151, 460396600, 946920847], [876244542, 135444497, 448504952, 115975047, 390279708, 687366012, 137183323, 152316201, 334905685, 267502196, 199577947, 78756717, 793413010, 409506835, 374252043, 588734588, 969104842, 534008947, 663179911, 484198016, 66391135, 869639342, 9258966, 504298133, 712850853, 620885397, 855351422, 122945284, 518245034, 681370219, 850932957, 675982282, 513401153, 88436255, 434550202, 500426493, 781415278, 165972851, 97267482, 549183297, 276835165, 859762196, 834951598, 566908082, 863410889, 18565806, 639797316, 701553534, 663970344, 928563101, 21749391, 747403620, 758715411, 433833290, 458071629, 438281609, 731391695, 278616904], [850561720, 702673166, 178685418, 521433812, 748634402, 126265353, 826850517, 496096094, 84576813, 215938724, 862136505, 226462606, 110716310, 384087884, 70472673, 532548336, 262826872, 804274227, 806762167, 504656821, 164658801, 585928299, 840739091, 502564672, 844175665, 928360257, 636917905, 302693318, 179388168, 32368954, 443188635, 664204880, 567082800, 841591746, 554778750, 436123, 380608593, 619093678, 799616118, 167001046, 978159631, 211391774, 520000071, 662422614, 696368288, 405620301, 305670301, 802359165, 213448833, 762877975, 159660356, 821017667, 540100799, 142559746, 664658186, 436931913, 933431918, 600296623], [762134978, 391777631, 475910470, 663368169, 33197980, 686500260, 614204358, 318391362, 148329829, 361731598, 885804409, 823181241, 38507799, 176145485, 321058046, 16041707, 374582868, 426487265, 289329158, 654836692, 831535023, 164941518, 980986039, 431734384, 526446785, 805894412, 316754207, 667037246, 505618631, 54943048, 846202339, 871281187, 39365458, 242970244, 393289670, 106677325, 654475647, 718525090, 668170067, 406947851, 90446919, 667526184, 969155932, 248541784, 596414444, 811128342, 646465071, 781845253, 760204183, 946558610, 93111512, 381936602, 766528092, 328928940, 573867364, 41822427, 438443422, 932670242], [241825925, 766135197, 646041197, 276845506, 94601867, 283666286, 827705339, 504212296, 294652095, 328628542, 818326456, 646330940, 990812004, 607667214, 264728590, 882838081, 768847132, 470102449, 792876408, 60339558, 166361858, 982197656, 487194185, 375221410, 102312186, 553037086, 147049873, 212229497, 29125331, 30299895, 371495879, 393802691, 200027296, 528078516, 244977811, 464393258, 928313313, 306075652, 565373780, 226399898, 466208882, 225626522, 961646327, 701473960, 992524635, 973188818, 627480152, 247480509, 771329859, 562791671, 938099093, 668685064, 907481616, 536673411, 946827151, 20201784, 164527555, 981887995], [872929255, 587756340, 946627209, 580643967, 776126854, 468448683, 435364688, 335888488, 42978212, 490921447, 229014298, 174295957, 817022655, 928646453, 65821398, 969568744, 308713420, 13584343, 196450623, 17977451, 481677619, 985029535, 975786876, 554867394, 104589062, 866799463, 151429984, 490449487, 198756546, 279654766, 150413654, 227457005, 815537152, 567110035, 219118870, 110620576, 759999154, 817156417, 201054032, 72668466, 950606140, 369563010, 870632331, 587105362, 235760130, 829549405, 252246314, 877496618, 176189248, 784645569, 478199173, 585737933, 174668471, 618003152, 838347960, 858071032, 967873223, 500770254], [903093652, 826440136, 887976313, 188573050, 675878210, 409331585, 557777378, 621894556, 604872633, 469708014, 461119719, 960919341, 647927916, 699420220, 44615556, 628224558, 761026060, 577900755, 928206285, 661930919, 810918411, 502811930, 847260035, 455042682, 149297470, 917378892, 704702374, 245313128, 64722124, 787430419, 483414601, 937024544, 477887532, 453650524, 801440019, 875135659, 710121621, 636724220, 624296116, 474793534, 458206489, 720750154, 255603256, 412990575, 71480621, 749321357, 662183719, 505005916, 592579776, 747795741, 738784188, 795906374, 612697153, 274719231, 688005590, 191101579, 157573075, 142963796], [409903303, 957620979, 660408440, 405317018, 870364243, 210770181, 81411676, 266739338, 20968449, 336249070, 503735084, 49702097, 638133276, 337664919, 192439736, 71609246, 191120090, 164308064, 21736934, 53282981, 362613952, 251804190, 78582523, 447538969, 233205947, 280775103, 456472534, 260403478, 78379590, 522916166, 262582217, 882212449, 783406219, 304588659, 561780054, 480697844, 760565179, 993456814, 692566238, 693326773, 764121988, 423576472, 747205270, 804869101, 423909544, 88067547, 712605983, 976090524, 844804462, 178061149, 747157251, 344856977, 248307543, 894950355, 295356007, 356600779, 782946745, 216016197], [981463920, 160347183, 709468050, 292915396, 841801664, 830321164, 124202125, 666237449, 950053404, 937922686, 78294767, 507275888, 488114118, 399628842, 156471968, 205681123, 427452978, 20358004, 251097532, 504792843, 328938715, 42953152, 964411948, 48580819, 399109833, 393993313, 400429221, 345398503, 254934012, 303933728, 460809417, 765289162, 69503961, 654688141, 671892315, 246705542, 536830309, 210044539, 658543529, 570462533, 315248378, 787872853, 414515421, 584178999, 918434489, 494929045, 531589333, 749070693, 590811263, 542463448, 802053114, 744931388, 776549469, 296803962, 955881753, 119730756, 467266996, 91936328], [557043278, 249911262, 570695018, 324503915, 299410985, 286661213, 739234500, 669458549, 968271575, 719157984, 978221441, 125438539, 488891604, 735277967, 585750459, 458980942, 993847462, 104142366, 458927241, 101751392, 349942297, 367644246, 150529196, 392667180, 488298256, 123032496, 164829025, 186599559, 13331555, 49632194, 857156202, 902771235, 785647102, 797428236, 401668241, 755220697, 52462450, 25529088, 425423860, 781003336, 825120363, 479246965, 966018270, 804275673, 583861575, 844212416, 661155825, 986413285, 502120462, 480544108, 339233223, 472704550, 599355493, 445014578, 854892805, 837937817, 719856555, 403560307], [477391927, 530714530, 283840307, 156656995, 328920117, 997730069, 163759724, 398893932, 361083741, 103458275, 653649807, 530983198, 775362916, 42388419, 11053956, 800934580, 225647276, 273754600, 278630788, 2331641, 863685020, 946328857, 160664276, 653403477, 753782528, 715693575, 293390860, 482017113, 583807607, 618351190, 434317028, 186900866, 289640690, 746817752, 219902814, 73958093, 866314562, 88857899, 930430069, 259776685, 325871235, 276891494, 835599514, 314484890, 482062836, 963906785, 315315343, 761155610, 993961479, 570904359, 425693471, 182155974, 413592733, 26185106, 978848144, 866777409, 839667609, 40888676], [434105605, 495383378, 755891534, 891084525, 788042408, 574698731, 484792252, 583962089, 132172456, 298364684, 344829144, 819755987, 448631238, 501184485, 550036882, 954359448, 302791927, 242055441, 188591565, 153030094, 71019226, 488232123, 316186507, 455724173, 390518675, 704179977, 228790461, 750080345, 980841531, 634450242, 504962059, 739012833, 647963907, 743248498, 298981900, 389898435, 433926661, 83987705, 83236132, 970252814, 836608606, 304426258, 145247374, 609657053, 56259577, 839466215, 590011873, 497762245, 148494551, 654446475, 114966222, 895593710, 401167108, 809574008, 732692532, 595927138, 763422927, 856963104], [753692628, 460968702, 269750003, 332333946, 923043819, 322929086, 580105281, 659858079, 605541597, 834113115, 405052339, 256693594, 875669898, 982131111, 641730793, 697151282, 649979173, 699673869, 694276091, 534221166, 245992048, 31762427, 138848853, 463267988, 631611821, 370057910, 214767807, 730419748, 796504221, 248441480, 801709322, 891226919, 341858709, 991457430, 972272523, 89810780, 558990170, 25427353, 643821736, 881737359, 358553099, 326483454, 780521857, 923681481, 553945419, 969846792, 425237853, 931196203, 171684678, 374091043, 26840529, 851410104, 982406916, 517116547, 77942844, 551619895, 258175757, 931765581], [891090918, 968586763, 908390262, 947150450, 880027863, 993561230, 44531085, 861417764, 939537688, 960798349, 919057701, 112552355, 321797607, 851366894, 314027171, 246599771, 639632984, 790835173, 370362918, 183027752, 783209100, 586698542, 917943418, 341026117, 289739124, 87822789, 292831015, 853983632, 139990847, 405797359, 848997245, 959264878, 375851176, 895413193, 431049351, 53458452, 621171691, 44820690, 136519032, 712406892, 69782028, 728244020, 966537630, 365598195, 737936426, 979714001, 555249076, 941825346, 467229909, 171502417, 783158130, 45410736, 757562499, 629638237, 761697522, 647021307, 926387421, 166829543], [366487211, 7125267, 268984417, 665344480, 825826025, 944595493, 882994487, 737618957, 167920775, 229232288, 225585846, 954148195, 999562261, 687061118, 117680410, 115008697, 922947078, 288300987, 43578702, 745225760, 196073792, 341714654, 97391036, 944569248, 571054728, 75882902, 497120589, 303161659, 710850157, 93413135, 838774858, 334599383, 986188706, 942987608, 709400668, 205699196, 838738987, 3398800, 828357790, 797059937, 805677321, 585442755, 941258952, 910536436, 994432384, 822780688, 913598818, 582645615, 886865425, 935665452, 609861504, 269610197, 528430847, 190653736, 359032900, 970560029, 802483393, 477962476], [744662708, 81714049, 326106357, 524342049, 2907585, 167490837, 945308614, 859143843, 332610480, 914882497, 51382473, 226111907, 710447887, 764139141, 198789389, 906963044, 492000823, 899200394, 172850328, 375847309, 587950206, 896983799, 596027294, 73686028, 870839267, 451341421, 670788490, 459270132, 910751965, 141946179, 366921690, 131884242, 409907996, 887449841, 936430106, 306904970, 925089854, 31225435, 486143869, 949954524, 213823245, 924134850, 496998589, 850103645, 914241625, 369422899, 148532188, 298301793, 495658062, 269176269, 320334213, 377122700, 433356568, 421417049, 528775543, 272312768, 256724459, 931269157], [839477360, 461637954, 365580958, 196089231, 800885614, 681462132, 166851103, 36477173, 559570287, 984467283, 537550494, 836053123, 847204833, 583182050, 144712225, 888341600, 293867851, 52577310, 484139251, 20469819, 85048654, 390745469, 712398126, 627989064, 941731541, 612360137, 66208388, 16304701, 657520221, 236860071, 284343202, 412417763, 177371289, 716924410, 797668040, 355025879, 505346002, 191887845, 163557229, 648136129, 617007551, 876825051, 478107753, 726131884, 259567755, 53952883, 848683058, 8655886, 199803101, 878157166, 682217304, 546881559, 31468621, 943272477, 403864067, 273949202, 782138968, 548447757], [155552079, 162897529, 781642616, 427659020, 649242798, 26688933, 504556277, 91641966, 74599461, 831643461, 930199831, 99169522, 449269983, 154905939, 230408611, 69978027, 395894483, 725751163, 416207230, 86813623, 104441613, 835534029, 788281777, 762277510, 804549201, 831278763, 455855980, 832844947, 816615083, 574048924, 898909553, 148102330, 480746408, 820416906, 777925729, 56873296, 96612323, 778033772, 105462007, 922069524, 519991895, 629449929, 785485083, 454301182, 823629219, 191348515, 154844661, 650363126, 232886452, 909003670, 741029241, 698604775, 634567229, 114711023, 514670670, 874149686, 437498199, 459341839], [565976554, 17692619, 710680848, 261604, 644530237, 871770238, 733421284, 93762027, 174534037, 692241542, 517697345, 851050983, 804001874, 8815200, 525425894, 773398486, 212625711, 439237648, 401924559, 841119922, 596676539, 718236822, 210673373, 574396693, 462376047, 680324488, 201238987, 572677965, 462594882, 938774864, 193431471, 530903135, 929542250, 877056698, 749976459, 130077031, 506800269, 278828653, 773747620, 644935043, 775268751, 811158309, 609192363, 266642558, 155116518, 670655186, 34982203, 448628390, 853302513, 636465073, 327599670, 444902764, 896786844, 631252546, 495820177, 990472432, 743129247, 741558949], [774313419, 480184944, 893552095, 142863721, 163225938, 612978973, 653257088, 941346437, 944956348, 438270509, 369635430, 489625734, 746769180, 895610288, 16384010, 138791977, 879274346, 770401284, 810052769, 372469784, 707973864, 219440218, 911636771, 179393163, 205512521, 884327273, 212399209, 585803642, 238577820, 211246360, 932787658, 596979618, 609364846, 242838971, 902426374, 560815401, 662084699, 959703208, 461548120, 610956484, 372934944, 189218527, 726476658, 547622701, 862526067, 765837615, 868001019, 488850877, 892285729, 923778436, 968832609, 909090822, 641154669, 968130181, 308913346, 251339687, 876943937, 541566763], [609325845, 630427772, 100152465, 620641483, 992969909, 565518799, 580963781, 536470578, 883752485, 816079463, 761921679, 631469667, 613716773, 733533043, 892334884, 535798893, 295823916, 164900701, 932263920, 228809448, 209328128, 546547124, 658916600, 280561131, 856146275, 950614236, 487725837, 19481665, 617350076, 982821541, 371831389, 985012408, 570499772, 217640140, 462421319, 741371579, 565040244, 649254650, 421230209, 248248173, 274145444, 985119919, 619389894, 757074145, 597567618, 635782893, 377023217, 776799105, 470792810, 491807797, 671690199, 429703280, 820641828, 293494215, 779861751, 656226860, 132702749, 653862468], [342324888, 268289801, 29020016, 39502332, 713751978, 142492078, 982859975, 991783176, 822183540, 432234425, 343660972, 944062684, 818507390, 52735141, 742903999, 516245816, 187950953, 253506267, 402271823, 423297133, 201151928, 976765527, 235427454, 729387144, 397108345, 361296073, 956418804, 651291451, 705326156, 194282904, 442270000, 253599874, 77334161, 98209325, 51264975, 362333921, 902885358, 280619742, 807880666, 169075264, 805540404, 562930234, 238146053, 479344506, 107127399, 420076099, 260358557, 867073240, 278789174, 307468291, 458432314, 102641544, 687047976, 998356644, 201829448, 544173087, 988039948, 19188571], [61074168, 518893890, 629435722, 590665391, 669102049, 863335607, 987656416, 927934782, 5823315, 126694167, 193405320, 177350331, 384960632, 78717208, 865201259, 882938394, 66088355, 887618086, 448403447, 149294985, 247211923, 253317994, 555754947, 169894842, 758331546, 676907142, 96975125, 740187393, 541932428, 387009156, 856847129, 593374658, 508354780, 236675082, 860934242, 980850298, 918787104, 891471286, 778955899, 496904718, 316893444, 3529955, 408424311, 901906359, 724617766, 539598503, 580995326, 182135292, 810485372, 101635623, 266765274, 436765910, 460402826, 192935679, 862703425, 276448967, 421575161, 366750736], [932531326, 454130794, 331481570, 430813366, 101700365, 565087365, 562317124, 332461611, 822833243, 869717731, 18921358, 743241383, 756744680, 687941012, 934122100, 550135915, 534180313, 462889698, 584627025, 461956311, 158795257, 179002216, 84585699, 953761225, 942528918, 552449837, 490850739, 745438931, 508016986, 766576466, 712549489, 448829320, 871634522, 68206196, 6661278, 815551897, 363248872, 198306854, 314356079, 258487912, 469715268, 466668687, 28900080, 738009616, 650583220, 252709220, 994601962, 121352462, 140093668, 68325315, 565795155, 683021494, 112193685, 642843260, 861748063, 473947018, 569827569, 15641217], [123377169, 924049605, 304188528, 750134511, 552548368, 792526030, 496332186, 138568706, 411303706, 449260223, 807400676, 551503382, 480157131, 554418708, 171904111, 507770535, 799631711, 486455270, 524400516, 136421330, 221777031, 878666335, 675621898, 51350180, 83880632, 755340234, 887223789, 341706166, 336199686, 555135139, 903740, 809791450, 966799249, 403174669, 468675146, 159846344, 244908034, 743636101, 239561868, 592183908, 573497446, 628483126, 796640297, 618524369, 753849779, 453418748, 207405398, 35518110, 918509417, 370828483, 828697204, 493030038, 953208726, 167775636, 101313428, 780269860, 367302052, 290889673], [208427077, 37817494, 576135383, 292705955, 577041605, 842938309, 716920706, 950003238, 849458452, 667714503, 451076779, 187055531, 404160841, 322158472, 222316582, 580279665, 637661175, 751028252, 204900387, 581507681, 881938183, 920647732, 814449805, 833193586, 282638488, 612526426, 803536218, 400956265, 802867943, 672195341, 172089123, 626305885, 939988044, 457005677, 356833619, 855708774, 629082320, 673923945, 525964574, 531441585, 831471601, 293699577, 215840763, 131462799, 40303670, 214772561, 648159268, 868498236, 921979922, 911886932, 478240206, 361351965, 379201504, 317161073, 20637302, 139276941, 914977429, 894931560], [213645902, 908927245, 735453088, 620838530, 96794374, 516900509, 34733846, 450411069, 290581685, 336946483, 55906656, 684038778, 421641507, 801030508, 545196593, 190995514, 779285513, 479822404, 505980635, 232933267, 318259733, 142598359, 257288585, 334020220, 641735732, 917702548, 52720512, 186792126, 696238452, 156755749, 461668091, 662826866, 263359295, 863802561, 912124758, 89066918, 921254247, 49482595, 873540752, 913167609, 734432387, 42422865, 781419100, 84469026, 823786558, 214645959, 763575153, 382951702, 893680259, 793888667, 542152618, 387864187, 678604793, 462310207, 660992381, 565792801, 693422712, 635224355], [863045605, 307242922, 311313253, 763656283, 57396610, 81766262, 903607051, 594491352, 201020633, 669364548, 5264211, 963427882, 285513864, 860375960, 308562838, 748194945, 291704873, 528323647, 298449375, 848694292, 384750166, 941203891, 951212379, 439089959, 236568366, 542360856, 695265398, 965816566, 593688010, 677680099, 551957486, 366161507, 471827305, 436329846, 761396999, 989059577, 994280438, 888893769, 365696052, 717157255, 884809066, 242903324, 756361609, 76635151, 252844425, 778395485, 954069463, 927348184, 536904300, 667333522, 365229066, 713587077, 625444911, 785902539, 785545418, 334100689, 699835745, 551015504], [653342195, 234252170, 744784995, 636646774, 951433564, 131971367, 899314745, 418841779, 969273258, 220504670, 842320413, 907071824, 490314405, 943709966, 757047, 798598680, 962423411, 836274370, 229321354, 276352930, 859619277, 956788284, 16334335, 218809157, 911232227, 29219825, 669270115, 565132529, 103387224, 562367056, 878902606, 91474522, 441508248, 119072259, 342655772, 46979034, 485598393, 251720916, 195600984, 873607563, 938097480, 866783790, 786845691, 466383067, 252963583, 191452864, 899562061, 52126850, 254048879, 479750429, 127128630, 186098471, 358923006, 729336368, 170933189, 362135840, 936027326, 757708230], [942812818, 26676171, 458690094, 109144632, 12803911, 118257757, 925619197, 634458117, 352079090, 298901620, 202689717, 183031667, 915447154, 450825909, 174096866, 175879530, 480259363, 457555459, 617360441, 918861453, 174111017, 519128490, 629317453, 89935061, 46741343, 856237850, 404233987, 130124924, 487832066, 623238799, 919099347, 177610231, 656490581, 454270764, 428563732, 309874943, 943080956, 500756131, 199980501, 808170867, 376530418, 49583450, 470274894, 208000465, 79402906, 212651432, 453726341, 420504435, 884813142, 615011001, 82832884, 779942218, 263593545, 287065942, 595727476, 360749854, 227112431, 816871950], [344289859, 148830904, 569104164, 215575115, 9089763, 944834623, 587936622, 460479153, 884492837, 871241560, 170097504, 850071299, 71999751, 273791558, 919919794, 824854842, 760608455, 198090498, 613572015, 177921834, 698194450, 775874256, 840630278, 466915734, 631302309, 938367569, 809591260, 9252741, 648648629, 123460602, 997414130, 582154596, 516115877, 65083759, 485065553, 18640197, 538108682, 801397193, 50451650, 60230567, 297291406, 184403349, 774836587, 200408376, 242604417, 609990204, 772460897, 807359866, 863524183, 660993810, 885896724, 360355279, 390529666, 563784400, 798870998, 878054423, 43945188, 187509373], [66916085, 224179343, 250463056, 16661671, 187974031, 795267267, 726875525, 941881173, 862487125, 645192750, 572026513, 320298599, 202956111, 996368889, 19535609, 104656302, 548446969, 418828182, 423061215, 512804425, 220125158, 12474400, 629746805, 865807173, 883716503, 344236778, 565852588, 353585871, 579774664, 600165261, 931321520, 979770121, 978616395, 756911301, 922301279, 687617694, 120414309, 295999475, 748349236, 964144580, 474626338, 795757236, 529981635, 270170726, 879984909, 582305558, 992521377, 395592286, 562403727, 593717365, 514352558, 127841545, 927228696, 304497822, 37003399, 681696526, 621942552, 47990640], [483678157, 876528559, 632080908, 371432180, 243719806, 630297108, 850569136, 419094980, 490730007, 910934064, 865162154, 524227881, 441429453, 403089272, 54647246, 693757358, 812061389, 246980664, 117202197, 627201600, 282666375, 624925835, 829572637, 840401164, 431718895, 243012076, 690279218, 574753739, 222338951, 924016160, 250647188, 621397441, 460286747, 832123459, 964926820, 698734229, 726463959, 426781190, 35728749, 933877942, 226193204, 230013229, 888598673, 296825636, 919237366, 997723445, 153559306, 564222320, 544783156, 641250297, 810277906, 34089752, 539926224, 24202416, 146479986, 859208926, 335920551, 369888201], [847375647, 703547212, 44290734, 463744621, 82446906, 63932365, 71204190, 790731628, 908280884, 608132245, 285639580, 73843909, 268410307, 142486965, 915286655, 980522510, 706745973, 517086881, 874492674, 714567344, 299995759, 145159667, 390468642, 314419443, 272747656, 140863614, 947231729, 376518838, 915461567, 163058993, 279444887, 425614417, 565575058, 466658608, 487301104, 821263086, 13881779, 519081733, 849052465, 908479850, 300183124, 950016835, 896743630, 766438701, 500087168, 948687890, 276515984, 666550482, 95416581, 245422757, 565020302, 909650719, 417252308, 269741348, 911460032, 141928179, 480830050, 795561031], [994318789, 214792772, 696056294, 594368323, 77536699, 933258921, 639836187, 21640147, 929066, 807451553, 425488243, 808644636, 967136168, 846828819, 409921599, 491347295, 122546568, 63106819, 306228392, 650118350, 257194333, 63643445, 406860854, 16197407, 958105863, 84959071, 991748263, 529018360, 99086810, 962107839, 273315456, 257669971, 87108076, 306063779, 540295438, 484280202, 385704962, 170327164, 310959676, 524628029, 194754044, 428786609, 645024971, 942714643, 772636922, 817950764, 700857573, 935599327, 670120251, 922229566, 523822283, 635086710, 949586949, 443110125, 732022936, 635480098, 315823102, 315244582], [519545678, 628706911, 308680194, 430740343, 915273244, 171125078, 692009152, 698232034, 26029965, 549547770, 221471852, 323209902, 728259935, 340770180, 42729616, 675469621, 709393041, 738251285, 886920245, 553503318, 844609239, 450878459, 365121767, 4523028, 44055271, 740823494, 389775784, 526847537, 238293307, 859324571, 62759261, 213114889, 548675180, 646050489, 367508574, 12480114, 98995497, 122267083, 37131593, 177840291, 846009834, 10078208, 433712794, 487918895, 198538720, 551173387, 237980168, 277296291, 397056562, 604663923, 64087337, 314339011, 896068667, 522151964, 118241347, 752311695, 980824122, 588400911], [718035449, 605579598, 914120204, 78374562, 935583147, 825630159, 891466165, 623923470, 397294267, 801700915, 817306510, 437116437, 144950232, 956730719, 290566056, 784380011, 204405722, 380531122, 767059803, 589918012, 432380826, 803928405, 116692061, 691879240, 746723209, 386378927, 223944220, 607641237, 974792231, 609461826, 311535896, 97200501, 887030120, 289440113, 382504496, 144008224, 420179560, 325648897, 278407532, 503264714, 790334319, 433213000, 709034067, 151149127, 786907824, 1329789, 419769821, 770721176, 803262111, 359210190, 76226308, 95004786, 317157768, 270689249, 289778030, 701711653, 382944027, 142849943], [793861679, 849464528, 630166881, 221372384, 404582126, 462285171, 712529065, 36805385, 398908557, 59039730, 814038245, 929442752, 778187913, 123383737, 667927796, 747739319, 752659794, 891970802, 167024073, 541898996, 174473161, 908524241, 802662248, 186115716, 626402204, 593973674, 147618389, 277082348, 773344158, 401302124, 263479925, 820258995, 817303366, 488061027, 879950192, 186120959, 16794825, 275977855, 227465046, 706002912, 716666834, 535767598, 186751204, 257927565, 799268742, 853538569, 967917280, 655742917, 50583159, 874044018, 317917841, 99938548, 355991243, 858674173, 793062947, 594526107, 320399187, 495758875], [278245687, 515064184, 348603706, 532922855, 308536976, 26359087, 41424141, 913585829, 680272944, 182172720, 154841402, 677357190, 523883668, 54506568, 50204441, 771898084, 192977115, 815879141, 162243794, 387555651, 464557076, 316337628, 78724387, 293176323, 330205205, 273218674, 24963875, 265600326, 404662717, 41950162, 947475210, 277081781, 142775223, 686534000, 61190719, 771914767, 767150560, 480581907, 214297657, 805355926, 593508910, 884405175, 433232717, 610730299, 730285010, 187780629, 298992294, 240991998, 818519478, 387843401, 117794448, 394058216, 243386509, 581673491, 429459379, 806914386, 499316238, 835385532], [809311691, 603798028, 490651249, 751171463, 747122818, 930339755, 355492580, 459143764, 445849086, 412993270, 350730915, 427720750, 375312812, 676750395, 739080809, 392782859, 490782861, 434441874, 291519111, 375791442, 286736227, 29293900, 483884177, 924658571, 81302474, 16792326, 245694084, 876873754, 162998235, 2366406, 421054458, 137859783, 842906747, 869449181, 486489816, 224923673, 578869884, 986371927, 882661389, 927775682, 465627857, 726188325, 977547649, 915653991, 159022330, 881821796, 780542416, 309831350, 887483667, 644062431, 652065803, 753358831, 33946067, 137978847, 582203432, 38219943, 437321483, 539311331], [316900274, 389332904, 609188349, 460833804, 352597152, 444088542, 396662747, 652335959, 912647992, 360610862, 832937047, 910728265, 696910162, 64460980, 71516075, 163532661, 575970114, 450692352, 667520562, 594847078, 311382526, 232989863, 227592276, 171138740, 365512669, 48223433, 148492506, 479413408, 110257823, 521843091, 713848212, 818138322, 828766710, 555538608, 388070642, 408114742, 230760967, 587504939, 507588017, 244630342, 130418722, 382929363, 349182539, 532650369, 439759, 240039813, 847871972, 624977260, 915452722, 331078680, 923842685, 427643712, 758121956, 366051360, 385128594, 424885191, 122794011, 601459251], [969648710, 140531707, 328761714, 281164379, 195633298, 872396447, 930748849, 640677986, 869957890, 877740431, 449521741, 210166, 932069995, 512023322, 987084081, 615064538, 1471496, 443652558, 433397535, 914097566, 530839557, 47388474, 607801392, 855516911, 833943190, 970607025, 276165221, 899871064, 791562057, 349504906, 980177687, 293876196, 972587279, 362325987, 501294236, 751030757, 855849084, 623450951, 649834014, 725792589, 792239477, 671806602, 188451833, 278900799, 146045379, 756734248, 626346100, 771345380, 542810428, 390931871, 478291220, 534960963, 734522420, 571633688, 504518509, 178394054, 668094166, 266699748]])," 1144674960115 (maximumScore [[790082025, 991879404, 543562661, 952595112, 128097644, 229094593, 41808791, 714078277, 49893556, 22167314, 190745832, 652435941, 657814917, 370192542, 446969592, 277988661, 969376969, 212193662, 632332464, 288512293, 957399085, 790777808, 135407362, 412838914, 508469612, 825461694, 473884649, 152949748, 385845299, 124609369, 253779789, 349616424, 810347225, 533343540, 908850987, 221917639, 275187623, 643412021, 816485639, 888824599, 766920739, 172771889, 897855382, 918067450, 294067301, 77331302, 901291971, 625132278, 457212603, 283795184, 313256518, 772162467, 208564297, 470742175, 342930915, 68637737, 232642268, 449084078], [793508211, 47286047, 858563711, 358553331, 860164490, 671785374, 856217899, 292622805, 984185105, 267811243, 622876418, 970441976, 411420439, 702594022, 867807094, 627288308, 616692017, 27644942, 724230019, 905292974, 383512706, 653603182, 611162106, 396216663, 47299906, 786760189, 805068254, 628065521, 350326171, 723049289, 97327637, 299020198, 934537823, 940411443, 300393558, 220752606, 266338092, 433700153, 513268887, 156962197, 931386180, 280720103, 698640389, 102848400, 730998001, 769957357, 605162661, 836605211, 38465161, 12946285, 477857719, 695150506, 251951455, 949115500, 136931094, 965823882, 995386762, 778280270], [571990780, 393565386, 907323014, 616717026, 202823360, 409138458, 957343965, 120019550, 39854261, 584736162, 347821141, 358769796, 402693073, 828203577, 195838014, 216667492, 48852954, 167570727, 152403602, 62195833, 443056318, 328451217, 592720842, 611276506, 234924941, 795602386, 641690542, 445431237, 56730435, 452415966, 335200766, 508597137, 731274319, 26003249, 45114500, 962315072, 951579360, 692524840, 902714774, 65264873, 196298886, 861818865, 852542679, 279869143, 560978817, 699638960, 845135135, 415891607, 77720718, 314231822, 81247220, 523265890, 12029190, 137015183, 571726665, 76949713, 504856618, 592702], [960576389, 142907052, 374804855, 983439754, 100361749, 858088353, 756062445, 819167255, 291541515, 306636470, 248199239, 617214287, 197253452, 766716012, 578217740, 813346172, 771306855, 430711820, 861592747, 978416990, 860735869, 594791357, 793137880, 871680942, 303283697, 980904463, 774248868, 651165420, 420733684, 523183851, 723757203, 73607928, 531875922, 575314261, 382954750, 421468828, 220695025, 970435658, 918170259, 333275364, 567532303, 792493439, 560988910, 208763901, 617637112, 217224501, 512694581, 888621410, 665896260, 629324035, 623215165, 748260747, 341806652, 942055958, 854476076, 704512901, 268292857, 44501065], [801289250, 214706329, 315454300, 515638774, 733935083, 532295053, 271315415, 86736178, 308402079, 671323697, 826584244, 745986641, 392629365, 503311046, 26862355, 502273423, 800131911, 630442105, 752119657, 975094880, 118107749, 884490091, 970375550, 194460858, 851300123, 777879846, 876996655, 313874163, 288356243, 50031798, 593974724, 423419895, 236409806, 626320634, 318610178, 848497245, 449933328, 409752910, 65466954, 571248801, 546549881, 256424293, 757931574, 828538748, 447799232, 970698900, 120170577, 262464819, 545418479, 324279983, 668746645, 418281409, 562979450, 117314659, 510292353, 987044744, 997564303, 903600702], [534667122, 501886160, 234693211, 538130944, 723620509, 541100793, 245752298, 474498424, 793510085, 524923536, 247218098, 388153094, 986479926, 298049561, 792570838, 153198574, 217371775, 447577936, 209705035, 303831556, 28457279, 865886421, 822209542, 262974837, 662310122, 171728582, 918699733, 249948512, 25485107, 227891183, 694173217, 223614474, 532038940, 679158286, 871798159, 371917859, 193666971, 556815931, 153659549, 644012418, 570073825, 709424301, 895434991, 838074329, 292439893, 530427185, 255918402, 693998998, 363781960, 983485306, 496610855, 587347854, 531375144, 341518506, 435377851, 131790319, 481430236, 477228340], [755839316, 247812608, 557634005, 547123842, 949676124, 205442574, 637797428, 182342448, 140165124, 972588604, 597914795, 659254396, 585798627, 4352469, 34077467, 462764135, 389292825, 129864202, 235111941, 398369708, 531037560, 707178066, 274915625, 129362919, 790679686, 396528477, 235716107, 280195946, 701585713, 415561567, 991682570, 505254117, 599380498, 538041709, 510595272, 317865398, 77373158, 327954339, 772193682, 986484884, 111611009, 685289481, 845156633, 354570404, 799292226, 551625041, 280608810, 343128141, 128360366, 807783903, 86730851, 425701490, 197897864, 695831970, 401596003, 692344396, 805346313, 489233010], [857017572, 638571923, 478626365, 151969569, 599710742, 165195854, 385626454, 556841393, 599855484, 241248399, 109867928, 928886633, 1555443, 331955480, 209466624, 7436020, 708278187, 626404213, 443787389, 201446911, 348103054, 451302534, 807354792, 759432991, 133996133, 937370097, 327039231, 133388154, 189427005, 235306938, 939181458, 791357863, 19064274, 24804702, 544365301, 943224337, 5905318, 336717871, 565953741, 198558164, 130388713, 120083679, 320473484, 285790557, 924176339, 406693789, 339070657, 767006609, 678947760, 80744252, 532547603, 701648679, 510253129, 383146699, 297160857, 225768035, 400295041, 63528087], [847385808, 202426578, 878456718, 887073446, 329522983, 236341496, 199951680, 399799374, 174931400, 592004280, 811204077, 74068351, 997908797, 98689259, 956189971, 286229521, 589979875, 632274518, 146358701, 632560510, 357372388, 470240723, 540024531, 125634194, 830430033, 430428390, 472856297, 953352455, 535297079, 787645555, 44651187, 943142883, 936548595, 971689084, 633938886, 178661266, 58671960, 316840453, 669633594, 759204641, 799954610, 146155599, 47369793, 900969758, 502309470, 650536608, 770931652, 14205790, 957910537, 232059990, 710695158, 719837835, 677070686, 526023829, 860482030, 410631026, 208901943, 734960071], [827004593, 156254123, 460256264, 609907630, 466509942, 387743096, 849635321, 341348604, 298971903, 732014053, 386462223, 410301634, 282848677, 412322512, 506063390, 924233461, 425412485, 314339895, 861783270, 142937732, 349337877, 202668939, 933234745, 709500797, 986179952, 142693638, 514759878, 938277061, 508417249, 883792628, 755953864, 865075754, 136235105, 715549218, 133212890, 92344873, 492029247, 74140378, 747543758, 413971951, 756518771, 103250080, 565258053, 379861974, 224325833, 936089675, 393193753, 941873220, 598406251, 675176858, 48265053, 745937279, 761799606, 311780371, 974197177, 119252244, 876749620, 878175225], [943400359, 230696755, 982295716, 947610707, 154815232, 247238854, 184285079, 940619490, 81213713, 245498169, 156534975, 925860692, 786513615, 143480412, 882202627, 712377314, 903048801, 224278658, 977840464, 913764147, 697489451, 144417782, 690197196, 67938972, 747858611, 804425195, 652235781, 955941404, 6461765, 661818408, 259651114, 339468344, 621614541, 766627429, 182264274, 88402557, 717123555, 295172974, 433649522, 303033847, 170500860, 18551812, 608504819, 785321461, 206625042, 768880092, 219560010, 697126618, 948675881, 598670079, 761939992, 534216903, 561701938, 745101191, 187323904, 600683754, 709651914, 6655166], [613169990, 44426367, 214626764, 330430614, 469086479, 420003412, 833368647, 196637503, 465781695, 31745999, 190475420, 496031575, 139117212, 713945123, 729401592, 580292497, 14314107, 509690449, 285054832, 737497053, 674863807, 373781381, 39996740, 814177956, 308960434, 954987905, 1800784, 819074789, 44502723, 678632057, 100341577, 554908439, 152281814, 725553705, 724070656, 580832070, 99923299, 722102193, 556694900, 495114467, 468995595, 963652263, 974655419, 262203225, 413086417, 883500814, 249566618, 601488585, 364135521, 437594744, 198146669, 933971776, 621781590, 879564325, 625728949, 734729631, 72930765, 116828830], [259757892, 277232942, 175058956, 358597948, 925740455, 546581638, 912093460, 641174746, 563346516, 784161465, 385322141, 514744010, 177292588, 559792139, 929657732, 333502460, 903113552, 805501340, 862478584, 926351555, 786552926, 809529253, 494486351, 686696465, 294411639, 521952230, 835891721, 203612749, 848603161, 828459617, 333177533, 364429284, 822402920, 803008274, 177997882, 689816681, 415311121, 486675393, 615818906, 795806585, 556890786, 953240904, 328582345, 5822066, 761027762, 109469335, 613937120, 865721905, 220552988, 853001807, 914684336, 165511751, 161364256, 781758466, 99345999, 54801139, 547112148, 208752371], [252295780, 791220429, 308315626, 454670764, 307099130, 338169954, 830413922, 903702681, 32141139, 510434710, 670088974, 842008576, 85733930, 907976654, 797502512, 164817243, 302439572, 43222164, 290946669, 364835703, 126696800, 644241179, 468690079, 155465199, 550693640, 533437736, 389141262, 115865493, 888878236, 272612979, 175263673, 288547808, 571316934, 154732851, 149967717, 195225714, 261703599, 351069310, 911414250, 943372298, 814756324, 454759097, 465971168, 640702093, 419544229, 725286140, 137656388, 975991973, 564229842, 529372283, 717793755, 141475336, 857299650, 820618339, 86087969, 558210631, 309422035, 497918127], [562040937, 190528692, 504248986, 187923959, 591610620, 319484213, 356204704, 413219074, 140373634, 438711836, 232830626, 16599519, 263236289, 289926751, 462941565, 130238568, 410176418, 627870054, 686696750, 534402984, 698080380, 192179448, 970257999, 807797286, 868674957, 605022823, 922379810, 728516753, 324433512, 308795098, 343393086, 748413944, 145749855, 270235603, 670177989, 875835519, 33433273, 859192980, 1833590, 274902382, 729257054, 420627820, 979043225, 63337180, 588839529, 232183297, 857623517, 219750652, 181505403, 161573445, 663168698, 355278394, 100462623, 137629575, 399423569, 711767239, 249854900, 803768467], [965706721, 709455509, 762174776, 808963157, 674157816, 910759251, 939232925, 756211790, 246773696, 664172964, 831318787, 995278097, 696625554, 201977939, 562430209, 841929634, 325895572, 335984233, 446616788, 682148704, 494109635, 81355573, 403516753, 417477677, 802698813, 16281270, 423837006, 51706962, 229566701, 88434094, 550542017, 70231460, 902864764, 124327375, 984008602, 691678508, 826017593, 510403119, 218066927, 220016457, 273428816, 296557944, 748619440, 6953855, 619008052, 179338672, 34177483, 200949189, 218293549, 985166055, 192679424, 374176409, 668898910, 200130956, 698689910, 629116312, 668902520, 823287288], [423000817, 109620102, 162669281, 62336694, 511219636, 408502511, 474533483, 129649114, 538782947, 89266973, 56057714, 780929848, 211241522, 220310741, 938711968, 172719522, 762055897, 614767408, 929579517, 310843633, 586886752, 117355086, 1805992, 366387656, 522963212, 622665826, 812896331, 537895580, 47393580, 858023540, 701384735, 348636222, 906727147, 418896585, 800140988, 618744509, 445503104, 642747072, 28600782, 315412332, 822210939, 836706154, 604505264, 180886624, 908247600, 767922179, 366373676, 172452714, 723978250, 239870490, 307321405, 551871694, 227721516, 931539164, 358553030, 335181151, 460396600, 946920847], [876244542, 135444497, 448504952, 115975047, 390279708, 687366012, 137183323, 152316201, 334905685, 267502196, 199577947, 78756717, 793413010, 409506835, 374252043, 588734588, 969104842, 534008947, 663179911, 484198016, 66391135, 869639342, 9258966, 504298133, 712850853, 620885397, 855351422, 122945284, 518245034, 681370219, 850932957, 675982282, 513401153, 88436255, 434550202, 500426493, 781415278, 165972851, 97267482, 549183297, 276835165, 859762196, 834951598, 566908082, 863410889, 18565806, 639797316, 701553534, 663970344, 928563101, 21749391, 747403620, 758715411, 433833290, 458071629, 438281609, 731391695, 278616904], [850561720, 702673166, 178685418, 521433812, 748634402, 126265353, 826850517, 496096094, 84576813, 215938724, 862136505, 226462606, 110716310, 384087884, 70472673, 532548336, 262826872, 804274227, 806762167, 504656821, 164658801, 585928299, 840739091, 502564672, 844175665, 928360257, 636917905, 302693318, 179388168, 32368954, 443188635, 664204880, 567082800, 841591746, 554778750, 436123, 380608593, 619093678, 799616118, 167001046, 978159631, 211391774, 520000071, 662422614, 696368288, 405620301, 305670301, 802359165, 213448833, 762877975, 159660356, 821017667, 540100799, 142559746, 664658186, 436931913, 933431918, 600296623], [762134978, 391777631, 475910470, 663368169, 33197980, 686500260, 614204358, 318391362, 148329829, 361731598, 885804409, 823181241, 38507799, 176145485, 321058046, 16041707, 374582868, 426487265, 289329158, 654836692, 831535023, 164941518, 980986039, 431734384, 526446785, 805894412, 316754207, 667037246, 505618631, 54943048, 846202339, 871281187, 39365458, 242970244, 393289670, 106677325, 654475647, 718525090, 668170067, 406947851, 90446919, 667526184, 969155932, 248541784, 596414444, 811128342, 646465071, 781845253, 760204183, 946558610, 93111512, 381936602, 766528092, 328928940, 573867364, 41822427, 438443422, 932670242], [241825925, 766135197, 646041197, 276845506, 94601867, 283666286, 827705339, 504212296, 294652095, 328628542, 818326456, 646330940, 990812004, 607667214, 264728590, 882838081, 768847132, 470102449, 792876408, 60339558, 166361858, 982197656, 487194185, 375221410, 102312186, 553037086, 147049873, 212229497, 29125331, 30299895, 371495879, 393802691, 200027296, 528078516, 244977811, 464393258, 928313313, 306075652, 565373780, 226399898, 466208882, 225626522, 961646327, 701473960, 992524635, 973188818, 627480152, 247480509, 771329859, 562791671, 938099093, 668685064, 907481616, 536673411, 946827151, 20201784, 164527555, 981887995], [872929255, 587756340, 946627209, 580643967, 776126854, 468448683, 435364688, 335888488, 42978212, 490921447, 229014298, 174295957, 817022655, 928646453, 65821398, 969568744, 308713420, 13584343, 196450623, 17977451, 481677619, 985029535, 975786876, 554867394, 104589062, 866799463, 151429984, 490449487, 198756546, 279654766, 150413654, 227457005, 815537152, 567110035, 219118870, 110620576, 759999154, 817156417, 201054032, 72668466, 950606140, 369563010, 870632331, 587105362, 235760130, 829549405, 252246314, 877496618, 176189248, 784645569, 478199173, 585737933, 174668471, 618003152, 838347960, 858071032, 967873223, 500770254], [903093652, 826440136, 887976313, 188573050, 675878210, 409331585, 557777378, 621894556, 604872633, 469708014, 461119719, 960919341, 647927916, 699420220, 44615556, 628224558, 761026060, 577900755, 928206285, 661930919, 810918411, 502811930, 847260035, 455042682, 149297470, 917378892, 704702374, 245313128, 64722124, 787430419, 483414601, 937024544, 477887532, 453650524, 801440019, 875135659, 710121621, 636724220, 624296116, 474793534, 458206489, 720750154, 255603256, 412990575, 71480621, 749321357, 662183719, 505005916, 592579776, 747795741, 738784188, 795906374, 612697153, 274719231, 688005590, 191101579, 157573075, 142963796], [409903303, 957620979, 660408440, 405317018, 870364243, 210770181, 81411676, 266739338, 20968449, 336249070, 503735084, 49702097, 638133276, 337664919, 192439736, 71609246, 191120090, 164308064, 21736934, 53282981, 362613952, 251804190, 78582523, 447538969, 233205947, 280775103, 456472534, 260403478, 78379590, 522916166, 262582217, 882212449, 783406219, 304588659, 561780054, 480697844, 760565179, 993456814, 692566238, 693326773, 764121988, 423576472, 747205270, 804869101, 423909544, 88067547, 712605983, 976090524, 844804462, 178061149, 747157251, 344856977, 248307543, 894950355, 295356007, 356600779, 782946745, 216016197], [981463920, 160347183, 709468050, 292915396, 841801664, 830321164, 124202125, 666237449, 950053404, 937922686, 78294767, 507275888, 488114118, 399628842, 156471968, 205681123, 427452978, 20358004, 251097532, 504792843, 328938715, 42953152, 964411948, 48580819, 399109833, 393993313, 400429221, 345398503, 254934012, 303933728, 460809417, 765289162, 69503961, 654688141, 671892315, 246705542, 536830309, 210044539, 658543529, 570462533, 315248378, 787872853, 414515421, 584178999, 918434489, 494929045, 531589333, 749070693, 590811263, 542463448, 802053114, 744931388, 776549469, 296803962, 955881753, 119730756, 467266996, 91936328], [557043278, 249911262, 570695018, 324503915, 299410985, 286661213, 739234500, 669458549, 968271575, 719157984, 978221441, 125438539, 488891604, 735277967, 585750459, 458980942, 993847462, 104142366, 458927241, 101751392, 349942297, 367644246, 150529196, 392667180, 488298256, 123032496, 164829025, 186599559, 13331555, 49632194, 857156202, 902771235, 785647102, 797428236, 401668241, 755220697, 52462450, 25529088, 425423860, 781003336, 825120363, 479246965, 966018270, 804275673, 583861575, 844212416, 661155825, 986413285, 502120462, 480544108, 339233223, 472704550, 599355493, 445014578, 854892805, 837937817, 719856555, 403560307], [477391927, 530714530, 283840307, 156656995, 328920117, 997730069, 163759724, 398893932, 361083741, 103458275, 653649807, 530983198, 775362916, 42388419, 11053956, 800934580, 225647276, 273754600, 278630788, 2331641, 863685020, 946328857, 160664276, 653403477, 753782528, 715693575, 293390860, 482017113, 583807607, 618351190, 434317028, 186900866, 289640690, 746817752, 219902814, 73958093, 866314562, 88857899, 930430069, 259776685, 325871235, 276891494, 835599514, 314484890, 482062836, 963906785, 315315343, 761155610, 993961479, 570904359, 425693471, 182155974, 413592733, 26185106, 978848144, 866777409, 839667609, 40888676], [434105605, 495383378, 755891534, 891084525, 788042408, 574698731, 484792252, 583962089, 132172456, 298364684, 344829144, 819755987, 448631238, 501184485, 550036882, 954359448, 302791927, 242055441, 188591565, 153030094, 71019226, 488232123, 316186507, 455724173, 390518675, 704179977, 228790461, 750080345, 980841531, 634450242, 504962059, 739012833, 647963907, 743248498, 298981900, 389898435, 433926661, 83987705, 83236132, 970252814, 836608606, 304426258, 145247374, 609657053, 56259577, 839466215, 590011873, 497762245, 148494551, 654446475, 114966222, 895593710, 401167108, 809574008, 732692532, 595927138, 763422927, 856963104], [753692628, 460968702, 269750003, 332333946, 923043819, 322929086, 580105281, 659858079, 605541597, 834113115, 405052339, 256693594, 875669898, 982131111, 641730793, 697151282, 649979173, 699673869, 694276091, 534221166, 245992048, 31762427, 138848853, 463267988, 631611821, 370057910, 214767807, 730419748, 796504221, 248441480, 801709322, 891226919, 341858709, 991457430, 972272523, 89810780, 558990170, 25427353, 643821736, 881737359, 358553099, 326483454, 780521857, 923681481, 553945419, 969846792, 425237853, 931196203, 171684678, 374091043, 26840529, 851410104, 982406916, 517116547, 77942844, 551619895, 258175757, 931765581], [891090918, 968586763, 908390262, 947150450, 880027863, 993561230, 44531085, 861417764, 939537688, 960798349, 919057701, 112552355, 321797607, 851366894, 314027171, 246599771, 639632984, 790835173, 370362918, 183027752, 783209100, 586698542, 917943418, 341026117, 289739124, 87822789, 292831015, 853983632, 139990847, 405797359, 848997245, 959264878, 375851176, 895413193, 431049351, 53458452, 621171691, 44820690, 136519032, 712406892, 69782028, 728244020, 966537630, 365598195, 737936426, 979714001, 555249076, 941825346, 467229909, 171502417, 783158130, 45410736, 757562499, 629638237, 761697522, 647021307, 926387421, 166829543], [366487211, 7125267, 268984417, 665344480, 825826025, 944595493, 882994487, 737618957, 167920775, 229232288, 225585846, 954148195, 999562261, 687061118, 117680410, 115008697, 922947078, 288300987, 43578702, 745225760, 196073792, 341714654, 97391036, 944569248, 571054728, 75882902, 497120589, 303161659, 710850157, 93413135, 838774858, 334599383, 986188706, 942987608, 709400668, 205699196, 838738987, 3398800, 828357790, 797059937, 805677321, 585442755, 941258952, 910536436, 994432384, 822780688, 913598818, 582645615, 886865425, 935665452, 609861504, 269610197, 528430847, 190653736, 359032900, 970560029, 802483393, 477962476], [744662708, 81714049, 326106357, 524342049, 2907585, 167490837, 945308614, 859143843, 332610480, 914882497, 51382473, 226111907, 710447887, 764139141, 198789389, 906963044, 492000823, 899200394, 172850328, 375847309, 587950206, 896983799, 596027294, 73686028, 870839267, 451341421, 670788490, 459270132, 910751965, 141946179, 366921690, 131884242, 409907996, 887449841, 936430106, 306904970, 925089854, 31225435, 486143869, 949954524, 213823245, 924134850, 496998589, 850103645, 914241625, 369422899, 148532188, 298301793, 495658062, 269176269, 320334213, 377122700, 433356568, 421417049, 528775543, 272312768, 256724459, 931269157], [839477360, 461637954, 365580958, 196089231, 800885614, 681462132, 166851103, 36477173, 559570287, 984467283, 537550494, 836053123, 847204833, 583182050, 144712225, 888341600, 293867851, 52577310, 484139251, 20469819, 85048654, 390745469, 712398126, 627989064, 941731541, 612360137, 66208388, 16304701, 657520221, 236860071, 284343202, 412417763, 177371289, 716924410, 797668040, 355025879, 505346002, 191887845, 163557229, 648136129, 617007551, 876825051, 478107753, 726131884, 259567755, 53952883, 848683058, 8655886, 199803101, 878157166, 682217304, 546881559, 31468621, 943272477, 403864067, 273949202, 782138968, 548447757], [155552079, 162897529, 781642616, 427659020, 649242798, 26688933, 504556277, 91641966, 74599461, 831643461, 930199831, 99169522, 449269983, 154905939, 230408611, 69978027, 395894483, 725751163, 416207230, 86813623, 104441613, 835534029, 788281777, 762277510, 804549201, 831278763, 455855980, 832844947, 816615083, 574048924, 898909553, 148102330, 480746408, 820416906, 777925729, 56873296, 96612323, 778033772, 105462007, 922069524, 519991895, 629449929, 785485083, 454301182, 823629219, 191348515, 154844661, 650363126, 232886452, 909003670, 741029241, 698604775, 634567229, 114711023, 514670670, 874149686, 437498199, 459341839], [565976554, 17692619, 710680848, 261604, 644530237, 871770238, 733421284, 93762027, 174534037, 692241542, 517697345, 851050983, 804001874, 8815200, 525425894, 773398486, 212625711, 439237648, 401924559, 841119922, 596676539, 718236822, 210673373, 574396693, 462376047, 680324488, 201238987, 572677965, 462594882, 938774864, 193431471, 530903135, 929542250, 877056698, 749976459, 130077031, 506800269, 278828653, 773747620, 644935043, 775268751, 811158309, 609192363, 266642558, 155116518, 670655186, 34982203, 448628390, 853302513, 636465073, 327599670, 444902764, 896786844, 631252546, 495820177, 990472432, 743129247, 741558949], [774313419, 480184944, 893552095, 142863721, 163225938, 612978973, 653257088, 941346437, 944956348, 438270509, 369635430, 489625734, 746769180, 895610288, 16384010, 138791977, 879274346, 770401284, 810052769, 372469784, 707973864, 219440218, 911636771, 179393163, 205512521, 884327273, 212399209, 585803642, 238577820, 211246360, 932787658, 596979618, 609364846, 242838971, 902426374, 560815401, 662084699, 959703208, 461548120, 610956484, 372934944, 189218527, 726476658, 547622701, 862526067, 765837615, 868001019, 488850877, 892285729, 923778436, 968832609, 909090822, 641154669, 968130181, 308913346, 251339687, 876943937, 541566763], [609325845, 630427772, 100152465, 620641483, 992969909, 565518799, 580963781, 536470578, 883752485, 816079463, 761921679, 631469667, 613716773, 733533043, 892334884, 535798893, 295823916, 164900701, 932263920, 228809448, 209328128, 546547124, 658916600, 280561131, 856146275, 950614236, 487725837, 19481665, 617350076, 982821541, 371831389, 985012408, 570499772, 217640140, 462421319, 741371579, 565040244, 649254650, 421230209, 248248173, 274145444, 985119919, 619389894, 757074145, 597567618, 635782893, 377023217, 776799105, 470792810, 491807797, 671690199, 429703280, 820641828, 293494215, 779861751, 656226860, 132702749, 653862468], [342324888, 268289801, 29020016, 39502332, 713751978, 142492078, 982859975, 991783176, 822183540, 432234425, 343660972, 944062684, 818507390, 52735141, 742903999, 516245816, 187950953, 253506267, 402271823, 423297133, 201151928, 976765527, 235427454, 729387144, 397108345, 361296073, 956418804, 651291451, 705326156, 194282904, 442270000, 253599874, 77334161, 98209325, 51264975, 362333921, 902885358, 280619742, 807880666, 169075264, 805540404, 562930234, 238146053, 479344506, 107127399, 420076099, 260358557, 867073240, 278789174, 307468291, 458432314, 102641544, 687047976, 998356644, 201829448, 544173087, 988039948, 19188571], [61074168, 518893890, 629435722, 590665391, 669102049, 863335607, 987656416, 927934782, 5823315, 126694167, 193405320, 177350331, 384960632, 78717208, 865201259, 882938394, 66088355, 887618086, 448403447, 149294985, 247211923, 253317994, 555754947, 169894842, 758331546, 676907142, 96975125, 740187393, 541932428, 387009156, 856847129, 593374658, 508354780, 236675082, 860934242, 980850298, 918787104, 891471286, 778955899, 496904718, 316893444, 3529955, 408424311, 901906359, 724617766, 539598503, 580995326, 182135292, 810485372, 101635623, 266765274, 436765910, 460402826, 192935679, 862703425, 276448967, 421575161, 366750736], [932531326, 454130794, 331481570, 430813366, 101700365, 565087365, 562317124, 332461611, 822833243, 869717731, 18921358, 743241383, 756744680, 687941012, 934122100, 550135915, 534180313, 462889698, 584627025, 461956311, 158795257, 179002216, 84585699, 953761225, 942528918, 552449837, 490850739, 745438931, 508016986, 766576466, 712549489, 448829320, 871634522, 68206196, 6661278, 815551897, 363248872, 198306854, 314356079, 258487912, 469715268, 466668687, 28900080, 738009616, 650583220, 252709220, 994601962, 121352462, 140093668, 68325315, 565795155, 683021494, 112193685, 642843260, 861748063, 473947018, 569827569, 15641217], [123377169, 924049605, 304188528, 750134511, 552548368, 792526030, 496332186, 138568706, 411303706, 449260223, 807400676, 551503382, 480157131, 554418708, 171904111, 507770535, 799631711, 486455270, 524400516, 136421330, 221777031, 878666335, 675621898, 51350180, 83880632, 755340234, 887223789, 341706166, 336199686, 555135139, 903740, 809791450, 966799249, 403174669, 468675146, 159846344, 244908034, 743636101, 239561868, 592183908, 573497446, 628483126, 796640297, 618524369, 753849779, 453418748, 207405398, 35518110, 918509417, 370828483, 828697204, 493030038, 953208726, 167775636, 101313428, 780269860, 367302052, 290889673], [208427077, 37817494, 576135383, 292705955, 577041605, 842938309, 716920706, 950003238, 849458452, 667714503, 451076779, 187055531, 404160841, 322158472, 222316582, 580279665, 637661175, 751028252, 204900387, 581507681, 881938183, 920647732, 814449805, 833193586, 282638488, 612526426, 803536218, 400956265, 802867943, 672195341, 172089123, 626305885, 939988044, 457005677, 356833619, 855708774, 629082320, 673923945, 525964574, 531441585, 831471601, 293699577, 215840763, 131462799, 40303670, 214772561, 648159268, 868498236, 921979922, 911886932, 478240206, 361351965, 379201504, 317161073, 20637302, 139276941, 914977429, 894931560], [213645902, 908927245, 735453088, 620838530, 96794374, 516900509, 34733846, 450411069, 290581685, 336946483, 55906656, 684038778, 421641507, 801030508, 545196593, 190995514, 779285513, 479822404, 505980635, 232933267, 318259733, 142598359, 257288585, 334020220, 641735732, 917702548, 52720512, 186792126, 696238452, 156755749, 461668091, 662826866, 263359295, 863802561, 912124758, 89066918, 921254247, 49482595, 873540752, 913167609, 734432387, 42422865, 781419100, 84469026, 823786558, 214645959, 763575153, 382951702, 893680259, 793888667, 542152618, 387864187, 678604793, 462310207, 660992381, 565792801, 693422712, 635224355], [863045605, 307242922, 311313253, 763656283, 57396610, 81766262, 903607051, 594491352, 201020633, 669364548, 5264211, 963427882, 285513864, 860375960, 308562838, 748194945, 291704873, 528323647, 298449375, 848694292, 384750166, 941203891, 951212379, 439089959, 236568366, 542360856, 695265398, 965816566, 593688010, 677680099, 551957486, 366161507, 471827305, 436329846, 761396999, 989059577, 994280438, 888893769, 365696052, 717157255, 884809066, 242903324, 756361609, 76635151, 252844425, 778395485, 954069463, 927348184, 536904300, 667333522, 365229066, 713587077, 625444911, 785902539, 785545418, 334100689, 699835745, 551015504], [653342195, 234252170, 744784995, 636646774, 951433564, 131971367, 899314745, 418841779, 969273258, 220504670, 842320413, 907071824, 490314405, 943709966, 757047, 798598680, 962423411, 836274370, 229321354, 276352930, 859619277, 956788284, 16334335, 218809157, 911232227, 29219825, 669270115, 565132529, 103387224, 562367056, 878902606, 91474522, 441508248, 119072259, 342655772, 46979034, 485598393, 251720916, 195600984, 873607563, 938097480, 866783790, 786845691, 466383067, 252963583, 191452864, 899562061, 52126850, 254048879, 479750429, 127128630, 186098471, 358923006, 729336368, 170933189, 362135840, 936027326, 757708230], [942812818, 26676171, 458690094, 109144632, 12803911, 118257757, 925619197, 634458117, 352079090, 298901620, 202689717, 183031667, 915447154, 450825909, 174096866, 175879530, 480259363, 457555459, 617360441, 918861453, 174111017, 519128490, 629317453, 89935061, 46741343, 856237850, 404233987, 130124924, 487832066, 623238799, 919099347, 177610231, 656490581, 454270764, 428563732, 309874943, 943080956, 500756131, 199980501, 808170867, 376530418, 49583450, 470274894, 208000465, 79402906, 212651432, 453726341, 420504435, 884813142, 615011001, 82832884, 779942218, 263593545, 287065942, 595727476, 360749854, 227112431, 816871950], [344289859, 148830904, 569104164, 215575115, 9089763, 944834623, 587936622, 460479153, 884492837, 871241560, 170097504, 850071299, 71999751, 273791558, 919919794, 824854842, 760608455, 198090498, 613572015, 177921834, 698194450, 775874256, 840630278, 466915734, 631302309, 938367569, 809591260, 9252741, 648648629, 123460602, 997414130, 582154596, 516115877, 65083759, 485065553, 18640197, 538108682, 801397193, 50451650, 60230567, 297291406, 184403349, 774836587, 200408376, 242604417, 609990204, 772460897, 807359866, 863524183, 660993810, 885896724, 360355279, 390529666, 563784400, 798870998, 878054423, 43945188, 187509373], [66916085, 224179343, 250463056, 16661671, 187974031, 795267267, 726875525, 941881173, 862487125, 645192750, 572026513, 320298599, 202956111, 996368889, 19535609, 104656302, 548446969, 418828182, 423061215, 512804425, 220125158, 12474400, 629746805, 865807173, 883716503, 344236778, 565852588, 353585871, 579774664, 600165261, 931321520, 979770121, 978616395, 756911301, 922301279, 687617694, 120414309, 295999475, 748349236, 964144580, 474626338, 795757236, 529981635, 270170726, 879984909, 582305558, 992521377, 395592286, 562403727, 593717365, 514352558, 127841545, 927228696, 304497822, 37003399, 681696526, 621942552, 47990640], [483678157, 876528559, 632080908, 371432180, 243719806, 630297108, 850569136, 419094980, 490730007, 910934064, 865162154, 524227881, 441429453, 403089272, 54647246, 693757358, 812061389, 246980664, 117202197, 627201600, 282666375, 624925835, 829572637, 840401164, 431718895, 243012076, 690279218, 574753739, 222338951, 924016160, 250647188, 621397441, 460286747, 832123459, 964926820, 698734229, 726463959, 426781190, 35728749, 933877942, 226193204, 230013229, 888598673, 296825636, 919237366, 997723445, 153559306, 564222320, 544783156, 641250297, 810277906, 34089752, 539926224, 24202416, 146479986, 859208926, 335920551, 369888201], [847375647, 703547212, 44290734, 463744621, 82446906, 63932365, 71204190, 790731628, 908280884, 608132245, 285639580, 73843909, 268410307, 142486965, 915286655, 980522510, 706745973, 517086881, 874492674, 714567344, 299995759, 145159667, 390468642, 314419443, 272747656, 140863614, 947231729, 376518838, 915461567, 163058993, 279444887, 425614417, 565575058, 466658608, 487301104, 821263086, 13881779, 519081733, 849052465, 908479850, 300183124, 950016835, 896743630, 766438701, 500087168, 948687890, 276515984, 666550482, 95416581, 245422757, 565020302, 909650719, 417252308, 269741348, 911460032, 141928179, 480830050, 795561031], [994318789, 214792772, 696056294, 594368323, 77536699, 933258921, 639836187, 21640147, 929066, 807451553, 425488243, 808644636, 967136168, 846828819, 409921599, 491347295, 122546568, 63106819, 306228392, 650118350, 257194333, 63643445, 406860854, 16197407, 958105863, 84959071, 991748263, 529018360, 99086810, 962107839, 273315456, 257669971, 87108076, 306063779, 540295438, 484280202, 385704962, 170327164, 310959676, 524628029, 194754044, 428786609, 645024971, 942714643, 772636922, 817950764, 700857573, 935599327, 670120251, 922229566, 523822283, 635086710, 949586949, 443110125, 732022936, 635480098, 315823102, 315244582], [519545678, 628706911, 308680194, 430740343, 915273244, 171125078, 692009152, 698232034, 26029965, 549547770, 221471852, 323209902, 728259935, 340770180, 42729616, 675469621, 709393041, 738251285, 886920245, 553503318, 844609239, 450878459, 365121767, 4523028, 44055271, 740823494, 389775784, 526847537, 238293307, 859324571, 62759261, 213114889, 548675180, 646050489, 367508574, 12480114, 98995497, 122267083, 37131593, 177840291, 846009834, 10078208, 433712794, 487918895, 198538720, 551173387, 237980168, 277296291, 397056562, 604663923, 64087337, 314339011, 896068667, 522151964, 118241347, 752311695, 980824122, 588400911], [718035449, 605579598, 914120204, 78374562, 935583147, 825630159, 891466165, 623923470, 397294267, 801700915, 817306510, 437116437, 144950232, 956730719, 290566056, 784380011, 204405722, 380531122, 767059803, 589918012, 432380826, 803928405, 116692061, 691879240, 746723209, 386378927, 223944220, 607641237, 974792231, 609461826, 311535896, 97200501, 887030120, 289440113, 382504496, 144008224, 420179560, 325648897, 278407532, 503264714, 790334319, 433213000, 709034067, 151149127, 786907824, 1329789, 419769821, 770721176, 803262111, 359210190, 76226308, 95004786, 317157768, 270689249, 289778030, 701711653, 382944027, 142849943], [793861679, 849464528, 630166881, 221372384, 404582126, 462285171, 712529065, 36805385, 398908557, 59039730, 814038245, 929442752, 778187913, 123383737, 667927796, 747739319, 752659794, 891970802, 167024073, 541898996, 174473161, 908524241, 802662248, 186115716, 626402204, 593973674, 147618389, 277082348, 773344158, 401302124, 263479925, 820258995, 817303366, 488061027, 879950192, 186120959, 16794825, 275977855, 227465046, 706002912, 716666834, 535767598, 186751204, 257927565, 799268742, 853538569, 967917280, 655742917, 50583159, 874044018, 317917841, 99938548, 355991243, 858674173, 793062947, 594526107, 320399187, 495758875], [278245687, 515064184, 348603706, 532922855, 308536976, 26359087, 41424141, 913585829, 680272944, 182172720, 154841402, 677357190, 523883668, 54506568, 50204441, 771898084, 192977115, 815879141, 162243794, 387555651, 464557076, 316337628, 78724387, 293176323, 330205205, 273218674, 24963875, 265600326, 404662717, 41950162, 947475210, 277081781, 142775223, 686534000, 61190719, 771914767, 767150560, 480581907, 214297657, 805355926, 593508910, 884405175, 433232717, 610730299, 730285010, 187780629, 298992294, 240991998, 818519478, 387843401, 117794448, 394058216, 243386509, 581673491, 429459379, 806914386, 499316238, 835385532], [809311691, 603798028, 490651249, 751171463, 747122818, 930339755, 355492580, 459143764, 445849086, 412993270, 350730915, 427720750, 375312812, 676750395, 739080809, 392782859, 490782861, 434441874, 291519111, 375791442, 286736227, 29293900, 483884177, 924658571, 81302474, 16792326, 245694084, 876873754, 162998235, 2366406, 421054458, 137859783, 842906747, 869449181, 486489816, 224923673, 578869884, 986371927, 882661389, 927775682, 465627857, 726188325, 977547649, 915653991, 159022330, 881821796, 780542416, 309831350, 887483667, 644062431, 652065803, 753358831, 33946067, 137978847, 582203432, 38219943, 437321483, 539311331], [316900274, 389332904, 609188349, 460833804, 352597152, 444088542, 396662747, 652335959, 912647992, 360610862, 832937047, 910728265, 696910162, 64460980, 71516075, 163532661, 575970114, 450692352, 667520562, 594847078, 311382526, 232989863, 227592276, 171138740, 365512669, 48223433, 148492506, 479413408, 110257823, 521843091, 713848212, 818138322, 828766710, 555538608, 388070642, 408114742, 230760967, 587504939, 507588017, 244630342, 130418722, 382929363, 349182539, 532650369, 439759, 240039813, 847871972, 624977260, 915452722, 331078680, 923842685, 427643712, 758121956, 366051360, 385128594, 424885191, 122794011, 601459251], [969648710, 140531707, 328761714, 281164379, 195633298, 872396447, 930748849, 640677986, 869957890, 877740431, 449521741, 210166, 932069995, 512023322, 987084081, 615064538, 1471496, 443652558, 433397535, 914097566, 530839557, 47388474, 607801392, 855516911, 833943190, 970607025, 276165221, 899871064, 791562057, 349504906, 980177687, 293876196, 972587279, 362325987, 501294236, 751030757, 855849084, 623450951, 649834014, 725792589, 792239477, 671806602, 188451833, 278900799, 146045379, 756734248, 626346100, 771345380, 542810428, 390931871, 478291220, 534960963, 734522420, 571633688, 504518509, 178394054, 668094166, 266699748]])) + +test5 :: Test +test5 = TestCase (assertEqual "for (maximumScore [[875112416, 225880896, 894426184, 993651704, 665107967, 932701064, 193356463, 312533013, 824444608, 648237147, 108336884, 28855202, 218012358, 29642254, 461486235, 545765348, 694395216, 229535591, 568534773, 246030647, 236319982, 444300501, 555949437, 341637570, 818353737, 460364580], [28743043, 916581094, 197402210, 352762453, 619691153, 971211330, 845440458, 363929300, 94770617, 964607981, 279887998, 64669462, 861382344, 697738505, 476635042, 416110405, 826457758, 327159049, 648579347, 377743671, 765055596, 298842140, 689651787, 223638269, 175393528, 70367026], [231875511, 57149252, 447405111, 363472878, 334741160, 876015046, 821602588, 147033574, 885224994, 489843185, 646317660, 246085765, 996801649, 510888821, 801772852, 517316591, 670841131, 791044340, 287405065, 841154106, 737381928, 487069093, 20935376, 713076146, 940220361, 388858677], [32711592, 467297801, 971241652, 678990178, 927627689, 145261941, 905061459, 39147911, 522060304, 145569415, 354804930, 235754579, 375667285, 972200797, 660161683, 809162109, 374270650, 199940824, 913326075, 492383359, 156048777, 358528379, 469758245, 412149230, 479412782, 117322302], [421912218, 75109462, 582287837, 280205062, 39242155, 229470489, 164781166, 431905260, 249462219, 735915091, 394625107, 195571355, 405970942, 805538801, 379349611, 161441099, 451498447, 554502660, 335332609, 738138357, 127958888, 361452388, 545743827, 70116651, 899607298, 19244718], [111563637, 455076567, 653306103, 651146642, 381271140, 561130054, 286289678, 890020052, 609499076, 81260846, 779510188, 534690533, 706572766, 846262153, 869198569, 808902485, 162982472, 816560557, 411721048, 700468399, 806164100, 599747227, 699141241, 363298233, 915482063, 762592449], [755972709, 61318641, 214677029, 997661434, 325208303, 203629452, 297722199, 705690771, 286192988, 351917383, 318127823, 696559111, 711205264, 221665049, 307863811, 687019003, 125943114, 604670954, 782346379, 181564162, 945912844, 488226725, 186919460, 51619505, 112438182, 923618519], [694637595, 70266236, 32469586, 112448428, 463536626, 551219348, 233304735, 207825016, 613214632, 756275083, 353806088, 807535512, 772190528, 282251411, 821411940, 973298820, 879000518, 210989377, 507284020, 310701430, 339554287, 220581179, 195307374, 760984989, 971388324, 388051703], [371840076, 819068192, 692313035, 962594057, 438083192, 974077119, 201768981, 827231129, 31493780, 942764910, 667959843, 256598101, 404880449, 29528916, 253720365, 375366846, 517058250, 701707801, 504363349, 138119811, 579683117, 965737762, 361011906, 734994532, 576625323, 941016722], [699951700, 90113999, 364622817, 365782474, 763451652, 461673409, 58107324, 631964134, 688922648, 107789170, 698803645, 493627290, 22204220, 195192077, 786401270, 626505537, 54483819, 39589520, 407115145, 465286060, 89679602, 821724377, 829552575, 961727544, 82229748, 664487838], [946531237, 657776580, 247007183, 269579677, 266160835, 64318119, 193100079, 192438993, 368024467, 317192029, 915567097, 192574122, 746716579, 851504429, 761918788, 673851307, 149153776, 405017703, 445259080, 475457397, 101914098, 857815824, 545587224, 795925958, 604353855, 368126884], [657810295, 178301880, 717543341, 504336072, 995333301, 26339568, 761929510, 948898860, 553952, 217784671, 397841150, 796912510, 281289707, 132933354, 774682160, 192466130, 606018250, 573171254, 94851416, 8572727, 656473936, 290410289, 599554375, 477304175, 995179674, 450576066], [364303631, 6472819, 578799794, 922649065, 350444378, 333557140, 461059881, 19484130, 640839674, 938049694, 25452857, 260719426, 406138136, 474335393, 791343886, 91533186, 926388252, 111999969, 281016185, 342173716, 718784697, 815575309, 478276178, 619830401, 596837107, 682988770], [152926036, 822855077, 81556944, 243011877, 188641592, 509461182, 919433328, 333881636, 673376139, 389158569, 171149527, 420497841, 724912935, 10843667, 265119629, 510053111, 895511860, 982700506, 600481075, 166300817, 878928838, 565964853, 858293919, 541886604, 650450024, 697868135], [122814407, 656856418, 665665608, 450642727, 37236395, 675397979, 534435862, 502330031, 107445215, 484681960, 990991350, 670676391, 455859734, 17367455, 154710638, 9143707, 454243048, 707743124, 291274117, 411923458, 322498136, 727368313, 366508695, 246733097, 606871771, 179923445], [901985708, 858906591, 38487465, 512205949, 775577245, 832872073, 298636045, 581731618, 409064142, 924893968, 223894302, 843276573, 360530407, 82329480, 145046520, 146702490, 163229478, 437310410, 357218482, 523464793, 198099237, 117252197, 667452000, 126909891, 361988608, 746753537], [514406784, 199001394, 101423618, 15615669, 45426854, 13146348, 675370662, 199261871, 240684340, 528356078, 73746124, 175154695, 134176798, 265192375, 120020620, 398324362, 981587909, 625589564, 221110919, 144651426, 140580224, 12357895, 872568824, 73437132, 609544352, 888821550], [264766966, 64920055, 794623714, 918441216, 933257546, 319944626, 60034726, 426567694, 435039545, 294662886, 10304689, 541667595, 146557635, 102921631, 760845372, 887035777, 827773147, 871589908, 28618659, 304057937, 292196214, 926231010, 314390952, 769467750, 899090880, 717445652], [727449010, 392361397, 912781505, 255057448, 204465973, 330120602, 120459434, 714174973, 431394768, 462025909, 265292489, 552911829, 937154838, 256119404, 748110927, 142784589, 577524892, 620474240, 661663439, 75784223, 792924048, 911491749, 789896983, 74330200, 424142648, 80982504], [92067014, 532227129, 560282125, 503785184, 603755044, 581244958, 899802447, 196660330, 223462502, 703604483, 455587602, 10466966, 427395540, 121784720, 143145548, 292978592, 606198460, 267837805, 519432450, 842935884, 117426218, 43591247, 111996814, 93310821, 119648250, 776069494], [669182223, 559461269, 105397424, 507813010, 903371882, 649475939, 385916631, 966895640, 488668063, 937234728, 871382348, 129619792, 619525, 532156241, 425836498, 271876812, 214571469, 16753689, 345464800, 103148846, 57844031, 762090458, 851172330, 962362729, 971383896, 251743055], [727172152, 21255364, 402498789, 147418750, 295887125, 17388260, 682240749, 371445091, 407950115, 441143379, 434826171, 767634315, 502696278, 765903716, 114222284, 464215726, 286785394, 59993260, 74823914, 6572331, 259821348, 642358070, 168649912, 462977831, 854633074, 567738662], [425335539, 645513480, 97828422, 381798621, 86486998, 93498914, 137356346, 199524529, 9526899, 305282544, 501007337, 811816742, 164530062, 938410050, 878217472, 626027368, 885579968, 726647866, 603275348, 823930200, 76317673, 516665203, 847409263, 311200445, 500230992, 309751492], [263566440, 603550478, 520424813, 835014383, 738304475, 725966396, 226526086, 568374069, 261438651, 763137494, 286515578, 921988608, 384427194, 158911684, 227079012, 15002335, 180107217, 12184703, 743021432, 994753293, 556619459, 699478062, 988968922, 521725821, 580160442, 444359333], [474225118, 484278398, 299421019, 893029789, 239086550, 749032261, 661752420, 467140899, 205994492, 450562089, 831957137, 946746619, 456405680, 781468029, 917164012, 921105401, 922067079, 531991269, 110787391, 323700064, 936896389, 973899008, 222110066, 452408684, 553270241, 171306955], [628256820, 805461699, 818782463, 38351156, 975311877, 748319533, 892357589, 238939167, 762637039, 960521784, 381676645, 63673330, 449303132, 941591583, 798757413, 510766529, 386964455, 7575996, 167122218, 582215165, 123808823, 223948312, 705605561, 993159380, 602842533, 425279771]])," 211805607998 (maximumScore [[875112416, 225880896, 894426184, 993651704, 665107967, 932701064, 193356463, 312533013, 824444608, 648237147, 108336884, 28855202, 218012358, 29642254, 461486235, 545765348, 694395216, 229535591, 568534773, 246030647, 236319982, 444300501, 555949437, 341637570, 818353737, 460364580], [28743043, 916581094, 197402210, 352762453, 619691153, 971211330, 845440458, 363929300, 94770617, 964607981, 279887998, 64669462, 861382344, 697738505, 476635042, 416110405, 826457758, 327159049, 648579347, 377743671, 765055596, 298842140, 689651787, 223638269, 175393528, 70367026], [231875511, 57149252, 447405111, 363472878, 334741160, 876015046, 821602588, 147033574, 885224994, 489843185, 646317660, 246085765, 996801649, 510888821, 801772852, 517316591, 670841131, 791044340, 287405065, 841154106, 737381928, 487069093, 20935376, 713076146, 940220361, 388858677], [32711592, 467297801, 971241652, 678990178, 927627689, 145261941, 905061459, 39147911, 522060304, 145569415, 354804930, 235754579, 375667285, 972200797, 660161683, 809162109, 374270650, 199940824, 913326075, 492383359, 156048777, 358528379, 469758245, 412149230, 479412782, 117322302], [421912218, 75109462, 582287837, 280205062, 39242155, 229470489, 164781166, 431905260, 249462219, 735915091, 394625107, 195571355, 405970942, 805538801, 379349611, 161441099, 451498447, 554502660, 335332609, 738138357, 127958888, 361452388, 545743827, 70116651, 899607298, 19244718], [111563637, 455076567, 653306103, 651146642, 381271140, 561130054, 286289678, 890020052, 609499076, 81260846, 779510188, 534690533, 706572766, 846262153, 869198569, 808902485, 162982472, 816560557, 411721048, 700468399, 806164100, 599747227, 699141241, 363298233, 915482063, 762592449], [755972709, 61318641, 214677029, 997661434, 325208303, 203629452, 297722199, 705690771, 286192988, 351917383, 318127823, 696559111, 711205264, 221665049, 307863811, 687019003, 125943114, 604670954, 782346379, 181564162, 945912844, 488226725, 186919460, 51619505, 112438182, 923618519], [694637595, 70266236, 32469586, 112448428, 463536626, 551219348, 233304735, 207825016, 613214632, 756275083, 353806088, 807535512, 772190528, 282251411, 821411940, 973298820, 879000518, 210989377, 507284020, 310701430, 339554287, 220581179, 195307374, 760984989, 971388324, 388051703], [371840076, 819068192, 692313035, 962594057, 438083192, 974077119, 201768981, 827231129, 31493780, 942764910, 667959843, 256598101, 404880449, 29528916, 253720365, 375366846, 517058250, 701707801, 504363349, 138119811, 579683117, 965737762, 361011906, 734994532, 576625323, 941016722], [699951700, 90113999, 364622817, 365782474, 763451652, 461673409, 58107324, 631964134, 688922648, 107789170, 698803645, 493627290, 22204220, 195192077, 786401270, 626505537, 54483819, 39589520, 407115145, 465286060, 89679602, 821724377, 829552575, 961727544, 82229748, 664487838], [946531237, 657776580, 247007183, 269579677, 266160835, 64318119, 193100079, 192438993, 368024467, 317192029, 915567097, 192574122, 746716579, 851504429, 761918788, 673851307, 149153776, 405017703, 445259080, 475457397, 101914098, 857815824, 545587224, 795925958, 604353855, 368126884], [657810295, 178301880, 717543341, 504336072, 995333301, 26339568, 761929510, 948898860, 553952, 217784671, 397841150, 796912510, 281289707, 132933354, 774682160, 192466130, 606018250, 573171254, 94851416, 8572727, 656473936, 290410289, 599554375, 477304175, 995179674, 450576066], [364303631, 6472819, 578799794, 922649065, 350444378, 333557140, 461059881, 19484130, 640839674, 938049694, 25452857, 260719426, 406138136, 474335393, 791343886, 91533186, 926388252, 111999969, 281016185, 342173716, 718784697, 815575309, 478276178, 619830401, 596837107, 682988770], [152926036, 822855077, 81556944, 243011877, 188641592, 509461182, 919433328, 333881636, 673376139, 389158569, 171149527, 420497841, 724912935, 10843667, 265119629, 510053111, 895511860, 982700506, 600481075, 166300817, 878928838, 565964853, 858293919, 541886604, 650450024, 697868135], [122814407, 656856418, 665665608, 450642727, 37236395, 675397979, 534435862, 502330031, 107445215, 484681960, 990991350, 670676391, 455859734, 17367455, 154710638, 9143707, 454243048, 707743124, 291274117, 411923458, 322498136, 727368313, 366508695, 246733097, 606871771, 179923445], [901985708, 858906591, 38487465, 512205949, 775577245, 832872073, 298636045, 581731618, 409064142, 924893968, 223894302, 843276573, 360530407, 82329480, 145046520, 146702490, 163229478, 437310410, 357218482, 523464793, 198099237, 117252197, 667452000, 126909891, 361988608, 746753537], [514406784, 199001394, 101423618, 15615669, 45426854, 13146348, 675370662, 199261871, 240684340, 528356078, 73746124, 175154695, 134176798, 265192375, 120020620, 398324362, 981587909, 625589564, 221110919, 144651426, 140580224, 12357895, 872568824, 73437132, 609544352, 888821550], [264766966, 64920055, 794623714, 918441216, 933257546, 319944626, 60034726, 426567694, 435039545, 294662886, 10304689, 541667595, 146557635, 102921631, 760845372, 887035777, 827773147, 871589908, 28618659, 304057937, 292196214, 926231010, 314390952, 769467750, 899090880, 717445652], [727449010, 392361397, 912781505, 255057448, 204465973, 330120602, 120459434, 714174973, 431394768, 462025909, 265292489, 552911829, 937154838, 256119404, 748110927, 142784589, 577524892, 620474240, 661663439, 75784223, 792924048, 911491749, 789896983, 74330200, 424142648, 80982504], [92067014, 532227129, 560282125, 503785184, 603755044, 581244958, 899802447, 196660330, 223462502, 703604483, 455587602, 10466966, 427395540, 121784720, 143145548, 292978592, 606198460, 267837805, 519432450, 842935884, 117426218, 43591247, 111996814, 93310821, 119648250, 776069494], [669182223, 559461269, 105397424, 507813010, 903371882, 649475939, 385916631, 966895640, 488668063, 937234728, 871382348, 129619792, 619525, 532156241, 425836498, 271876812, 214571469, 16753689, 345464800, 103148846, 57844031, 762090458, 851172330, 962362729, 971383896, 251743055], [727172152, 21255364, 402498789, 147418750, 295887125, 17388260, 682240749, 371445091, 407950115, 441143379, 434826171, 767634315, 502696278, 765903716, 114222284, 464215726, 286785394, 59993260, 74823914, 6572331, 259821348, 642358070, 168649912, 462977831, 854633074, 567738662], [425335539, 645513480, 97828422, 381798621, 86486998, 93498914, 137356346, 199524529, 9526899, 305282544, 501007337, 811816742, 164530062, 938410050, 878217472, 626027368, 885579968, 726647866, 603275348, 823930200, 76317673, 516665203, 847409263, 311200445, 500230992, 309751492], [263566440, 603550478, 520424813, 835014383, 738304475, 725966396, 226526086, 568374069, 261438651, 763137494, 286515578, 921988608, 384427194, 158911684, 227079012, 15002335, 180107217, 12184703, 743021432, 994753293, 556619459, 699478062, 988968922, 521725821, 580160442, 444359333], [474225118, 484278398, 299421019, 893029789, 239086550, 749032261, 661752420, 467140899, 205994492, 450562089, 831957137, 946746619, 456405680, 781468029, 917164012, 921105401, 922067079, 531991269, 110787391, 323700064, 936896389, 973899008, 222110066, 452408684, 553270241, 171306955], [628256820, 805461699, 818782463, 38351156, 975311877, 748319533, 892357589, 238939167, 762637039, 960521784, 381676645, 63673330, 449303132, 941591583, 798757413, 510766529, 386964455, 7575996, 167122218, 582215165, 123808823, 223948312, 705605561, 993159380, 602842533, 425279771]])) + +test6 :: Test +test6 = TestCase (assertEqual "for (maximumScore [[512602831, 447811242, 239109927, 477303364, 98370277, 586772309, 662706792, 841526783, 111400207, 562789593, 396637493, 650319600, 344425843, 843325589, 422614872, 524231558, 374105983, 747057377, 211626289, 459470488, 650255942, 72434315, 813567559, 866917214, 474541492, 369252787, 996590420, 196074812, 247822528, 365088224, 165136145, 205249013, 764906192, 320979405, 865573882, 437085792, 328262628, 347108203, 351268872, 182473351, 596145835, 758586643, 83210379, 711685923, 395034967, 253380492, 655188788, 861266310, 876713740, 990833708, 302120009, 541316479, 530714221, 497761699, 381980869, 164171880, 994739399, 770539843, 917542161, 16599200, 505909085, 495737837, 392690203, 944928486, 300604543, 529857112, 980088550, 804863180, 149487379, 99642043, 478808445, 591357997, 458688185, 513761785, 597640318, 847874503, 781548048, 341935032, 402640718, 804736685, 776251083, 128131060, 374542297, 154868470, 544194748, 74777229, 321544087, 899620704, 723110493, 794246529, 149377296, 131520895], [729904078, 550792391, 284474771, 531466131, 734974184, 594030522, 116493361, 903551308, 971478205, 449383070, 125742390, 317747751, 22220333, 887781478, 844860403, 683771735, 670428506, 850805344, 536745517, 444647144, 891117926, 214038697, 808447675, 543653835, 212143761, 398910837, 230282447, 289715251, 212494925, 921491959, 99918975, 114869531, 179380181, 302272441, 902561273, 471202828, 890654525, 997587723, 433840205, 633425105, 684318210, 238810862, 474955648, 568876413, 511192290, 951044900, 950795498, 210082242, 936006522, 730510393, 618641174, 440226185, 383556377, 579266289, 145576324, 86267787, 101092316, 963397511, 988316112, 647207220, 154214570, 414471998, 656043048, 307125214, 646394907, 179790565, 600940594, 25352186, 919073808, 864079045, 77616770, 613954093, 418810344, 873927759, 401696799, 170841397, 720054877, 943079198, 485007391, 864515166, 478889427, 174678931, 56210613, 132686702, 269256027, 66660038, 988704242, 351190941, 352020215, 707489191, 956945249, 564578992], [535602717, 665300451, 806742662, 318707175, 320945266, 373664897, 946864276, 824116869, 254780143, 761508335, 583412014, 666846647, 411502535, 222003491, 14454391, 267529835, 614831647, 571366198, 433385627, 436066588, 910026372, 514697452, 510433877, 928636897, 94030279, 652391910, 520734238, 972957245, 922180570, 67002814, 80133219, 752369281, 616382990, 305508830, 20449787, 548498325, 559496279, 602407673, 781875576, 824703763, 612226020, 234543786, 343765618, 34388855, 342165468, 872632236, 346004294, 984582453, 793603337, 550080452, 189841732, 740714155, 793836372, 779783571, 541752453, 337467374, 540349937, 820716510, 834321377, 5467418, 206407196, 473382067, 70290210, 614300065, 447736101, 216651228, 831089612, 68067750, 28001206, 267486553, 637523138, 322006456, 856842768, 39466665, 481101014, 69164781, 438324948, 448402519, 51264616, 846662875, 624565758, 248844547, 277007947, 907639460, 398226839, 763012264, 208626708, 45708152, 256419619, 961721947, 842932471, 202829824], [266550482, 452657410, 89845183, 76732478, 488430106, 188437354, 907546746, 707260811, 516726689, 874693949, 350415881, 108323221, 881175416, 448511311, 745751397, 688162828, 205000656, 49079988, 963339189, 235701652, 972206295, 780871163, 397809906, 426241720, 566262958, 520631737, 89346132, 892349594, 917455537, 265174745, 446581391, 842494200, 230435896, 65814511, 761390217, 36912343, 808479105, 947313177, 399341429, 371173591, 302709458, 588412194, 680086501, 410061672, 196336905, 622353409, 528397968, 492568307, 445980328, 763426243, 919031482, 151148197, 297161370, 759872991, 353679791, 460557469, 732878902, 292180942, 939608669, 987152300, 817220773, 478355499, 447234145, 480644090, 785893894, 696644350, 262201609, 878191032, 359550957, 547716740, 604928796, 50752742, 253393716, 23798635, 955685389, 537583086, 661552377, 280470416, 28439145, 752628262, 852953122, 39836644, 915941955, 280210664, 929128316, 55353404, 276039851, 422210511, 104318709, 129537056, 634826234, 957090700], [247995038, 595187050, 729646789, 751694966, 697696626, 546240203, 35761219, 893605025, 494603226, 260151793, 705308691, 174713525, 478974866, 809418982, 787708061, 537653294, 729678800, 606059122, 684280245, 603805466, 673743968, 390491207, 164407773, 995897895, 932895456, 367473407, 773438306, 61544196, 621677357, 880681486, 23024471, 168160563, 490954828, 517433851, 643817185, 18130267, 800223643, 446610453, 197230305, 172444502, 528901070, 992811616, 225221233, 370807837, 29831384, 800055853, 35887662, 834579503, 883001130, 669040405, 725142085, 426347051, 355465428, 632852079, 621925475, 821366589, 771379418, 46731402, 72557942, 767174608, 692412673, 786598882, 995336575, 681843094, 990272132, 678234592, 270547515, 860075154, 396407864, 556072384, 446129456, 104715828, 248448887, 981468979, 512968480, 301264257, 817084649, 822169733, 437172497, 671469696, 967576344, 803766775, 27397757, 973131308, 342412793, 25788073, 921964473, 538923925, 597202558, 314747760, 200478127, 672160235], [163603091, 880390153, 893116155, 700945007, 761331339, 37545565, 393235566, 569239241, 774747508, 390242195, 876079429, 445671556, 929436123, 51832284, 565080756, 392719383, 120621192, 88148860, 460761350, 764034088, 893433535, 629278948, 120637436, 230080387, 87064544, 264039853, 527052719, 732462822, 348701892, 33764276, 570374537, 210822039, 433186185, 937535018, 212966119, 365404247, 329654737, 356675576, 520107396, 603679958, 490352978, 323516172, 522046958, 225796732, 467603595, 832913132, 257269006, 454579180, 907851793, 333894534, 13506551, 754929631, 777779646, 168289927, 500478986, 915391212, 507303673, 151832143, 31531389, 145176354, 324233648, 120793860, 318321002, 153440750, 95885378, 246836001, 995950400, 448219670, 292958146, 494060817, 107753476, 881781969, 24309871, 516993960, 327659693, 826559186, 444946784, 254749634, 191301604, 409013456, 618524618, 954343677, 714429625, 656404595, 837498231, 394252915, 71420166, 756590635, 689701765, 849753869, 202341763, 417538523], [864456099, 172660079, 510833323, 894574874, 282868296, 700933715, 86410965, 663994045, 507807892, 392647306, 169675808, 766627153, 367075266, 616865828, 608983573, 885408889, 905363176, 643921101, 927707947, 812793564, 48426664, 354242721, 393374184, 934051014, 511380873, 492162660, 538568724, 365074085, 576247094, 206104114, 125864331, 849285367, 997844878, 771880907, 305463713, 853307006, 891483753, 78524711, 501227551, 286952454, 752781876, 499064852, 679954733, 812423653, 368297691, 221485727, 570041435, 826610300, 724892674, 623607771, 440340062, 836995042, 175277667, 107102068, 581214850, 870432081, 758732454, 992314869, 708501779, 463347983, 318497910, 9228217, 556523448, 369230548, 600022316, 329192926, 96387772, 106363435, 179145073, 999838837, 408057063, 666064650, 131455763, 329482862, 879099375, 179116731, 352184631, 297583777, 625471087, 541867274, 10952914, 659685445, 346788596, 512042484, 791890836, 36095219, 465976198, 73302938, 761459239, 824893332, 992094644, 953403829], [830753593, 401844417, 781894620, 134139739, 979733244, 840187584, 454274715, 231365083, 491198043, 483900639, 255228967, 447322456, 323042894, 352257247, 188602538, 774463383, 169937704, 54590329, 805550059, 832620232, 912393139, 453819619, 475780840, 346902452, 110615149, 315491199, 920825120, 936272277, 407429521, 662197714, 616716895, 875843784, 34143959, 172172464, 602694889, 752369715, 775311115, 941378115, 122592845, 19418533, 771670898, 745333164, 424830465, 669109992, 483106358, 633085216, 75201422, 324706332, 174515989, 780979961, 507874280, 592987935, 520941532, 744571502, 189644047, 961265152, 532441495, 514913634, 699596460, 564217246, 294667559, 493125902, 642293957, 441687841, 6702135, 70419432, 883115039, 112915062, 47997672, 703881009, 543191090, 181107747, 211090742, 611489890, 411509280, 698971321, 812958312, 732409549, 394912981, 393015606, 653385082, 23936855, 307907428, 75547869, 900930886, 912179986, 17137497, 1300753, 427148100, 289171048, 199617904, 340660431], [618389247, 290780608, 690165323, 257008805, 701593300, 135413214, 447268652, 326455545, 642802633, 870309823, 296601022, 705108572, 668355026, 548415450, 568972174, 865873470, 780754674, 229226580, 390720728, 973447687, 325227746, 764090032, 351862289, 82829181, 603128748, 323371759, 107350639, 401054531, 541410098, 203809087, 187476789, 997856250, 166813001, 589290022, 822027518, 314838311, 428476267, 220990997, 71894766, 579987511, 40409641, 731774436, 927477685, 79833684, 642335911, 627893520, 621071268, 356623132, 996829775, 71641087, 479013915, 739045430, 119368672, 730222864, 848655227, 537502384, 269803903, 628043459, 421318987, 270988833, 828343701, 74883812, 237807707, 594765840, 892452855, 168227636, 295283151, 397055348, 840540823, 838605623, 72870998, 311992988, 523524658, 669810448, 868432613, 109981472, 705877313, 993093460, 451097562, 876340221, 213776351, 529051329, 601595581, 480640069, 963929510, 206683085, 62759265, 294225942, 952971833, 107525005, 513097732, 988276704], [400749388, 188545657, 456175971, 30798505, 704762246, 390923603, 776092950, 435273220, 461538782, 474000154, 988856086, 296700457, 647370020, 67942563, 496832443, 364254904, 877779849, 922404421, 465288584, 108006433, 397526990, 96521486, 226673658, 61391380, 540961954, 317433459, 232854864, 119651834, 655380204, 279984392, 551713983, 469973927, 640101977, 73772424, 365130733, 584836927, 349821088, 60876690, 699491448, 938679005, 920814189, 611767509, 367980502, 430778434, 996084267, 280752679, 566736004, 49589513, 767106106, 90504780, 828294508, 9225447, 751455743, 850837375, 583603351, 171849611, 913819473, 44273169, 282497031, 446669688, 265330771, 772153466, 963464180, 704339454, 766149978, 200189191, 46761501, 759364406, 774139390, 370731199, 726588795, 711257624, 461087452, 492262240, 225190094, 532112135, 19703872, 279086972, 619246306, 976948326, 354306393, 936530009, 232353844, 791610118, 310304568, 706020125, 218986445, 273019832, 231482321, 450625218, 528323816, 869265144], [193380556, 404113959, 606973939, 736253203, 614854119, 743649438, 765765392, 146986321, 548218721, 64665768, 247741439, 276708713, 655482700, 251936992, 523982229, 462356693, 825135077, 123495171, 420155304, 856378779, 121777019, 758436198, 516013448, 913802320, 127470564, 753750229, 726160190, 704259957, 58382448, 432246558, 672980713, 645926444, 160339072, 116446017, 780545356, 268407806, 119429733, 473330664, 56040352, 641799157, 467523265, 730374449, 473422131, 720676630, 226187126, 728919258, 738044400, 401450869, 796023440, 259286991, 639110575, 691431070, 534315084, 937894740, 697794353, 310295122, 622759629, 437300514, 672744832, 467924045, 588158628, 70401656, 345101257, 231641298, 945693076, 738537439, 722373540, 238018470, 844673570, 911180827, 260725301, 529433945, 816656966, 18049370, 182577657, 345493249, 812787317, 692280226, 801021638, 864832382, 596182172, 467064291, 738656375, 155699453, 674229640, 78027047, 177228310, 135762404, 614026169, 682198688, 727701892, 136093790], [557838879, 13233874, 440494225, 933811687, 227080422, 374373869, 987994996, 283797552, 555632603, 308998715, 629629786, 145625439, 338271539, 213778798, 688057530, 690534315, 100835052, 288343201, 344958685, 344680675, 97253314, 689212893, 821673829, 268981477, 575017086, 222654930, 109170461, 951247166, 764478287, 166122843, 539807656, 881668337, 122175018, 127060960, 597290112, 237353320, 571877636, 268264318, 773194509, 334503664, 923042772, 226317194, 586433502, 829917071, 100178599, 490184183, 608849391, 429693898, 843183985, 467363691, 706596701, 747539641, 898572195, 952063689, 166564759, 406702243, 218807667, 237598717, 296609361, 243923655, 233702743, 912599774, 743050899, 755737659, 272784963, 408983901, 311858101, 838331890, 717895204, 455942438, 990613334, 162684442, 203982440, 120757778, 128281462, 389508786, 405562299, 414559129, 307388999, 67785830, 552271394, 646863814, 780196758, 116070569, 901586009, 829295478, 779060556, 873300599, 145261266, 800779377, 604794185, 13398867], [871093521, 912488088, 224875916, 696386094, 821653687, 6313114, 60955655, 565175670, 196270395, 463301180, 274527501, 502125047, 58625254, 889711356, 219165063, 157001954, 279085360, 541410255, 296287738, 467851345, 25566728, 302182190, 192130846, 385563685, 111211590, 220662471, 249868810, 128376717, 669763358, 535281136, 838939934, 17206591, 67105127, 858920518, 121797458, 827345602, 347166667, 630309247, 707135218, 351430069, 534808615, 374102532, 651854194, 885913924, 877150924, 228374687, 227603601, 241413705, 820479489, 333714708, 971429289, 129736363, 993917107, 368466635, 243244391, 407168421, 570620424, 768697011, 408201569, 18716639, 751022101, 717864055, 739401545, 852986577, 655474782, 592931306, 459911658, 243699826, 241774760, 352458179, 205698021, 24373747, 232649452, 558082507, 258940976, 791249523, 730269922, 188845661, 250481234, 878859875, 767483560, 334408550, 308829455, 938434005, 352019177, 932623730, 39307524, 263990159, 227850342, 84945151, 903250095, 161439233], [930276091, 601241748, 525339656, 804997449, 594384611, 644594572, 48753895, 917735611, 599560253, 484017953, 944507003, 388107469, 64269245, 534176022, 483240182, 750410906, 328958096, 485549534, 510504954, 392335219, 260019615, 914238513, 59363444, 461719915, 837613009, 633586304, 841758376, 321956059, 167343786, 655951177, 406902705, 103161428, 894662738, 607022266, 968200565, 667088598, 989166899, 772802990, 14256072, 308050281, 809009409, 471642472, 798890363, 34779234, 871228, 211217725, 894991623, 818989481, 698207275, 822714499, 622465720, 637531973, 313196613, 500739398, 553170920, 114616186, 942937824, 136551806, 507138602, 246260156, 216000142, 346786269, 598133145, 460239759, 840915604, 328255007, 852239542, 689479155, 412477523, 513514228, 265244273, 41835417, 308865927, 983799905, 633262523, 31954658, 70054476, 34539771, 663871241, 428855433, 73303537, 320806972, 579095177, 261043261, 476177155, 524488782, 264541109, 371868929, 690310800, 284787285, 86105794, 503880977], [819073190, 176020831, 575993065, 677092589, 655660178, 250349910, 71524719, 506612084, 38757278, 905469556, 687599387, 802870575, 986974684, 837305739, 219559192, 236501686, 153058914, 855075168, 82325807, 22355826, 105058827, 256392940, 955692231, 717044050, 456184015, 362882998, 133083128, 89944150, 817842875, 962020686, 109396370, 93567243, 997289956, 260451373, 794526132, 43473864, 412526941, 908591250, 869330572, 294578805, 758556229, 290012609, 796992362, 134377900, 89895262, 263660737, 957722899, 684195655, 145511494, 743300733, 18756623, 701345776, 873559866, 455509300, 788524763, 274340250, 750969924, 857501372, 546679600, 279002968, 89491046, 705433548, 685374492, 47673557, 175194398, 652444446, 486560844, 921139716, 735111778, 117080203, 372755241, 104914750, 870891487, 740182458, 768242077, 773570958, 200087268, 689733297, 19517186, 569069985, 130592008, 425628005, 154962417, 935904448, 481432834, 626858875, 203695148, 430126806, 439928135, 104404646, 860575561, 419538241], [374597921, 448164861, 554179849, 901584542, 732989798, 317864985, 159492603, 667941663, 996443046, 198932429, 284146415, 306596608, 543575860, 748540173, 323616607, 288185803, 538159363, 412144034, 660094212, 210172646, 916594278, 330255111, 172516462, 184102263, 386414915, 440162731, 264286655, 569140748, 392158093, 327233552, 121760335, 430746159, 467638608, 2695453, 661927177, 779702226, 847810951, 245243415, 695860450, 238610186, 487160872, 154989586, 802017162, 265168684, 933457074, 283248553, 990107747, 795072011, 255126940, 972105077, 769918567, 943918678, 437582397, 913509625, 753222482, 326066360, 282088327, 740638725, 689978736, 118524751, 405571316, 132731951, 645864822, 738755154, 682182896, 633784975, 371724380, 284881361, 740633410, 375877853, 792009049, 309395663, 181109113, 711984793, 55025864, 258967436, 576826688, 652141436, 596444506, 823574237, 471406033, 23837618, 213687593, 995767165, 635185261, 230010152, 554654806, 15151657, 5565473, 286960084, 273571245, 944502841], [511705171, 686309172, 75494002, 829413335, 98259726, 194324354, 324158915, 439231461, 889937134, 977554180, 711789533, 792221881, 508609494, 91203040, 303878291, 998236637, 870975117, 666930508, 23147238, 28483326, 530591400, 157742342, 26820295, 590806335, 640261602, 73634503, 283599519, 556205278, 697012717, 430526511, 633391848, 615908600, 121255631, 239390067, 209697228, 362376686, 349940361, 641365350, 833200718, 921245618, 586276876, 920555601, 744160794, 92555531, 286893597, 577217819, 41418423, 642555703, 930155100, 392092317, 881149842, 975389374, 564861408, 71338127, 709063405, 564679276, 556609428, 450076224, 759164012, 504572904, 443444301, 63255691, 105190685, 499795661, 56505531, 904201788, 41969614, 19369249, 678607079, 497514287, 830536098, 106008855, 618054788, 957739792, 145832861, 885211667, 352431424, 413065801, 176647358, 945055074, 369178570, 475141010, 575399963, 481183409, 851461246, 827122190, 648571738, 80180289, 184439119, 652269430, 951595388, 434888777], [901629031, 286701285, 455070843, 435855045, 297232889, 308242261, 974719554, 68979076, 379469489, 874756282, 310343555, 418488920, 425307452, 58891903, 390523008, 629826502, 573403019, 445996696, 714578195, 794685605, 548470777, 774521593, 751435837, 809336227, 888687308, 971800827, 817149612, 770538659, 482522661, 239282994, 283665861, 757210280, 489836697, 143403946, 701911802, 691295542, 89619966, 911593757, 591437447, 467236318, 408124656, 438062618, 380118903, 752593822, 325327913, 420540316, 739345184, 161563267, 177167464, 995462825, 188635742, 709955259, 924819564, 632538462, 631612930, 449832735, 25290004, 233333099, 296191261, 455242028, 253708472, 77579415, 412320353, 376828702, 200805392, 604915829, 537425434, 914360523, 74468195, 730487077, 449745651, 337841690, 15432210, 611929953, 617720840, 981380602, 153155458, 635621836, 528873893, 744093326, 134514615, 462130867, 597092869, 773809711, 958701653, 284499438, 445420629, 417017086, 148512489, 103051353, 622519902, 701349113], [988196094, 50900840, 363961029, 65503491, 876024738, 539138729, 838090782, 429214869, 603960205, 567228912, 322345405, 249354855, 962679136, 716857593, 807901571, 160126958, 684069122, 759967746, 161376962, 85960805, 78796841, 88759881, 152361946, 474951450, 548450084, 808432364, 281105891, 458772498, 480614697, 707309610, 75630539, 576456221, 126585735, 273321431, 856580023, 453722185, 829603293, 944641655, 239116947, 661491082, 811435257, 411114000, 63847674, 409295806, 691959429, 188146022, 425883610, 839688814, 330652579, 528947906, 324755105, 980972691, 888160115, 610277594, 366595839, 878658471, 798095748, 839670237, 600738827, 375561710, 281034831, 815930740, 5944206, 815870041, 303870999, 883335342, 679803206, 662702738, 96439163, 76012834, 584099789, 318486279, 559541683, 171335132, 318562810, 242015188, 461491903, 586410319, 346502077, 964778985, 173971552, 532514448, 466353857, 718879082, 306553701, 185478552, 173181713, 968903348, 302272336, 190678326, 455090086, 673138986], [365352423, 773296679, 983619425, 319738597, 566360385, 951964627, 498732601, 764943710, 283499379, 285188443, 809008885, 822211608, 771960554, 971195982, 991217436, 963511181, 82635047, 422167941, 41791332, 245646988, 260056238, 27661178, 682317212, 339264697, 58599370, 906564393, 458626560, 303825116, 796356502, 629876478, 622086281, 756115443, 367132041, 229939824, 491460821, 707931909, 503252295, 962131197, 892646903, 249635426, 561458950, 377406132, 879940379, 120595255, 144260982, 299494142, 563037715, 817981478, 202258347, 910456821, 309103374, 790328564, 949216190, 150823834, 80713334, 65990814, 968301507, 313526956, 426090367, 61092656, 794807634, 646458903, 245334448, 679415402, 760552715, 740369147, 387632515, 117910522, 474740511, 476566640, 21009488, 692266362, 765900467, 929095260, 206143541, 818893425, 701340228, 760469723, 674827346, 462240255, 216171254, 815076961, 844600407, 447724130, 220286056, 782485088, 76570304, 19437207, 736038405, 269909289, 778902773, 112164546], [434128700, 568777476, 437062660, 245308570, 668477913, 251131382, 234825654, 985607972, 105114476, 470424288, 624838268, 332169315, 48356657, 539514525, 246911323, 930328684, 514129549, 424984518, 488023760, 840692972, 427367282, 378938142, 260755607, 47377955, 198842850, 716072193, 876823376, 117099457, 243735857, 985493440, 482079889, 76983593, 578572692, 588516429, 105321286, 20416272, 918329457, 684273628, 567462278, 32694026, 398157595, 422778766, 233228718, 162679189, 877177337, 696258232, 669820812, 231689396, 485458926, 621515466, 634644961, 972903541, 263251684, 265093997, 414575246, 173701478, 332465185, 237276847, 982255956, 239182162, 470299092, 948000186, 762174444, 630924660, 539624288, 107593853, 460307536, 827755140, 168017343, 728456851, 954584019, 644211745, 65221261, 707837215, 899100099, 105782597, 905167376, 359438552, 136158559, 890112939, 32068309, 606986435, 91071771, 994990059, 441931752, 164951803, 98873006, 721814706, 959214200, 313166354, 961940701, 606843675], [502649296, 301571168, 524079706, 227561531, 570643364, 871776792, 697011136, 923518428, 822352070, 659828439, 938465325, 728055379, 502296915, 671121020, 886303324, 821337940, 933426648, 57137737, 760367108, 978695505, 223452052, 131201345, 626571063, 530967052, 928293111, 672599733, 865864740, 401223337, 827166862, 778807024, 992817212, 201643011, 905848875, 899680545, 797007076, 788520586, 387138249, 503721377, 554637723, 298141376, 227394822, 132437999, 633066816, 223259525, 281381106, 568034346, 841997802, 568423547, 630636880, 71811037, 428046332, 102698422, 543962818, 552767184, 420182748, 16902743, 944570314, 90624891, 780513377, 95278224, 982136371, 685397277, 604065961, 310305592, 514475340, 732895998, 42006205, 247151703, 665448698, 68986128, 955857666, 896127232, 106901139, 673440918, 835132840, 672840179, 184812769, 849544741, 744537224, 449273238, 997543773, 905395687, 574387474, 110679495, 483572864, 313725474, 98945697, 843463009, 981173145, 494061686, 338198691, 828244038], [503733420, 720136975, 325465684, 290394175, 620410074, 858458351, 870490369, 379849034, 501374255, 783912452, 691124589, 396349596, 900139408, 729679954, 858149797, 308193910, 75212388, 247379293, 425788229, 915551142, 321203156, 500387597, 553795029, 117860111, 645554748, 4278489, 798621151, 157367918, 443615250, 394638711, 134508652, 171817420, 586729282, 833454090, 42749497, 263258159, 693485203, 615960002, 718475937, 204118915, 795344800, 203423706, 519549015, 223726868, 587394062, 755796231, 164662817, 601347731, 386649651, 638190633, 387600447, 729758581, 569612764, 659240697, 889880211, 499536438, 124851862, 522090606, 193657147, 143006207, 894700751, 25322178, 313860525, 129473376, 302301138, 625168211, 169443864, 496982403, 356002325, 798107092, 225736970, 621965129, 719160123, 4435141, 934791482, 174157141, 322960060, 609423065, 61612618, 429410860, 546810139, 651716762, 671951, 635109005, 425673166, 282405771, 340898316, 395761027, 805216549, 822049076, 649191853, 741988766], [792583729, 678682212, 715187674, 757446729, 602532407, 370138593, 425736063, 478147513, 711158848, 693386382, 100155870, 297067750, 959103343, 150957178, 334919615, 374272499, 750979463, 326454683, 915843911, 755938635, 781216648, 999958636, 520868765, 70615214, 694980696, 54029985, 113544813, 322017818, 662265547, 699718659, 548165472, 338877913, 635726789, 890884851, 538601633, 302993738, 912254615, 399585995, 144199114, 751963906, 762390972, 407925294, 423413908, 262633178, 531616191, 966179931, 350849353, 170954539, 287011322, 559485228, 590191721, 550454511, 529795272, 992304425, 234056495, 630146100, 294384702, 382449378, 812404597, 818580953, 220857608, 152467619, 14585016, 776927891, 605539683, 494585172, 445757975, 299269509, 712321497, 727974895, 752935249, 518726668, 757511042, 8744423, 241284773, 570778740, 78606432, 679810032, 19251963, 381970208, 249964522, 512068115, 257963957, 177768912, 196260103, 535820553, 672021517, 408906293, 119560019, 117698177, 774837395, 368574129], [266888707, 226423766, 148532311, 709359127, 840147778, 259815654, 244156682, 410863572, 673541550, 467467100, 431688970, 648579763, 633234740, 480976553, 21723787, 179603443, 258959813, 80143891, 360292339, 683231983, 57191786, 295093995, 357739346, 958126635, 548766988, 865326330, 562931197, 14452305, 606520804, 542762858, 583303470, 821787929, 541268474, 47133449, 117499461, 231074481, 793497299, 765883606, 588221246, 856082418, 771731610, 368340306, 196947156, 738400708, 779149296, 337005719, 172519463, 541578413, 287095445, 557802705, 386304991, 408317528, 423160304, 171072218, 209535081, 183952551, 842835836, 175320320, 401054041, 628698350, 749787032, 97206172, 494822070, 889125513, 769411785, 897562593, 181484490, 916835095, 508228980, 561962802, 149878804, 649165727, 503443139, 696244559, 726933722, 596411184, 515761092, 857734528, 799854087, 598806130, 167921737, 338742666, 825967853, 522016036, 4066386, 550932943, 249423389, 470399952, 440809264, 195929639, 167675742, 718084690], [940487624, 526036122, 980390490, 526935692, 452753748, 307928921, 440625441, 738391302, 294645586, 952419368, 493233774, 255210563, 375328712, 150793886, 913261835, 589449012, 459759802, 234749399, 228470465, 450414814, 464093143, 122171677, 946272427, 925969524, 209121308, 24115324, 837481070, 463551317, 802101504, 599706617, 270625759, 980345330, 63297664, 578536215, 631027212, 949796886, 707428070, 647623166, 655996842, 646230320, 960583115, 738944569, 863428687, 842219586, 251713010, 468573665, 530928310, 133622591, 469714305, 157673464, 42042718, 152934768, 934247947, 165729753, 222413888, 971623629, 25072734, 214709226, 982769532, 667261554, 882380522, 229537277, 593448964, 104767936, 321310367, 607462519, 319519124, 521883758, 758360904, 354594098, 823286582, 161143324, 868776401, 166818544, 722740483, 165896150, 66194604, 19926930, 284503462, 848732921, 208703648, 69610972, 883468227, 497175811, 105098666, 929698282, 729823884, 537845774, 890134791, 347325155, 93374864, 312723756], [598317520, 711348655, 555686293, 333730172, 746093659, 423671283, 579689422, 596235793, 433980786, 940949583, 272796234, 51205278, 262232235, 909420695, 187602718, 512366562, 996513932, 760245383, 284302768, 253908126, 620803456, 877637199, 657101548, 38263373, 744583082, 968928546, 852272679, 123642188, 533509645, 122632558, 815380722, 287953445, 253682048, 814104622, 339359871, 947631977, 730358384, 147447858, 396793594, 365961041, 145560187, 264169555, 517598811, 90361302, 502647166, 795764936, 785226073, 671731768, 388990808, 682366420, 208945033, 211297457, 586271300, 673167753, 138705531, 499265881, 938960969, 557846144, 688847523, 173436838, 329421203, 857308082, 588339519, 46675519, 987918626, 500011234, 482821721, 778974127, 829617017, 817469571, 160804251, 803933649, 814508367, 699269226, 991012949, 272759185, 432456487, 916381451, 711146429, 331726864, 39818717, 454644975, 496031662, 318649620, 45661959, 331040719, 267345131, 602004658, 791800655, 706075667, 2075238, 849399218], [961332586, 404358188, 71135098, 284925146, 225370139, 886013219, 646955512, 446060588, 81189334, 854451793, 8672680, 658256762, 55508871, 230529668, 743397980, 900909552, 202737192, 618127768, 170236000, 655639085, 698718875, 64224271, 754475953, 127363478, 130071179, 582326068, 872768235, 267600355, 141663119, 477051356, 188856798, 966067348, 350702285, 997639832, 960520456, 59839522, 123312394, 794482924, 519174715, 674853324, 373077011, 597914376, 848282686, 354491573, 528302167, 366499564, 499602386, 914380372, 384046677, 181623283, 701038102, 339571632, 77134839, 440784415, 970850991, 128439810, 505045257, 912101486, 396988739, 437382988, 794586783, 929812536, 946527123, 45637991, 377058300, 113756821, 229289651, 60297162, 990145819, 913988546, 179518582, 292983739, 300021992, 345495486, 1919862, 293876620, 413002237, 774514004, 226183070, 603370064, 998406873, 159094579, 277665391, 284058154, 221268057, 496413397, 279184149, 741306189, 392416320, 699639148, 132334533, 556714189], [109096703, 758957495, 396626101, 769621653, 856817900, 596367846, 136724559, 336643356, 272497260, 213698976, 613167695, 752333245, 177087670, 592736494, 65833289, 818406692, 36431471, 808915672, 922997448, 984401627, 627114282, 520150178, 665629707, 855124102, 20806302, 793466893, 297022714, 874282470, 668752438, 145913788, 899613563, 836040584, 526347535, 79918734, 699889502, 24929368, 996008473, 935518791, 686203574, 839800223, 495999003, 951552160, 681507053, 581389845, 502400712, 750139484, 846283667, 967123601, 589868150, 63227338, 691381406, 169967480, 690541426, 95233762, 535412431, 683420846, 110332129, 779424685, 351829818, 772646724, 574805640, 958688828, 641090214, 964313682, 740534609, 160256047, 427848584, 722542168, 876140663, 560469354, 858066982, 722525323, 330127151, 628690123, 152145774, 114688147, 233664793, 665726603, 456904355, 218734575, 707411045, 845077595, 37168603, 342948609, 278932776, 506726502, 577589517, 120846145, 777374845, 525337444, 179454836, 620274176], [727505047, 263965986, 838133329, 685282207, 983461519, 412122695, 82893675, 637759255, 803898882, 836394035, 474225527, 219320631, 73534475, 9955760, 772606390, 342498836, 391314000, 113226985, 173547032, 468347645, 354077660, 651130045, 162091213, 695639813, 254785557, 663333694, 918603252, 28844270, 873702364, 54901200, 518233631, 18594501, 240222423, 812758324, 713589781, 728768274, 645944381, 990904991, 981328152, 946320864, 254434678, 371587636, 630744482, 175542978, 334672708, 743154510, 969432896, 107585350, 542727824, 385052638, 309413128, 516876205, 335669282, 40805093, 914601893, 994690609, 509225827, 268723637, 211432790, 936934016, 865289513, 67327954, 168610086, 783760204, 175564071, 269332840, 661641347, 201252574, 787089951, 288977184, 475431572, 840943178, 954844428, 72838866, 732065293, 839175538, 715149752, 669981331, 74677551, 721132440, 32392561, 959364114, 514011595, 798215761, 328924117, 155123112, 915634503, 328260773, 595601118, 252508302, 258867424, 306612306], [550710728, 126559349, 978582836, 428258783, 941311728, 943774886, 387142195, 226914189, 921009094, 404550834, 830440549, 612969836, 743351144, 785372827, 237685146, 930460440, 89634957, 292292061, 731702436, 364329010, 630082693, 936421727, 987117096, 283308606, 881919927, 875138922, 496041094, 209258942, 797419253, 9920595, 914183584, 624142032, 447589365, 91190306, 711786857, 963882279, 318244738, 753809915, 751689607, 409026285, 262076266, 945297845, 219039248, 730683858, 715620834, 925976773, 927520020, 76984968, 127013696, 585543789, 629336791, 193115071, 98091355, 128720792, 881177637, 480662203, 802575658, 59110710, 410562284, 863070757, 422139475, 891256361, 178430138, 522982876, 136073873, 206705270, 320022988, 132804582, 526440459, 666803543, 717620643, 184501489, 557624418, 151784561, 599105042, 767456753, 477784411, 705167119, 485023013, 310799460, 640522346, 532762879, 605706042, 953860031, 996941354, 701310357, 801583949, 143537260, 833467948, 564949953, 959892030, 529147665], [158208831, 805553043, 506410223, 20467475, 626050138, 845566736, 530010807, 72530149, 193826534, 145949220, 189778094, 302098784, 699737780, 51940708, 362829769, 28779330, 612253254, 568785319, 19651220, 9349614, 37596826, 25529000, 885538671, 919222758, 597984299, 52022891, 665606797, 453716047, 839727788, 548878201, 149020096, 421804460, 757160707, 393373994, 650222440, 921654379, 131567036, 936371630, 966127885, 730736821, 945078604, 968801154, 559975100, 291931722, 292552865, 787872863, 346011341, 632512197, 905549344, 333818365, 269009132, 455731470, 968212062, 917103169, 478779408, 715586892, 2895076, 382863032, 343603477, 686601272, 844154544, 602351826, 744594198, 826040548, 704163540, 482448788, 972689716, 115667706, 871180350, 271271648, 27429781, 861994778, 525407510, 823305215, 238465867, 22911624, 183072270, 965887351, 3694147, 990361617, 702027024, 450529552, 795475955, 928540928, 677630001, 378824096, 623136957, 943141442, 874334641, 608348631, 690920271, 521391934], [544761657, 890704805, 870123785, 380370395, 933933824, 151991782, 978322538, 187675367, 871074296, 23401503, 50279647, 182738354, 391070939, 626358160, 966240491, 989968311, 33408989, 890839672, 619023262, 781130182, 865863131, 664092493, 733646285, 972318076, 330952639, 202406730, 22963982, 8674196, 366966951, 147414372, 728872089, 988290836, 875208996, 992932051, 389600004, 410243430, 628829468, 712845911, 581536063, 605740220, 974607650, 962944185, 938415766, 247797606, 302281255, 430968266, 435884329, 365626430, 271089170, 607237622, 333925152, 84615898, 923526173, 168222842, 223757679, 609785427, 609130232, 285935999, 835641615, 141500571, 432392294, 386380627, 816602470, 737608488, 631005666, 258401972, 947133561, 902176287, 254370178, 576925095, 917352728, 369811019, 54530844, 166633209, 760882499, 670679334, 283522867, 921042862, 555776146, 212084650, 168005578, 83633534, 770586968, 362058712, 914474962, 888314000, 456346263, 263443399, 171572334, 643525717, 449775990, 300342366], [579862542, 433386143, 639415424, 83859862, 901481034, 825042745, 781532238, 414140904, 738604031, 679033451, 53397327, 188080321, 911825524, 533560655, 499123449, 585222396, 779924063, 106739260, 651038509, 226683794, 932637643, 344222571, 782980673, 636630282, 849176839, 469247807, 64165072, 196193266, 148269039, 489671475, 526231699, 895649667, 299677877, 686362595, 553268854, 681384553, 409928981, 344049557, 861058507, 199272978, 419214852, 416527246, 293549475, 376276340, 845432443, 662252005, 464127645, 263768915, 702271504, 399760342, 878037841, 576120627, 275193550, 641894176, 211793757, 720952723, 776499689, 314829794, 313053132, 578479313, 948840362, 623248910, 989124602, 647931378, 671941541, 199371445, 601531232, 306689460, 42671269, 127706821, 41994421, 938779580, 184888721, 59436388, 929989084, 838093701, 446497870, 541383612, 162553202, 713828454, 926180263, 290123842, 701398267, 723291936, 105995658, 917051130, 552745184, 334121726, 68443037, 654204114, 781677951, 462308060], [398631673, 695166826, 554954836, 10602753, 850039675, 746729321, 811688758, 62197686, 545807244, 226862519, 629251591, 870355245, 208119266, 894175587, 664656640, 436498663, 436107508, 980677671, 458260735, 905917303, 157748372, 111993939, 772193596, 313628319, 774542302, 588172244, 150297379, 963887535, 130271788, 277626951, 801437661, 782214331, 63280894, 374266394, 94698235, 158245881, 688139698, 174070474, 659543057, 843123947, 458883053, 910876713, 299659514, 532082882, 908066231, 385067915, 36215525, 613924058, 774281532, 892122156, 788609900, 210683414, 765699388, 337095547, 717684154, 434962449, 968027598, 611467154, 975467980, 111660630, 572194475, 746191889, 584985472, 964582505, 452242109, 992871951, 652351359, 94558195, 245258268, 12086508, 368023352, 590133545, 726044413, 79225484, 666836286, 819358868, 787229763, 69016490, 49623387, 529295526, 834205210, 342846991, 852152673, 181223844, 564100434, 710478905, 886587869, 848716040, 220173153, 180054508, 568235765, 726253220], [601120603, 62731464, 340203075, 294108336, 308014727, 295904282, 98773081, 205416541, 973953047, 38350597, 562838225, 998378036, 55438280, 129621432, 821797195, 938219856, 567692685, 254194634, 878440682, 251730454, 356255249, 481949672, 40418594, 158883940, 760641897, 18447368, 523476498, 94602698, 412991713, 117106907, 961081997, 196863029, 891027597, 4273203, 241462582, 147748577, 477369947, 500239774, 577483581, 36069392, 745750664, 838536211, 282014682, 51445572, 199868892, 239420770, 641224332, 319393176, 243465515, 739207632, 655946727, 283957238, 352830939, 988374640, 59619323, 898214490, 191946464, 756315887, 356349241, 680606112, 378535833, 756832198, 330371316, 418684008, 889462680, 861185998, 329049477, 817205828, 548331661, 735972277, 732734838, 319792188, 243963775, 883282098, 811993002, 416419225, 404928048, 181572782, 590204174, 567031717, 655153099, 115541, 417979124, 757307730, 273637216, 872451420, 233560799, 277324416, 243031825, 502800783, 987731355, 608522599], [24897571, 467838433, 863319357, 568924083, 877235296, 569147852, 882572801, 860378465, 588967122, 364018995, 338629357, 682897111, 324325335, 541358596, 498456561, 108047941, 786309728, 724826936, 62667547, 994225737, 197696653, 990011319, 157127165, 756562806, 970664728, 170363211, 723666594, 484448949, 290270184, 405714658, 900971172, 317912586, 449850755, 311235265, 32204810, 191877788, 626494149, 177409278, 689646521, 619996635, 244418195, 782078309, 297561758, 89458862, 859557479, 228743046, 467656626, 532250578, 674070541, 208221458, 132036792, 415790506, 256404572, 559981021, 343093530, 928898835, 712177145, 754089580, 794786258, 924676914, 215422027, 806794334, 533669837, 575777124, 910877347, 270518644, 772745836, 650988509, 57770266, 930562429, 216297890, 103412987, 45625771, 218007483, 650743134, 915254296, 668372189, 523886334, 609407708, 565560614, 999080034, 191376246, 474906103, 965405283, 360975569, 957269558, 7968339, 579370139, 339886359, 736710977, 933390570, 451483997], [350216812, 768715024, 480531199, 98842962, 991009597, 908720182, 968174561, 834351286, 982519948, 966958545, 961651153, 223437120, 115314145, 285078174, 188451441, 960209583, 679927422, 193785596, 601647188, 305624403, 79390928, 239805537, 319842883, 34568174, 492890557, 456595247, 391967333, 971021616, 468586778, 860692781, 789426743, 332237365, 6757750, 103396474, 623803113, 618931486, 4921988, 946694994, 740057680, 332860428, 281809676, 695503600, 458593510, 500601246, 829552102, 143581359, 673097899, 602165727, 639470035, 187377893, 598165587, 518796170, 907515733, 774746777, 815725138, 408054865, 290665178, 870172591, 977780983, 218777270, 354166473, 878991861, 105427005, 510487655, 145244753, 243875095, 262088151, 237080574, 832014912, 743245927, 403038263, 150945271, 228994954, 445725049, 107375604, 824691031, 495135427, 605268878, 756897901, 129997634, 26860963, 943393668, 900174962, 165149219, 446166101, 536214862, 877879423, 695095226, 373343181, 204808406, 227481697, 814499471], [243195117, 853823723, 651954779, 598022847, 554771392, 20367128, 663764167, 690402853, 667253007, 496913233, 520375585, 784000878, 295761528, 579436369, 167001054, 55360826, 785714691, 183436795, 582376051, 81844085, 723354541, 498621732, 731420077, 132081004, 82413744, 522608804, 172289543, 159378717, 417289197, 138533362, 490305562, 402271460, 237679146, 507468664, 913950306, 684312674, 331760493, 926514249, 362521484, 825500346, 196203101, 88727192, 938343892, 511336792, 342179477, 406341971, 500197971, 286241877, 844488188, 842836137, 385992248, 618345112, 235356043, 828504377, 135544416, 471732139, 686334589, 713793682, 274158683, 743763931, 582741484, 214982787, 911051201, 421777631, 206373143, 196336214, 412150285, 780401124, 194749818, 72945466, 564170866, 339439753, 306548942, 348491508, 746560843, 284752097, 547758502, 837702807, 108144314, 168823031, 669170237, 774839705, 911055386, 63537257, 14722866, 79293084, 945886410, 718517647, 396398170, 142580961, 175520755, 263910727], [34313333, 385936459, 978211438, 602838545, 122248779, 621795188, 335437136, 401873038, 218421113, 945464634, 949566742, 171447476, 890167961, 363876878, 781374858, 110671001, 205453887, 190914390, 591498783, 744380468, 525524645, 387087640, 26299466, 25832123, 311920865, 403709204, 275776110, 459885202, 4340640, 829898489, 910812348, 57851835, 838054467, 326621062, 335280379, 671855657, 468184796, 770482394, 942885755, 323086720, 245254482, 829253085, 192759164, 102721266, 538258808, 110668105, 980880121, 216400858, 825882779, 990913618, 233651627, 799834789, 740654975, 977905637, 359047497, 500010673, 152521362, 274284330, 780348176, 288949882, 788128519, 308502406, 304857404, 157541069, 648532603, 766787009, 798916627, 655107825, 675878070, 722848007, 521666741, 586937544, 183118112, 274408401, 453161223, 810449123, 962997084, 86578045, 740446981, 245123260, 356359175, 425821749, 264151102, 287218355, 62955569, 482227706, 307915797, 368086324, 762478915, 281247820, 563964097, 76954111], [710540397, 645209097, 434418301, 545400215, 105331631, 533984229, 157458165, 520871387, 683491889, 506489506, 579172467, 423983318, 358090058, 115410783, 574210413, 966053007, 665272405, 408192157, 461135766, 482600056, 463734374, 510903493, 983752709, 673627522, 202634480, 966954343, 999546300, 261697148, 59092139, 561425749, 931171374, 292131544, 615092390, 85381045, 931848139, 2294373, 348085532, 997063089, 919867354, 783776374, 935660625, 970402186, 222249891, 916075325, 952923508, 449137003, 367489632, 952770294, 929644268, 739944120, 11191883, 198981621, 775019739, 340044983, 806525516, 732743025, 599085931, 15520387, 223008637, 492760577, 328171320, 277954081, 949918902, 912357631, 300847255, 665562243, 943524823, 581790439, 71242538, 583074847, 739329004, 865443387, 804200988, 790306332, 343224593, 748104397, 637220382, 961287971, 333219248, 236698192, 244014719, 628081919, 507025221, 724649593, 437545288, 999168905, 624306214, 778356594, 536346060, 770515714, 253973477, 490064565], [718523852, 608412459, 952648195, 330970583, 486401280, 944955119, 454086407, 808020404, 854305829, 456201674, 930840991, 722767918, 206190500, 523888055, 305014789, 337062797, 727284548, 16579405, 634879508, 579591725, 541893510, 400596573, 196457774, 639369962, 324108152, 897494643, 114705937, 603190510, 241424205, 795583608, 443966994, 483094793, 512260124, 659065669, 110052971, 549144874, 930150515, 298312048, 897870177, 2109691, 893033285, 575568946, 819990539, 489552699, 669510559, 661795122, 923060353, 787310119, 782055700, 301856351, 177048909, 975088734, 558378049, 21853282, 747673564, 285808349, 887351283, 189389933, 925904490, 600206839, 21381753, 402589071, 620815606, 822194886, 473673312, 101843056, 809905374, 615158229, 326316794, 839621316, 366335783, 928557776, 245757317, 82979511, 757055121, 843278366, 787127372, 642349206, 102723236, 197775553, 498465702, 494734899, 261892827, 128439650, 830538665, 713854728, 996141411, 885823159, 434030107, 696153568, 455171442, 323846478], [334825523, 790057958, 506782920, 23736876, 233238572, 741588397, 372447822, 427007958, 847207752, 396018253, 342235763, 770815509, 677844184, 95268914, 72116561, 165152685, 164633031, 455036697, 207962828, 226450889, 256780152, 124533439, 747466488, 946026075, 372665239, 697279787, 83837547, 458041555, 238781055, 146526371, 633757782, 294491399, 654370896, 440206067, 770428333, 789101170, 774570732, 127555975, 715989450, 39682600, 479820681, 132094673, 850524394, 565595262, 964014201, 355659578, 737082843, 721798603, 670800174, 639519351, 737193908, 119234359, 417953881, 910676815, 510205349, 662464995, 511046250, 878027289, 83216663, 545693578, 764009769, 981891422, 959537332, 296325698, 70796939, 60142777, 181847810, 541775948, 734196944, 384799516, 459178251, 839012358, 304029155, 962105817, 997802144, 794209987, 860189083, 469362547, 42260468, 714920821, 412494791, 541715242, 338243509, 831011010, 247308900, 11412463, 344163352, 72314213, 605427924, 414523527, 704617107, 834016103], [666623647, 754410124, 108838815, 42784790, 515495468, 861652780, 823958908, 31019423, 163281051, 317663916, 889937957, 491943758, 142642000, 651411842, 928115437, 815384053, 995011295, 694637858, 338725151, 538589149, 657829852, 819149513, 568624944, 148443421, 566150252, 508153065, 628504898, 28701862, 634599994, 799738873, 251504506, 293167526, 558165937, 680453013, 738677886, 116790223, 630547329, 316274068, 706369495, 304516697, 701365004, 6095, 582899212, 410704200, 505074165, 501674188, 702488543, 681869865, 558939928, 671420547, 569826265, 197247944, 636919117, 745227846, 457704331, 635760449, 616236048, 935713444, 273349291, 297860723, 628459533, 776202960, 62570271, 849924133, 290152975, 428045451, 739182228, 592554520, 989992664, 553290970, 608349530, 631194960, 654460156, 879041052, 116125827, 704875649, 996852969, 220184883, 615664532, 302114546, 313906933, 377235812, 593817871, 602023329, 402802615, 941817315, 330285587, 269098807, 961182608, 964336873, 404500373, 323002833], [279542520, 210531514, 922844949, 23433134, 961211231, 118163681, 873691802, 268653867, 809035860, 850623804, 104116608, 529832322, 793292080, 971083609, 389760153, 609176981, 731284590, 700840124, 695290304, 637905000, 920759964, 48239368, 382865429, 282319529, 878803561, 387464005, 759360037, 753497716, 770615747, 465000453, 998299532, 620516557, 854977491, 613635589, 384455120, 796508293, 578480397, 282890673, 348507138, 312408572, 822377680, 614772746, 365144440, 991775874, 237943699, 933314212, 269238565, 630231968, 703562057, 218959054, 661925473, 402249239, 645859106, 754866250, 606833819, 657994362, 80940748, 325890551, 574215540, 516285220, 790642064, 992996712, 82403919, 574601030, 742158471, 147334987, 245922135, 939230128, 531905063, 642011292, 268653662, 63032436, 47535748, 45352430, 378949008, 7649965, 92339148, 689522685, 54076138, 567733748, 312558782, 920064689, 118584826, 655120106, 494215187, 197699741, 84316243, 245226073, 390904559, 675703357, 483040609, 245153476], [821792962, 999641065, 171255111, 814030185, 549099036, 447232385, 71230997, 470065859, 966434925, 583951535, 709101122, 716068935, 48167851, 761506383, 398479032, 525275778, 136726872, 630519278, 987749971, 17310333, 564766741, 870885683, 175023956, 840404987, 339572736, 899351930, 149557259, 190716490, 430686760, 813507016, 214311482, 341120583, 730047084, 396748324, 874484253, 685688576, 467099227, 752566966, 304823092, 138147014, 742346961, 762929860, 175160005, 467268976, 410945807, 992495297, 57259836, 960237478, 299058960, 863163360, 318225196, 845112422, 868017042, 331194337, 950720689, 658394699, 738827288, 917037065, 237701832, 754513052, 440067549, 899184497, 971543275, 648578627, 532100160, 286060096, 810652689, 26941742, 713205773, 591186908, 519972658, 552714661, 759427469, 706581387, 825942660, 356418239, 178501500, 654523082, 467103428, 101142405, 140291499, 105035233, 86805950, 552563716, 899426079, 117309413, 671051619, 516977308, 163559860, 998479121, 25460110, 862992769], [948725345, 360071298, 234016873, 403539581, 837657879, 323107587, 866141869, 803878695, 812895440, 898032129, 299492584, 20805053, 663971124, 523875966, 585670329, 139181293, 11147825, 41373968, 219551547, 19252342, 854710367, 353740845, 337170969, 112789597, 454470968, 737773491, 569429981, 932018183, 288984561, 170893393, 646092309, 560441114, 774034175, 48448396, 482039084, 892170717, 573597343, 757362014, 689887853, 858840305, 996282445, 765790913, 875837797, 824118880, 254501802, 998086361, 237928700, 223518446, 83292837, 665954010, 190672938, 831388634, 883043710, 158712936, 560469267, 837486876, 4502712, 416750181, 937507939, 637268097, 926605943, 997406734, 945528147, 492378740, 443804410, 667247285, 312077792, 618322076, 229967239, 293340977, 206725027, 253189566, 76873675, 548587113, 294751826, 904349174, 108641592, 938822597, 720069869, 876403667, 576572299, 947570523, 215665504, 302852325, 324416339, 680197550, 957558642, 922430068, 147871527, 495818333, 926145220, 25279822], [732770936, 675835994, 460357464, 356292217, 567365121, 69801840, 119767961, 668269421, 733425385, 907130077, 488943545, 759030094, 442942629, 136968166, 600575524, 421901228, 599610122, 646460524, 352972246, 789400214, 694452911, 624375124, 840959011, 264219300, 405166192, 991661227, 919139036, 594173906, 594684552, 525755153, 408714810, 340806064, 262696197, 359292942, 780248655, 348371980, 802370389, 18878101, 386516935, 502584112, 544388770, 215373583, 252388711, 630030254, 660524151, 666804009, 592624704, 471189772, 48110419, 204798640, 873775502, 712896077, 755672975, 51105433, 639038241, 724825533, 258244624, 724899556, 217377241, 952454991, 861410745, 879342928, 733159391, 326712327, 434765872, 995330300, 942144581, 746696303, 317394435, 505559916, 842715031, 822332718, 575325556, 505655658, 452895689, 837081708, 27993443, 778320842, 904975459, 867483289, 527951347, 972379371, 987586336, 72356057, 836409414, 769308297, 820790118, 576071008, 259506321, 261351696, 701539654, 576007240], [384670835, 531155356, 338809811, 327596982, 332694721, 894711511, 748673181, 55073437, 161942899, 69212239, 469572602, 179001337, 964466366, 785541605, 602907515, 295205705, 906736456, 256706839, 934422739, 243232725, 258856569, 67953322, 575093079, 255568115, 87767654, 810386652, 671234675, 968207404, 711323906, 226046958, 365186766, 8404243, 338605611, 672034348, 302910765, 910641947, 93917851, 769076392, 798960040, 706552626, 760668946, 905651275, 480039541, 12195176, 890825702, 802296603, 271032023, 363970216, 220227118, 740074630, 578955805, 703469933, 8815847, 71041166, 638690497, 133549837, 621071571, 849703175, 449584536, 931640326, 801821539, 903682409, 174218339, 941274483, 567137272, 685854289, 21135421, 403245288, 864164023, 779424254, 724471585, 796093412, 241359815, 938707833, 592657402, 38571325, 629544471, 388520512, 675095342, 278776115, 337603509, 748420789, 870187667, 72304849, 136500790, 844817528, 679243963, 199188734, 417136444, 746216158, 25189116, 932146500], [871690609, 329849226, 597870141, 580878145, 27757804, 124443110, 574895630, 151459370, 85597968, 821371622, 242864538, 554424589, 899125236, 502934028, 864916838, 300010169, 742081114, 967807465, 419444704, 90505838, 710395594, 820659411, 746134261, 617511090, 168680447, 865750838, 348145044, 790946083, 526983060, 412987362, 814381452, 876660445, 795177214, 677637057, 74519710, 910051385, 461365580, 430003498, 448750232, 368829861, 515327749, 673181417, 519826885, 14636438, 577564032, 298293916, 405941515, 235028194, 666285987, 633073069, 802562509, 677789102, 495461979, 976181430, 11221424, 783526497, 327174030, 956729691, 357408149, 617226562, 563718783, 402629938, 429268250, 199495757, 715579000, 833701789, 896938034, 301079116, 680391294, 964262577, 965691342, 584860398, 836230096, 165179324, 925064311, 653220456, 831219948, 698337840, 164149860, 285692355, 445844306, 340919227, 331053317, 150670458, 294512176, 527855660, 691902323, 325982616, 346922908, 203553266, 694385846, 178763674], [585278893, 591157114, 179855914, 35783717, 952122866, 83900788, 832079655, 99849770, 24320003, 782449263, 286450509, 618656992, 944870592, 418481408, 860038885, 980623254, 285405264, 469572965, 175252155, 923892950, 63980717, 978488741, 366139961, 228171332, 446633004, 137479954, 51575364, 162649744, 747882627, 85317361, 952532275, 151829619, 831415211, 61738743, 196467761, 286029840, 419506100, 834533865, 473673895, 141433719, 641258965, 799020278, 373791519, 524470599, 205516973, 764377691, 20636101, 368866218, 254279643, 150954734, 649136929, 595807217, 384704702, 448101779, 330764512, 151455895, 135543328, 856965829, 508365182, 385989424, 507432432, 940035000, 915886809, 467276805, 333944814, 158044910, 991862777, 637185399, 441617918, 104892545, 178490544, 657702035, 864414665, 787541126, 875832497, 485912027, 331772234, 783074162, 444898345, 289799485, 477802767, 589011524, 563347594, 878390557, 95498713, 655928320, 194295711, 229842941, 422420791, 591722183, 25378272, 587132798], [401750675, 925937877, 27261143, 40962017, 582561610, 67308895, 112501336, 765716447, 599395232, 121678435, 336812939, 875260670, 72140878, 451074610, 851764690, 175403998, 14510843, 862092518, 353893756, 499825259, 174254982, 705523461, 397075846, 937903354, 339762416, 400242513, 639654638, 602110445, 352656975, 185828633, 732951367, 678860316, 129752665, 710336994, 576415404, 681781018, 785688955, 975273919, 989900377, 542410461, 184827291, 590379873, 275501381, 531758274, 181151034, 670145138, 542368386, 36168087, 258984055, 745371532, 212578512, 865401838, 915898067, 75947262, 914503687, 660286456, 885689793, 869152014, 769203577, 496716199, 511899920, 475985088, 770521852, 603871066, 230584320, 65358029, 125612630, 859063038, 698826054, 358485106, 37499640, 187347588, 402118373, 265129900, 644155885, 705945245, 497074059, 274367666, 452953113, 161650657, 46502096, 466329460, 718236716, 600581253, 669430716, 483021094, 943270394, 22489942, 325250059, 902690613, 816909827, 910274064], [391127521, 372459004, 694316956, 605033021, 796787912, 467669729, 744547665, 963049841, 363834110, 39320555, 566466236, 9303157, 313454860, 890749783, 847638248, 731358037, 393910250, 765780986, 347460682, 558683315, 234110897, 951937611, 463576814, 318388175, 23087649, 354742747, 936273943, 181751497, 16526886, 379440733, 284011955, 408564239, 878916951, 293154290, 875435663, 398645080, 433899339, 994919051, 977254446, 960747978, 264527491, 855355769, 810867282, 563826786, 444462267, 15272306, 77717104, 918431526, 835629337, 996596466, 222038266, 401401546, 679011816, 207881562, 281864543, 36598384, 599078044, 514966071, 405259534, 106900080, 703727571, 628422528, 35175556, 505195747, 822865259, 836607620, 423728502, 331047944, 539819863, 619850598, 765832754, 806529958, 265255725, 437679643, 47407964, 122052969, 184890928, 939455206, 209078107, 616463487, 236731318, 895614585, 68857803, 671904192, 639000353, 743460658, 377660688, 131120366, 384632256, 741233505, 184981204, 499808371], [351457938, 321789529, 195400949, 35137505, 251345435, 236960352, 257530822, 884118977, 426612288, 942259456, 44796019, 664346970, 87730094, 717031354, 271818340, 263224293, 435202192, 585902450, 393960643, 664213755, 712357024, 150198459, 400635242, 998824320, 811862215, 736073286, 772861168, 834176104, 789762640, 681897266, 480189286, 864382806, 301313579, 850080988, 163621387, 242328389, 696585068, 588003721, 804148453, 792835909, 519342574, 344370469, 55047319, 79193734, 420315231, 983840788, 407102202, 954135730, 502053411, 771920723, 809841766, 411189817, 452001953, 411373352, 750426919, 894294636, 749489269, 953849923, 625693859, 453858673, 10919482, 449135263, 354626068, 367443497, 245736980, 995536124, 453351677, 335088645, 799175761, 895849634, 619256088, 317149564, 636248735, 698864912, 281953843, 562564562, 119607410, 592981528, 129351351, 642507697, 425141847, 30174932, 596086983, 944456897, 314300045, 841048868, 142467795, 250661503, 983525503, 635966107, 873551267, 765712584], [438144056, 270291764, 74415321, 61431320, 934736287, 971602125, 531874243, 490188802, 208483074, 537146231, 103644506, 164192309, 137803148, 248869556, 108848085, 884399677, 66071427, 721368888, 761268872, 513339786, 686850741, 773120123, 28222509, 32259457, 187702577, 339323349, 679800761, 215885501, 154224544, 913575797, 231467378, 341541639, 613755129, 463741580, 592999477, 591780991, 686269173, 329958331, 615191837, 197835710, 78222350, 714561080, 220206966, 3235139, 622738418, 750442797, 804529235, 493564648, 989211227, 540170210, 133601630, 828956219, 703340029, 226843622, 550799120, 750824682, 564253020, 895925109, 442344873, 873825345, 815342794, 367275328, 680505777, 640754223, 449384483, 551055143, 665080438, 247047289, 113207423, 572816642, 142155444, 276542557, 999498580, 208007474, 201650258, 734215265, 207305164, 928052513, 534688721, 227065579, 329429803, 959001823, 831871526, 391788164, 299561494, 721905139, 656046511, 766352159, 308655318, 697088559, 842382533, 623627552], [66859358, 317618869, 409231919, 852988441, 851698844, 983349325, 111541235, 687356674, 430244802, 665398389, 40444129, 965684949, 210917619, 626999204, 874049989, 635699969, 153801423, 139781844, 922347623, 569796795, 729888516, 84611137, 316150296, 617974337, 816634942, 624256609, 802549725, 452190669, 323767559, 922126473, 304272264, 25676129, 500093239, 169456535, 598135532, 930951125, 109661902, 726474218, 630336546, 922768646, 874840242, 506608455, 272414037, 194352100, 60873733, 476743545, 509191139, 58610166, 607088422, 278327609, 864135021, 384934721, 574579633, 827226364, 132026610, 557714840, 943492915, 420846616, 129936945, 551574558, 103036776, 379879671, 237933144, 86287995, 833624204, 667567479, 154726875, 326687668, 786749453, 147522769, 18540448, 513235618, 461509736, 240179953, 369998258, 895015549, 255753141, 815679450, 660338404, 714734170, 221904990, 944741098, 770072649, 117442802, 416290142, 760913479, 505927739, 82626526, 458470837, 105259360, 621658609, 755312547], [998153875, 29324252, 51556036, 573811942, 167878269, 121494890, 20159597, 91493259, 387139816, 319156304, 384278185, 89815450, 250082333, 838490037, 968511272, 212209127, 87213282, 680976410, 999582438, 177509676, 334298040, 641776312, 633373587, 984155828, 654748834, 564484973, 400833722, 277563127, 34684297, 152576820, 152147270, 781291525, 901482672, 122848358, 718555100, 466067332, 980176480, 901663231, 402711702, 920416308, 357406636, 403658220, 606724334, 625469975, 172683367, 726452166, 34587007, 750380229, 802527057, 499176265, 995585578, 900357392, 265823076, 261318416, 725697243, 24545805, 697498215, 2861680, 527145039, 484798918, 413004901, 435006082, 470084229, 183371666, 842521321, 102680061, 415200836, 663520747, 708224758, 25622958, 102743904, 872799589, 979319317, 234882579, 197351800, 264611464, 376907005, 829447189, 254276797, 407154727, 396006443, 632611124, 846801476, 157015193, 981581174, 582501735, 194282310, 820191505, 717123132, 60910292, 807359487, 579471480], [689408, 955713035, 234557967, 617838614, 756278961, 357408426, 968040756, 330310261, 68017391, 16073718, 923500754, 616521783, 918761735, 819565891, 54277210, 516546447, 415830693, 115321797, 16140801, 868025401, 323208723, 219764934, 778622009, 584840724, 362934654, 399118743, 79766090, 441835318, 497038236, 975461573, 272955584, 849785788, 901260262, 379559727, 655553698, 116363787, 474583932, 695517247, 928926877, 415448947, 478595107, 982790834, 893088283, 581116417, 791779294, 541375691, 652805915, 327686074, 698663097, 860692193, 809727037, 618409680, 270650397, 114516813, 320862410, 227698768, 83481147, 973971679, 317775257, 876028110, 225463793, 240005204, 118500379, 927308040, 277135748, 827981705, 880720653, 822054779, 984682085, 36475938, 489807909, 442115374, 220148160, 329062856, 404665504, 880217096, 182121108, 539569203, 524881293, 690129772, 388118359, 287093136, 808425985, 690682466, 502355110, 751290764, 387225827, 748796361, 349628959, 67078825, 45789053, 611965776], [485748142, 497259101, 575494463, 409935625, 942762441, 377223104, 95789380, 453333675, 362986755, 347312170, 424702316, 79444092, 39017023, 592999572, 421807429, 789727643, 960587653, 119901425, 847343086, 307868341, 669044939, 421423130, 789175373, 13735470, 782646028, 139617541, 11648302, 97931900, 411614386, 10483299, 584596106, 988884294, 142954177, 362909584, 493064702, 130951073, 279660378, 968636702, 344137295, 287406805, 301212740, 114959305, 92836590, 727894215, 729329223, 555598245, 313220698, 851466092, 609445262, 921503887, 573986605, 896530939, 838916279, 41904975, 419577993, 850577913, 508882503, 873258277, 731330256, 664644524, 907713433, 57535658, 761042664, 645140328, 700449605, 559070511, 913032142, 237146588, 649576263, 309376600, 268825674, 200943745, 462850589, 823112664, 214181958, 407675442, 490090317, 756093043, 577674115, 662319473, 847436218, 343847689, 569580820, 643208858, 845662796, 443294623, 684563873, 48833239, 32019534, 657006841, 302299648, 301184984], [405813109, 580221316, 509767551, 774116240, 200975909, 216733312, 142822170, 585884465, 693137731, 799210472, 586661834, 333627163, 759108551, 665813496, 242727273, 607598614, 459412472, 36488817, 402754453, 109832210, 603625708, 68087274, 486311134, 792121024, 991893725, 185498225, 468077149, 303106852, 134886184, 493618815, 206050295, 614354774, 835815244, 487038994, 239159119, 141440061, 49022156, 251206434, 949625314, 115951811, 425550720, 682156651, 615543173, 700731847, 229842697, 408200953, 295972260, 590198159, 182896328, 726880695, 979787350, 20004304, 992276328, 64107948, 70678921, 203773273, 758879293, 46720910, 598316013, 963453971, 269119757, 783125927, 590983061, 45351430, 364969715, 42737796, 847342753, 263881455, 417418850, 976726381, 945522436, 187477011, 770345648, 807707916, 212227355, 724621013, 542833080, 905932121, 864483509, 503652118, 301912538, 925534898, 889978066, 886462840, 547129392, 960926162, 338487113, 869465261, 346343599, 213978365, 305627812, 861324385], [383932426, 569791734, 452753001, 942895742, 334373069, 251472809, 969684186, 125518158, 692535068, 48284972, 64932971, 858608059, 384106599, 103867405, 558459617, 888872830, 95981197, 389964377, 850134782, 532499795, 487824546, 253878457, 162520253, 994848181, 995580556, 987148116, 496315562, 435574816, 668032242, 981124867, 530374854, 74208959, 904792804, 75179875, 724735507, 183636053, 323005103, 857626642, 578604422, 553429655, 942658155, 194757887, 295602024, 688217030, 763894430, 291331835, 774838760, 783623995, 121982082, 960209944, 789149680, 490644219, 58982706, 226904725, 585411392, 756582580, 808934165, 114804860, 87876800, 685949032, 53392429, 147618749, 770278001, 826512451, 135874971, 838591361, 312711130, 415517330, 310534888, 748786407, 983253727, 29617900, 147733030, 148689938, 510488665, 570799835, 335242502, 315219723, 138041533, 481775007, 812980611, 927847627, 643132112, 358181218, 614369616, 906935822, 255538344, 144383146, 34181772, 899929056, 14096109, 34267820], [639754846, 305472543, 989818478, 868190507, 954717317, 173129108, 972746267, 691837051, 856585214, 77232437, 548318720, 896346464, 721154589, 349381865, 288145303, 352398315, 473123233, 159454367, 610055629, 213166852, 150154994, 159439135, 550490023, 524118880, 716102016, 910590381, 852534838, 364517047, 777797136, 219737664, 587739129, 509407334, 212614010, 250031109, 336747448, 398488476, 482614463, 481176748, 14435360, 949259897, 571933250, 697683051, 675247418, 252670066, 259158795, 660221811, 380946330, 89520744, 117417191, 959259062, 915273112, 994187922, 554026153, 391950022, 358271039, 892399298, 887592445, 193275729, 849964126, 567943201, 620370980, 347615743, 158579943, 551823149, 663755185, 664736395, 871709708, 667292699, 274919798, 919500064, 545989231, 618332903, 378640781, 90264990, 274070985, 543412146, 603550769, 182890251, 507116223, 826561703, 19297196, 791613181, 167482442, 290813477, 395406722, 655290416, 511661441, 980028939, 608342410, 65053581, 231329300, 311524162], [786683663, 325764610, 295422681, 587048937, 348348991, 918901474, 241013565, 872031705, 165132249, 657554725, 509790705, 274751179, 948485700, 500066226, 700245923, 966635683, 645120920, 609326301, 712891124, 495633152, 9909090, 565173467, 204096470, 186380104, 465072252, 243870042, 748454242, 351149854, 828603764, 539645233, 514932160, 831406184, 993452192, 696856928, 490919876, 861823209, 510844252, 259769647, 206267721, 619426055, 589443195, 365727491, 793429529, 879529174, 437206592, 839424146, 226955497, 119226072, 653471072, 493702326, 668723159, 115131579, 273390867, 823798726, 637094879, 118076945, 537662327, 494084526, 906646187, 531168838, 463633688, 111432997, 477797970, 999250854, 253680008, 511086691, 131144787, 663761817, 322657130, 164749410, 839435323, 68583026, 704288999, 459030904, 715255087, 199959920, 22233072, 4283269, 127624500, 324598014, 674623230, 591446436, 574279692, 662505395, 178019711, 745645060, 247080920, 486902247, 522750079, 439642688, 789422004, 661118057], [942687481, 515910565, 281451677, 25739892, 887515858, 572250694, 633966476, 858202039, 99564058, 483319005, 404088296, 356629415, 394488323, 428989444, 932799109, 328366939, 206236982, 788511718, 246769205, 811579549, 593095086, 820485181, 641655843, 684088383, 80148876, 315181162, 371685931, 893999643, 249120788, 993154235, 295589098, 625628684, 607165635, 668996468, 550481004, 146313607, 964728413, 143051128, 299839690, 545506865, 458503195, 356854682, 755057557, 177068630, 897130705, 204005137, 518450074, 881001555, 528144316, 790885627, 156858516, 978356233, 781042946, 809941795, 270563027, 745494437, 881730082, 460861023, 167190404, 219165866, 835798866, 799941485, 693298301, 355991735, 234719512, 617148900, 163237416, 725936601, 346903009, 246611713, 235887320, 478673095, 568134030, 611534730, 214655568, 877281629, 863843803, 698475389, 254316815, 670491847, 720094027, 320581075, 750864884, 36504097, 274961662, 194129912, 497089215, 5463344, 192615421, 868581817, 75876883, 766303149], [124497515, 160453627, 716125379, 598987533, 534749293, 728010068, 200683130, 112956835, 584678804, 991685877, 914861150, 255066512, 427811532, 2509918, 192667485, 158841789, 953854328, 241035169, 312433695, 214565311, 890165858, 441971587, 756851118, 947070099, 311169294, 985264717, 479816217, 551487019, 952765427, 33558528, 659179297, 497501724, 758641311, 142066350, 324057598, 322585574, 72012712, 851296355, 784845725, 998938498, 584907562, 429073995, 45788603, 558441713, 159790398, 40183485, 435233684, 702416094, 525700512, 14703525, 144033602, 997103623, 38795198, 20134470, 314197897, 856852992, 316182300, 46083141, 175949086, 213500249, 248164304, 997933156, 189109312, 173642612, 933522726, 480304706, 581026542, 637209717, 651447341, 811821670, 560973521, 638992728, 399848187, 986326551, 548337091, 240415860, 811378340, 332983140, 923007412, 913546978, 193620734, 387135206, 790624555, 757307286, 724861919, 594038993, 366465970, 654660601, 603039076, 623203005, 393921792, 888651377], [835564981, 391439957, 1657718, 528349747, 163988483, 976554216, 726340842, 130588960, 690086358, 519968079, 911122723, 692560254, 893987790, 140134954, 435059687, 168828277, 544841533, 441730703, 671928103, 525517209, 667729080, 283755170, 279641296, 518458402, 178267563, 281042509, 229473254, 121032978, 527656820, 503229450, 41712019, 958623179, 851518585, 446669718, 267038879, 937625368, 990224109, 496526360, 702153830, 471026573, 306673183, 445815799, 496055948, 41161324, 202763250, 602104576, 570234136, 333060754, 743474925, 983071620, 460565736, 851100806, 660009564, 395241167, 579371369, 486356099, 159172770, 223462897, 543401406, 496646824, 619468774, 755789726, 910139348, 432588167, 433163209, 782841533, 374678291, 683004139, 722565144, 324446756, 823110648, 585561699, 184364972, 672943269, 184775257, 428004163, 261729654, 168343295, 365362584, 724680767, 511046435, 580728965, 490477774, 17378399, 150284982, 344982994, 187847203, 915285241, 789841191, 496650980, 434975378, 982789800], [157672194, 357636099, 940310413, 476337842, 694503346, 440777162, 56195995, 244340472, 307726494, 541109503, 615002928, 158656103, 356599916, 957029720, 442748972, 545819154, 275514593, 838761370, 367995471, 343718615, 508885463, 327866823, 411074852, 594263247, 119131099, 609558236, 962763228, 195833355, 4996026, 46103513, 696668220, 965560842, 383482421, 366796161, 633484028, 895090784, 794838451, 795435971, 762801898, 840334346, 249497610, 876197888, 814295831, 35062001, 608844617, 328680732, 933859682, 467020729, 397675788, 768327550, 346888815, 285115024, 936884038, 847469191, 205867246, 509535569, 78631783, 592204981, 363436617, 731937629, 94895981, 923874051, 71035780, 91337837, 428271675, 366270996, 152039720, 174107887, 53741826, 543909576, 428988568, 263993861, 954464500, 387144252, 453925452, 128647285, 90415654, 518889164, 867941352, 371295659, 556919251, 657532643, 934365934, 222011448, 383260638, 639952498, 332731907, 581665477, 399665757, 478814433, 440313061, 149183926], [782649766, 905341688, 435789355, 315111253, 718643742, 395961359, 805394923, 793500427, 544378250, 832429966, 6226150, 513095332, 641545211, 632956527, 662712930, 533534573, 808315564, 980724511, 164749216, 444938954, 950416627, 36976676, 293411283, 186327836, 623134542, 823976833, 879494236, 319593595, 402081218, 172805344, 405355214, 947071349, 965141564, 567292156, 167821356, 344310753, 88039925, 254846303, 159230456, 749460035, 469324397, 685613559, 997108516, 823817152, 98212199, 592620223, 969404165, 67926692, 182917493, 169900294, 374968394, 599735173, 284730077, 705433161, 396192116, 620900947, 61767423, 474242291, 31837483, 573726710, 470777807, 787741988, 120300674, 559796243, 827296433, 915188701, 293803453, 455537296, 159104764, 178805817, 269044205, 503203561, 583533389, 517250426, 383610443, 504738496, 40489459, 507052858, 417613900, 63808720, 594385713, 587583289, 403415125, 759230753, 6529563, 641668161, 654098826, 461253305, 236966723, 422669800, 648900868, 657416249], [780446732, 548243125, 440811411, 443135150, 267006084, 841003862, 126831629, 605189567, 70173661, 721763417, 620978029, 61091777, 457621908, 974188048, 246619762, 439393942, 908479729, 919761452, 474161626, 661141527, 971743610, 946060710, 496794272, 114525693, 716518812, 827053554, 986515804, 676024163, 771367314, 259574854, 580894427, 182062149, 443779674, 91360796, 248002940, 637206986, 312831682, 374089993, 778798049, 191027414, 431709952, 561230937, 203208115, 468314396, 396315487, 368449210, 593229833, 576354743, 706585556, 798148043, 85242159, 819676628, 384470444, 808775162, 758324924, 943361569, 57938758, 661299395, 473684544, 781200675, 702626429, 206853619, 319933871, 662940660, 871855550, 41944516, 535296256, 770891416, 425055440, 141460368, 593978733, 303478715, 422234759, 535208941, 624879099, 461198597, 816766251, 829385996, 750374528, 6930307, 123436946, 305363160, 253372879, 703332419, 727628036, 548813844, 637450019, 845739952, 651297380, 437821221, 663275056, 704697609], [464922121, 980653391, 176527600, 651889049, 958458506, 324720879, 236055244, 199601114, 212517891, 696397160, 334589896, 718469941, 613556639, 152415715, 919282212, 756217442, 71262029, 170474309, 590461183, 605738096, 526126726, 667033628, 878539369, 999259763, 767232562, 953911601, 654886979, 702914494, 48933949, 194490705, 407088522, 491592086, 725693336, 238148502, 739449661, 501542149, 86668807, 764991908, 350744382, 845783667, 267557294, 234502066, 962475891, 415215474, 136804405, 167460823, 366276620, 805668310, 82781229, 436301922, 356803695, 459409164, 498299627, 959325206, 703505930, 547287422, 707065823, 791404837, 42178483, 545719993, 124205997, 207737609, 576935141, 516114942, 140392087, 847250242, 188420400, 468430970, 874962079, 372383324, 435230343, 636387116, 380597627, 394018853, 58348524, 975733098, 735445944, 417919182, 330813882, 711041333, 496624433, 399855571, 823166391, 264121822, 461618550, 296206773, 219932581, 688793703, 627409447, 88717733, 397445975, 679569295], [950685142, 672665264, 871054751, 34940042, 981211572, 332772747, 844794093, 341939199, 169391524, 402513880, 659104211, 932136997, 205047891, 735832865, 29375792, 251219925, 690549344, 168998874, 240955108, 414724671, 7531371, 982153682, 172539997, 228125938, 602349154, 383784174, 179976022, 587271917, 801359846, 406405938, 991710963, 162188382, 88017904, 187880343, 454904965, 10292985, 171436222, 209271588, 144170223, 923815492, 4880729, 349018901, 123119986, 221179650, 814961289, 661743433, 320653102, 332299289, 943148144, 962123687, 175083786, 328078477, 52202139, 621606732, 21457255, 428906082, 233575106, 733284799, 221726226, 63781033, 346842481, 646559678, 449842748, 71992700, 457435497, 687616864, 595373138, 853331755, 280654962, 242511003, 577426048, 187807908, 968430473, 800714617, 4353491, 817366352, 236480125, 883904708, 393181860, 913106774, 156567266, 757622589, 372254347, 513058867, 767490430, 445622185, 2281737, 343404558, 473978237, 966973974, 571658410, 38044445], [37032513, 838105721, 271807367, 800209117, 797276420, 812521087, 926840334, 989032756, 624617757, 596118489, 565794968, 306014663, 421768657, 56531256, 463876987, 23198254, 309577295, 592172889, 18451995, 946705690, 606569886, 111516430, 397995678, 437192871, 111394411, 490527481, 329910992, 652514521, 385754697, 500776060, 89949219, 491459896, 578944342, 486796142, 992768238, 491384826, 280628995, 558733837, 370449351, 722645454, 812341607, 998600931, 762271404, 234031170, 98017980, 131479449, 845875218, 172571448, 593129598, 289983294, 970952793, 176570679, 589778076, 692595547, 279767883, 733876242, 329141766, 218587031, 855671096, 314792521, 169758229, 289118443, 44213273, 41698431, 756475113, 268408629, 525216651, 168946481, 481273945, 507055547, 260335118, 455948822, 737438901, 598711660, 199343493, 715268857, 777644, 666499654, 172449506, 499582255, 465953499, 508825809, 547492068, 74775910, 199442474, 782821009, 137724827, 174115123, 66142472, 32905259, 467730698, 424059545], [209689619, 485782455, 608393374, 870915157, 915627938, 945802347, 394071938, 423694307, 492264309, 969395590, 176425628, 970744602, 262386087, 897295653, 976553557, 520812660, 307213044, 810305134, 651539391, 29861766, 839533163, 904616119, 803266009, 156496158, 914446571, 174938709, 5308666, 87921455, 635428020, 478268995, 804892122, 659540107, 112586150, 479770137, 327085614, 821124028, 325768440, 82107550, 853991289, 681631382, 182948441, 469842791, 110502833, 251037578, 612048334, 455758150, 159624553, 972805459, 12703039, 742982494, 275230446, 969017992, 627049031, 281157162, 546650616, 965303582, 260334771, 555749880, 796460833, 294652968, 966462196, 766266933, 17039066, 570858771, 635288948, 856603069, 208685831, 222703153, 243901451, 402789874, 652400992, 8858650, 907731610, 211868472, 952496116, 839796840, 642800984, 500079833, 255647717, 776565018, 46958191, 453660642, 605201811, 804265532, 466632398, 308533385, 132625227, 789480598, 149789556, 77962374, 839322333, 99704642], [92913524, 80873306, 286316579, 119385240, 14209508, 40306977, 370047940, 299318809, 752123299, 950793337, 298915086, 136144614, 898409914, 769803608, 276009319, 525026878, 475283444, 939558306, 847342912, 584073752, 219743724, 648740469, 274556400, 887362961, 330318591, 946903345, 960116153, 164412199, 720514751, 712796331, 311847960, 185077779, 674653454, 274502738, 921342830, 782643511, 137318711, 608097166, 493518131, 352437394, 388097601, 474548297, 555840381, 234377151, 508355479, 300412115, 897065311, 994375135, 258336491, 503764143, 352110400, 689891608, 265784181, 152388091, 114346186, 292483760, 41877988, 623254108, 591744126, 662783190, 570693021, 255595195, 766162177, 468226734, 195264370, 504854475, 988802669, 133472440, 913418951, 316884918, 713304176, 917491073, 222115022, 746378928, 952716796, 84753201, 612053215, 811335740, 563475571, 863598740, 798723515, 829544226, 513100057, 864658501, 819501000, 364605478, 912456546, 155080722, 403610914, 819568067, 611889807, 920199882], [618371531, 118851452, 423031185, 952714262, 287328190, 171400937, 311174167, 922747095, 628219145, 296434556, 823775636, 554854030, 110520401, 667637432, 91661163, 136177490, 879708369, 610241295, 293197341, 728711630, 984136775, 506904227, 187440200, 536464259, 17648471, 875400176, 881610909, 591516127, 651338901, 971608493, 997810519, 643020090, 420199297, 278100195, 196256649, 884664028, 701580472, 44095726, 953394465, 369943909, 304178730, 980998191, 85651945, 584135334, 245314991, 18325506, 681742095, 794617846, 397158397, 132823318, 424152233, 348064574, 902195724, 67237494, 353471343, 130557009, 823753654, 385260658, 483925461, 816069488, 280104753, 19588742, 521077960, 929697582, 236799975, 299718302, 512534009, 952525541, 700406055, 898025826, 840024678, 926649964, 973229858, 123440631, 174634820, 949007159, 479000557, 730178063, 459344656, 745504563, 853766684, 177422747, 250441843, 98112409, 992204275, 762102322, 742322587, 380280749, 583268073, 335819612, 505499706, 339545634], [541413248, 172069523, 960037235, 301404113, 572097694, 833713836, 64009439, 793852186, 213032966, 859436437, 968910218, 645268257, 749769064, 552888823, 277137569, 44391067, 647016835, 294524765, 754691017, 17612104, 158582012, 184588736, 581174268, 937243737, 800302952, 107358194, 253848018, 52390417, 20359072, 804867633, 933408306, 136993094, 600943865, 890750238, 95741135, 944741907, 644667566, 169434301, 154261140, 773253618, 991059267, 998079347, 6575218, 535585520, 274656584, 127451742, 709012709, 597670615, 810137777, 372856459, 612030411, 196169897, 580686820, 750569034, 119146207, 516551267, 431263792, 193730996, 286992049, 668977045, 159530174, 517682390, 324724081, 652639201, 671789000, 58731810, 115454546, 986066289, 450346445, 303155298, 159135999, 202174540, 875339502, 207143945, 182375597, 494519842, 235009567, 468020316, 243888443, 450164426, 380505401, 247395642, 255100348, 50230301, 297021977, 136042033, 437283956, 317048057, 180862085, 236743357, 441054555, 310555854], [592624000, 74635926, 716394176, 144605275, 545158009, 869012442, 183800190, 589478766, 177262090, 723372310, 983886711, 106235963, 951490020, 574428351, 518711773, 132506715, 564564796, 104659974, 495272435, 328394308, 740896089, 940134718, 294111110, 666593656, 880805918, 40398474, 437311997, 934437668, 693303252, 612951192, 957922578, 609458358, 750138245, 845995699, 489792992, 815889649, 334584663, 937410242, 305594264, 453191604, 93126998, 317556814, 443967873, 734054817, 166356238, 733587921, 498411068, 702306271, 195513818, 86648904, 131108414, 665518384, 53768788, 929659384, 974890363, 290552593, 196265354, 402720447, 938000183, 350387689, 84410336, 243946606, 31176494, 142513755, 154663376, 327779877, 298029541, 218998368, 387649299, 651590356, 188622430, 646193192, 746937621, 943606317, 543366107, 615538444, 148805720, 160034190, 467420865, 635681816, 436661973, 664289751, 565262284, 894604422, 74659904, 225218365, 736432295, 501135907, 824975739, 383234887, 173077161, 663201648], [924348474, 324659362, 178239979, 382308264, 593473348, 908924162, 26290042, 423462825, 100422990, 468973637, 865278758, 902323825, 191442454, 131216551, 440051056, 197835201, 405019622, 715351062, 881765408, 239817079, 704642723, 165274591, 489142287, 346556677, 739884342, 124963867, 132882799, 586556092, 821852839, 509160592, 869130753, 758165413, 235401673, 796031469, 717275476, 45720846, 809095493, 3581477, 784234261, 538149691, 436851947, 357024314, 519600082, 159041943, 234930947, 961435190, 375994987, 371032685, 378404262, 71680588, 625395214, 994025913, 715195753, 552344488, 254768824, 442480726, 164226405, 251416114, 576568336, 633513240, 198196445, 307358256, 316363376, 431718724, 67403129, 511970524, 48226892, 1729680, 608667414, 391533361, 19752676, 689561763, 850864796, 731831120, 424114660, 4943778, 974793230, 836872535, 933282895, 884986520, 235462325, 500959142, 756276016, 831896252, 303353598, 429343865, 661315615, 773735063, 863871862, 626601955, 497908919, 658996302], [705485359, 571212531, 643079342, 625013346, 129192431, 126226221, 177912619, 853645124, 620392229, 555722940, 271107464, 762921963, 165512501, 702743301, 425390338, 597171819, 108791567, 133881967, 251401622, 930626669, 461810730, 778045047, 141062613, 293358188, 362502513, 248336476, 544969712, 17364458, 153046284, 964240317, 75769965, 240731412, 346341537, 741184971, 486865275, 860311327, 729465481, 86612279, 561775394, 386363370, 885186816, 141971310, 676565123, 38068322, 139648537, 103742704, 824327254, 849412867, 886741632, 45711845, 97974618, 253101728, 155103010, 688463220, 797845712, 739638618, 676795596, 423309224, 552524266, 437220072, 807742079, 304861212, 20000138, 53636534, 992944014, 75804573, 660411110, 38557126, 532230363, 959520870, 234894610, 500176339, 38089799, 496019016, 192834798, 232742664, 240591381, 953256436, 352478478, 369990115, 327353818, 86060636, 226357895, 73248305, 107264956, 822702099, 976627987, 385134629, 346276171, 360293525, 996097979, 489094607], [810424797, 440834907, 566657234, 181158859, 124202637, 270383191, 527553222, 771727120, 297015874, 410371415, 603246194, 48718386, 23425337, 916292208, 925266572, 873361182, 508410593, 741790728, 51813971, 333384852, 774562260, 825062402, 676527299, 462655841, 58182889, 652605890, 22016057, 750426189, 785723094, 406794683, 819864557, 590478803, 506735634, 341145141, 404304879, 312924929, 638732260, 147647323, 475542101, 413248105, 710546805, 453953357, 51328285, 327555232, 645284915, 743889455, 406264203, 590053168, 769653631, 543496854, 963303244, 746898590, 907065114, 186884111, 475606818, 247717917, 67216544, 872069213, 718215760, 964328042, 706040014, 970142289, 763839185, 420279344, 586038476, 404905004, 553266721, 5228652, 709280849, 902186633, 834233112, 521254813, 260561110, 34648260, 656096560, 77342207, 487983607, 341127361, 720250739, 175643559, 774266853, 524428625, 375368521, 558550284, 930068123, 365794819, 647985626, 793426943, 54237186, 711613460, 335736941, 398848507], [932385571, 287022762, 761843108, 196725094, 14087654, 970092786, 521441836, 475785278, 364049576, 438560613, 389585022, 684786533, 238007502, 791352725, 76830801, 15134796, 211575688, 896048184, 579601931, 765950760, 157917389, 695224298, 418879789, 136150753, 888955778, 561645411, 981020724, 838307279, 163246593, 304790750, 805266757, 169372241, 108967172, 345259866, 204913927, 187350635, 890731095, 236013965, 101719460, 183137322, 756001758, 749548224, 261701795, 72803578, 866576573, 410887658, 228903714, 515810492, 866676673, 958600262, 174934136, 161630438, 674276473, 895074675, 477170876, 57305414, 701093280, 263857086, 584492961, 475266682, 571706927, 503603187, 714088661, 422187116, 398316512, 284084564, 370792352, 644244852, 740433118, 332244988, 523368955, 897245888, 2383248, 554110679, 809925739, 428100026, 547297919, 654896560, 675339848, 242439992, 89252198, 211203148, 27075453, 683809111, 666529471, 829980147, 432921927, 469293110, 169728816, 706951579, 691521973, 791930870], [208015398, 206987850, 290952340, 131287320, 250844234, 955508000, 516912935, 204376287, 539401114, 622468146, 895658353, 73889386, 195612142, 740773069, 955785119, 399276347, 827704847, 347530186, 813752902, 65263762, 55334787, 446864415, 560789977, 763190754, 370504732, 377192837, 685855927, 725458475, 560465991, 100825808, 894026068, 972640394, 865305409, 744185366, 287743845, 975024986, 956850810, 871314426, 251180425, 671616157, 215692676, 268911619, 151218903, 531086954, 553339861, 594718219, 762307308, 625563976, 43870865, 300096952, 672734515, 497338946, 449627475, 136708765, 781073202, 380450607, 963913720, 607541213, 805231002, 236467618, 842539501, 79486427, 393412855, 454598538, 873777136, 187543755, 755522060, 748072965, 965875303, 515188466, 335401577, 361435659, 357565599, 461799222, 551410707, 994417845, 7149352, 228076566, 920740545, 515697227, 443920612, 313291759, 104870178, 788980624, 42571565, 856705043, 568850452, 861893509, 178982597, 712294119, 422955129, 142483190], [711969081, 713258772, 368595062, 18417136, 995115296, 105238085, 486794227, 893756062, 245464377, 668124453, 641523511, 875904462, 323869050, 28017360, 366565435, 494612852, 624136219, 969048466, 976924932, 910621284, 526312389, 177662147, 763446251, 576885783, 695647339, 617157929, 293942905, 154042196, 70852187, 888254317, 894928141, 79085383, 403517567, 398990877, 874928058, 537835939, 55601801, 823460377, 590060026, 962633741, 637668444, 937809753, 839620777, 94867985, 711601440, 21982180, 893961581, 267105270, 209147338, 854954352, 766140241, 159300676, 984084801, 275593987, 888573716, 41912536, 328522700, 707104386, 195373582, 270447318, 511351920, 148178965, 738399963, 197080852, 697215059, 859330954, 411457964, 852046723, 190423722, 456267113, 565264547, 640438508, 950435724, 948017464, 717811591, 567167344, 176456846, 811170547, 198596143, 116072343, 958895578, 649085202, 267521318, 251640098, 146699256, 360949344, 610965105, 528574913, 529422763, 906088352, 557620959, 491298787], [973483103, 828624270, 177699068, 550666590, 180117680, 850287022, 516389279, 951915122, 183140131, 182992197, 420883229, 207570249, 2584980, 686656006, 666502269, 554244726, 332737175, 433150268, 21316781, 872674153, 222767450, 180662074, 452997473, 294876642, 582456031, 705356600, 860455901, 182186237, 998016321, 825243130, 430147705, 526164156, 335306959, 918970195, 516029285, 425273440, 307012396, 608066299, 971946067, 422053452, 89078490, 357196877, 484858510, 857279805, 249594624, 286463343, 475401311, 101511635, 638717288, 704864588, 329537941, 908862754, 940030704, 707984697, 336026251, 143759075, 79940103, 101958412, 455465225, 665901167, 795060623, 979257972, 332524956, 667172685, 177317155, 108784114, 107115381, 703676134, 756681767, 759249989, 886298679, 426114478, 167196031, 549294845, 977130221, 310419608, 376578621, 820004152, 344938021, 298503716, 346900512, 906052227, 606189382, 706119011, 349688949, 65180034, 268034791, 19565983, 114102092, 270154478, 54729781, 304473734], [406557649, 615317014, 385250862, 411134308, 369304204, 472680040, 991341089, 362875963, 508688062, 2477327, 757319866, 458387824, 918119400, 564600696, 630354091, 755301745, 750269215, 867776979, 687223708, 500363644, 915799424, 265815486, 791243422, 283517885, 730178330, 441538275, 734120392, 433891827, 19260901, 714850200, 420107118, 253209915, 767572544, 787266016, 483221219, 786991987, 1420087, 473139236, 187355912, 806075310, 584265697, 571770834, 341734112, 509793480, 13556848, 302147812, 806753658, 256323557, 510290612, 969046595, 104610274, 978743751, 690307819, 164315677, 281488553, 582289453, 244189637, 584228551, 810265665, 428064745, 665563520, 455465468, 710004465, 90875318, 944506825, 835042816, 303221269, 515265793, 424095212, 583950290, 814985456, 906578361, 412070217, 296273518, 480158396, 18946622, 105226467, 990454638, 173286454, 700771709, 253077793, 489918500, 765106682, 66283793, 416554363, 485894969, 348345579, 113332290, 314119299, 418732992, 837834165, 57247847], [108705557, 792598705, 651178682, 154056096, 965228060, 703426452, 203791049, 7693436, 987363722, 525977894, 493507754, 546940673, 868384022, 5855187, 906291704, 551084832, 797568383, 549902487, 316390754, 873454634, 892613842, 97345912, 343583241, 83123181, 31769897, 252885106, 877595823, 286899839, 671640257, 37065337, 182531588, 232537954, 87844971, 599400875, 612424073, 55265530, 117312725, 740413120, 966626217, 574516279, 182365827, 681697631, 405348068, 872372525, 833718920, 249111875, 248999083, 884944451, 33057434, 440480834, 310772466, 800223169, 555803059, 313946477, 814790142, 335671787, 225529957, 48696591, 159300226, 103345753, 382698894, 562255903, 91928976, 781840033, 817620525, 449187758, 83889530, 802190369, 916597936, 949056925, 453166436, 499763418, 38101314, 56077774, 212591122, 502474482, 694301056, 567960078, 514667802, 553721972, 158547505, 989372272, 725061472, 703050601, 361801966, 702400028, 828438085, 556084222, 899747914, 490592069, 502524847, 393063023], [656508380, 991411164, 25498897, 236523984, 274471788, 933857656, 745281065, 486916153, 619458263, 205313195, 99905802, 452760177, 912260939, 363481408, 35089781, 253824251, 943666970, 297429318, 881263022, 632709079, 866935831, 569136892, 545604016, 681762247, 642676532, 159738667, 372941361, 704104986, 109178017, 31746188, 223233539, 965112920, 773497635, 125266763, 618530051, 821976692, 162819183, 713672781, 960241167, 248752838, 102918355, 546016150, 239622737, 307991085, 409042979, 728944760, 661585185, 603084228, 800768350, 74272005, 116350248, 117181863, 317334779, 428453698, 311066047, 316233680, 814095948, 271677708, 718029898, 691276518, 695428658, 373745673, 912671103, 952421400, 843541222, 225777872, 95316962, 181520003, 198292010, 617879942, 609296694, 909306943, 388817544, 330165103, 945623729, 904642768, 864860831, 374772051, 98583310, 516532758, 31235588, 343389802, 312034014, 84715912, 367242159, 363905295, 225158889, 386822886, 263047288, 483862906, 248714587, 994160841], [699335348, 664503198, 235539547, 756754075, 578685797, 73636355, 489633833, 229759678, 260821250, 285649404, 441974490, 319312278, 69563347, 352430697, 695994878, 798020858, 759041549, 576832629, 142873607, 933117765, 107500560, 898058303, 63647117, 836708650, 6438308, 895530829, 277156164, 512472423, 447255871, 379438496, 245744618, 49569487, 727712165, 288157754, 651008424, 901393424, 166013200, 200986226, 545946207, 790009703, 232718299, 238749717, 101075900, 879385180, 875174835, 871598225, 260485836, 260121272, 907998548, 691067981, 98387140, 629817892, 46188496, 326361500, 587658811, 35898024, 483861808, 431350580, 978086, 637275690, 389386794, 747692692, 795599251, 594741820, 854560727, 357679996, 296120011, 585604914, 486540610, 16259249, 115938866, 622899815, 271963754, 411430980, 389579194, 89241005, 246499638, 999343300, 12442111, 92530752, 395011519, 874053693, 174150891, 748529659, 152065961, 382986186, 910241117, 986506628, 290060732, 214981284, 633880158, 442989049], [189155475, 246319175, 980469007, 226453256, 834794611, 47575039, 871355451, 571632192, 965966933, 29334624, 4588514, 464049993, 84441412, 623808445, 888545115, 585111979, 574432047, 126787845, 325293891, 514268351, 262660894, 72569703, 960161023, 220428731, 494653303, 379900602, 722814409, 909165399, 711676745, 48650717, 810443704, 710467385, 920206085, 4759622, 344810670, 633042350, 646386485, 742349514, 414272210, 13835768, 722326828, 486005327, 722531895, 122344108, 706183642, 325896861, 422389461, 290346147, 38915100, 554335170, 673062974, 391745816, 894222894, 940330523, 552097149, 207002615, 300051184, 86236139, 459650443, 933545545, 970707861, 741673827, 292584777, 901632773, 775059225, 943843540, 383898686, 733006795, 358736860, 288447281, 967039453, 256473262, 753222368, 945236735, 743203588, 178829949, 169232251, 959098735, 589369796, 478017981, 614767393, 642225362, 323024600, 979279497, 552988884, 223693524, 313184493, 200568417, 921174339, 138772720, 882066801, 980790026], [51711056, 337529550, 151344097, 490906463, 90952147, 221868393, 655581303, 498566476, 949691348, 304134661, 768380328, 84210461, 849847760, 765274244, 316654295, 446820820, 616003706, 502675132, 450184090, 270911378, 441034370, 586159834, 161950302, 460294062, 853174445, 3742148, 670292824, 881389205, 279051935, 542380376, 936995078, 211485895, 514074833, 582758636, 119319252, 441713173, 696051941, 217468499, 19180611, 423048511, 767728613, 125201009, 616196320, 64717280, 771867248, 361810285, 919626150, 190912298, 756370418, 112644079, 818979257, 98755375, 744258053, 257428428, 137291327, 783115077, 18614661, 390912236, 372971289, 568749571, 374865221, 12121895, 249307558, 558020805, 606502051, 89375127, 946175954, 534507443, 92449083, 806159277, 910413037, 706050018, 756628895, 392491061, 772008245, 120343642, 405779237, 283748459, 612040322, 781094302, 54434714, 434494719, 199989606, 659580695, 224724900, 752967908, 477064118, 99972267, 68485843, 566824498, 588947836, 178370774], [488230199, 726360324, 865151122, 247756165, 170123869, 712601318, 983087346, 612108589, 875837916, 7109089, 751659513, 153742700, 48135347, 380667554, 200928626, 847220669, 359509458, 946724991, 577449856, 454808114, 554114317, 303579569, 235617424, 59193083, 438455373, 896405644, 549189541, 398693954, 282113593, 856394822, 54422100, 433252258, 942192443, 476759462, 473753198, 235782058, 204537170, 627571983, 323361463, 10543674, 788808718, 605649141, 672988670, 238390924, 197376581, 535620753, 620278161, 982285958, 90053139, 693143395, 223770999, 555211491, 783073964, 504870507, 751562444, 709458203, 174248627, 993284573, 451924701, 615037742, 418443626, 783629001, 275707396, 947171737, 426150463, 961274701, 53891570, 940535544, 620644297, 127637971, 592791382, 201668567, 514726755, 64015207, 560124198, 281280464, 273826617, 786770640, 807154507, 249241405, 619578485, 593748284, 411003605, 88116416, 105880854, 644933213, 580941029, 684095347, 722805108, 813150311, 564494962, 312424048], [348201166, 867526543, 108696304, 469085915, 515886620, 826606916, 102497399, 771776598, 772519626, 336846947, 554059977, 155529885, 808029398, 529135940, 733276151, 562600883, 948652546, 787577865, 840509823, 966530159, 590710586, 895871967, 496226750, 346145626, 276919362, 506248719, 717847335, 801274834, 615401332, 285299973, 976162788, 768420474, 761153406, 486648994, 548560764, 967010763, 420179986, 265171187, 218644026, 479978815, 715762807, 403477500, 644805088, 439477552, 937067903, 814170022, 152361209, 172668870, 331150253, 41673191, 875510378, 825370676, 952895245, 904486493, 503196334, 404243469, 910150502, 968596058, 323168164, 472847375, 913731268, 537556648, 602697310, 729898659, 218438733, 475655446, 437585272, 568041076, 331237190, 317208118, 984726920, 771781261, 334884630, 753746726, 604224253, 186660330, 311396483, 588707789, 76572483, 551996024, 285763070, 519670000, 888319679, 632449590, 636591837, 133935657, 967439510, 704373248, 87731540, 640446460, 390326984, 418506649]])," 2832164834445 (maximumScore [[512602831, 447811242, 239109927, 477303364, 98370277, 586772309, 662706792, 841526783, 111400207, 562789593, 396637493, 650319600, 344425843, 843325589, 422614872, 524231558, 374105983, 747057377, 211626289, 459470488, 650255942, 72434315, 813567559, 866917214, 474541492, 369252787, 996590420, 196074812, 247822528, 365088224, 165136145, 205249013, 764906192, 320979405, 865573882, 437085792, 328262628, 347108203, 351268872, 182473351, 596145835, 758586643, 83210379, 711685923, 395034967, 253380492, 655188788, 861266310, 876713740, 990833708, 302120009, 541316479, 530714221, 497761699, 381980869, 164171880, 994739399, 770539843, 917542161, 16599200, 505909085, 495737837, 392690203, 944928486, 300604543, 529857112, 980088550, 804863180, 149487379, 99642043, 478808445, 591357997, 458688185, 513761785, 597640318, 847874503, 781548048, 341935032, 402640718, 804736685, 776251083, 128131060, 374542297, 154868470, 544194748, 74777229, 321544087, 899620704, 723110493, 794246529, 149377296, 131520895], [729904078, 550792391, 284474771, 531466131, 734974184, 594030522, 116493361, 903551308, 971478205, 449383070, 125742390, 317747751, 22220333, 887781478, 844860403, 683771735, 670428506, 850805344, 536745517, 444647144, 891117926, 214038697, 808447675, 543653835, 212143761, 398910837, 230282447, 289715251, 212494925, 921491959, 99918975, 114869531, 179380181, 302272441, 902561273, 471202828, 890654525, 997587723, 433840205, 633425105, 684318210, 238810862, 474955648, 568876413, 511192290, 951044900, 950795498, 210082242, 936006522, 730510393, 618641174, 440226185, 383556377, 579266289, 145576324, 86267787, 101092316, 963397511, 988316112, 647207220, 154214570, 414471998, 656043048, 307125214, 646394907, 179790565, 600940594, 25352186, 919073808, 864079045, 77616770, 613954093, 418810344, 873927759, 401696799, 170841397, 720054877, 943079198, 485007391, 864515166, 478889427, 174678931, 56210613, 132686702, 269256027, 66660038, 988704242, 351190941, 352020215, 707489191, 956945249, 564578992], [535602717, 665300451, 806742662, 318707175, 320945266, 373664897, 946864276, 824116869, 254780143, 761508335, 583412014, 666846647, 411502535, 222003491, 14454391, 267529835, 614831647, 571366198, 433385627, 436066588, 910026372, 514697452, 510433877, 928636897, 94030279, 652391910, 520734238, 972957245, 922180570, 67002814, 80133219, 752369281, 616382990, 305508830, 20449787, 548498325, 559496279, 602407673, 781875576, 824703763, 612226020, 234543786, 343765618, 34388855, 342165468, 872632236, 346004294, 984582453, 793603337, 550080452, 189841732, 740714155, 793836372, 779783571, 541752453, 337467374, 540349937, 820716510, 834321377, 5467418, 206407196, 473382067, 70290210, 614300065, 447736101, 216651228, 831089612, 68067750, 28001206, 267486553, 637523138, 322006456, 856842768, 39466665, 481101014, 69164781, 438324948, 448402519, 51264616, 846662875, 624565758, 248844547, 277007947, 907639460, 398226839, 763012264, 208626708, 45708152, 256419619, 961721947, 842932471, 202829824], [266550482, 452657410, 89845183, 76732478, 488430106, 188437354, 907546746, 707260811, 516726689, 874693949, 350415881, 108323221, 881175416, 448511311, 745751397, 688162828, 205000656, 49079988, 963339189, 235701652, 972206295, 780871163, 397809906, 426241720, 566262958, 520631737, 89346132, 892349594, 917455537, 265174745, 446581391, 842494200, 230435896, 65814511, 761390217, 36912343, 808479105, 947313177, 399341429, 371173591, 302709458, 588412194, 680086501, 410061672, 196336905, 622353409, 528397968, 492568307, 445980328, 763426243, 919031482, 151148197, 297161370, 759872991, 353679791, 460557469, 732878902, 292180942, 939608669, 987152300, 817220773, 478355499, 447234145, 480644090, 785893894, 696644350, 262201609, 878191032, 359550957, 547716740, 604928796, 50752742, 253393716, 23798635, 955685389, 537583086, 661552377, 280470416, 28439145, 752628262, 852953122, 39836644, 915941955, 280210664, 929128316, 55353404, 276039851, 422210511, 104318709, 129537056, 634826234, 957090700], [247995038, 595187050, 729646789, 751694966, 697696626, 546240203, 35761219, 893605025, 494603226, 260151793, 705308691, 174713525, 478974866, 809418982, 787708061, 537653294, 729678800, 606059122, 684280245, 603805466, 673743968, 390491207, 164407773, 995897895, 932895456, 367473407, 773438306, 61544196, 621677357, 880681486, 23024471, 168160563, 490954828, 517433851, 643817185, 18130267, 800223643, 446610453, 197230305, 172444502, 528901070, 992811616, 225221233, 370807837, 29831384, 800055853, 35887662, 834579503, 883001130, 669040405, 725142085, 426347051, 355465428, 632852079, 621925475, 821366589, 771379418, 46731402, 72557942, 767174608, 692412673, 786598882, 995336575, 681843094, 990272132, 678234592, 270547515, 860075154, 396407864, 556072384, 446129456, 104715828, 248448887, 981468979, 512968480, 301264257, 817084649, 822169733, 437172497, 671469696, 967576344, 803766775, 27397757, 973131308, 342412793, 25788073, 921964473, 538923925, 597202558, 314747760, 200478127, 672160235], [163603091, 880390153, 893116155, 700945007, 761331339, 37545565, 393235566, 569239241, 774747508, 390242195, 876079429, 445671556, 929436123, 51832284, 565080756, 392719383, 120621192, 88148860, 460761350, 764034088, 893433535, 629278948, 120637436, 230080387, 87064544, 264039853, 527052719, 732462822, 348701892, 33764276, 570374537, 210822039, 433186185, 937535018, 212966119, 365404247, 329654737, 356675576, 520107396, 603679958, 490352978, 323516172, 522046958, 225796732, 467603595, 832913132, 257269006, 454579180, 907851793, 333894534, 13506551, 754929631, 777779646, 168289927, 500478986, 915391212, 507303673, 151832143, 31531389, 145176354, 324233648, 120793860, 318321002, 153440750, 95885378, 246836001, 995950400, 448219670, 292958146, 494060817, 107753476, 881781969, 24309871, 516993960, 327659693, 826559186, 444946784, 254749634, 191301604, 409013456, 618524618, 954343677, 714429625, 656404595, 837498231, 394252915, 71420166, 756590635, 689701765, 849753869, 202341763, 417538523], [864456099, 172660079, 510833323, 894574874, 282868296, 700933715, 86410965, 663994045, 507807892, 392647306, 169675808, 766627153, 367075266, 616865828, 608983573, 885408889, 905363176, 643921101, 927707947, 812793564, 48426664, 354242721, 393374184, 934051014, 511380873, 492162660, 538568724, 365074085, 576247094, 206104114, 125864331, 849285367, 997844878, 771880907, 305463713, 853307006, 891483753, 78524711, 501227551, 286952454, 752781876, 499064852, 679954733, 812423653, 368297691, 221485727, 570041435, 826610300, 724892674, 623607771, 440340062, 836995042, 175277667, 107102068, 581214850, 870432081, 758732454, 992314869, 708501779, 463347983, 318497910, 9228217, 556523448, 369230548, 600022316, 329192926, 96387772, 106363435, 179145073, 999838837, 408057063, 666064650, 131455763, 329482862, 879099375, 179116731, 352184631, 297583777, 625471087, 541867274, 10952914, 659685445, 346788596, 512042484, 791890836, 36095219, 465976198, 73302938, 761459239, 824893332, 992094644, 953403829], [830753593, 401844417, 781894620, 134139739, 979733244, 840187584, 454274715, 231365083, 491198043, 483900639, 255228967, 447322456, 323042894, 352257247, 188602538, 774463383, 169937704, 54590329, 805550059, 832620232, 912393139, 453819619, 475780840, 346902452, 110615149, 315491199, 920825120, 936272277, 407429521, 662197714, 616716895, 875843784, 34143959, 172172464, 602694889, 752369715, 775311115, 941378115, 122592845, 19418533, 771670898, 745333164, 424830465, 669109992, 483106358, 633085216, 75201422, 324706332, 174515989, 780979961, 507874280, 592987935, 520941532, 744571502, 189644047, 961265152, 532441495, 514913634, 699596460, 564217246, 294667559, 493125902, 642293957, 441687841, 6702135, 70419432, 883115039, 112915062, 47997672, 703881009, 543191090, 181107747, 211090742, 611489890, 411509280, 698971321, 812958312, 732409549, 394912981, 393015606, 653385082, 23936855, 307907428, 75547869, 900930886, 912179986, 17137497, 1300753, 427148100, 289171048, 199617904, 340660431], [618389247, 290780608, 690165323, 257008805, 701593300, 135413214, 447268652, 326455545, 642802633, 870309823, 296601022, 705108572, 668355026, 548415450, 568972174, 865873470, 780754674, 229226580, 390720728, 973447687, 325227746, 764090032, 351862289, 82829181, 603128748, 323371759, 107350639, 401054531, 541410098, 203809087, 187476789, 997856250, 166813001, 589290022, 822027518, 314838311, 428476267, 220990997, 71894766, 579987511, 40409641, 731774436, 927477685, 79833684, 642335911, 627893520, 621071268, 356623132, 996829775, 71641087, 479013915, 739045430, 119368672, 730222864, 848655227, 537502384, 269803903, 628043459, 421318987, 270988833, 828343701, 74883812, 237807707, 594765840, 892452855, 168227636, 295283151, 397055348, 840540823, 838605623, 72870998, 311992988, 523524658, 669810448, 868432613, 109981472, 705877313, 993093460, 451097562, 876340221, 213776351, 529051329, 601595581, 480640069, 963929510, 206683085, 62759265, 294225942, 952971833, 107525005, 513097732, 988276704], [400749388, 188545657, 456175971, 30798505, 704762246, 390923603, 776092950, 435273220, 461538782, 474000154, 988856086, 296700457, 647370020, 67942563, 496832443, 364254904, 877779849, 922404421, 465288584, 108006433, 397526990, 96521486, 226673658, 61391380, 540961954, 317433459, 232854864, 119651834, 655380204, 279984392, 551713983, 469973927, 640101977, 73772424, 365130733, 584836927, 349821088, 60876690, 699491448, 938679005, 920814189, 611767509, 367980502, 430778434, 996084267, 280752679, 566736004, 49589513, 767106106, 90504780, 828294508, 9225447, 751455743, 850837375, 583603351, 171849611, 913819473, 44273169, 282497031, 446669688, 265330771, 772153466, 963464180, 704339454, 766149978, 200189191, 46761501, 759364406, 774139390, 370731199, 726588795, 711257624, 461087452, 492262240, 225190094, 532112135, 19703872, 279086972, 619246306, 976948326, 354306393, 936530009, 232353844, 791610118, 310304568, 706020125, 218986445, 273019832, 231482321, 450625218, 528323816, 869265144], [193380556, 404113959, 606973939, 736253203, 614854119, 743649438, 765765392, 146986321, 548218721, 64665768, 247741439, 276708713, 655482700, 251936992, 523982229, 462356693, 825135077, 123495171, 420155304, 856378779, 121777019, 758436198, 516013448, 913802320, 127470564, 753750229, 726160190, 704259957, 58382448, 432246558, 672980713, 645926444, 160339072, 116446017, 780545356, 268407806, 119429733, 473330664, 56040352, 641799157, 467523265, 730374449, 473422131, 720676630, 226187126, 728919258, 738044400, 401450869, 796023440, 259286991, 639110575, 691431070, 534315084, 937894740, 697794353, 310295122, 622759629, 437300514, 672744832, 467924045, 588158628, 70401656, 345101257, 231641298, 945693076, 738537439, 722373540, 238018470, 844673570, 911180827, 260725301, 529433945, 816656966, 18049370, 182577657, 345493249, 812787317, 692280226, 801021638, 864832382, 596182172, 467064291, 738656375, 155699453, 674229640, 78027047, 177228310, 135762404, 614026169, 682198688, 727701892, 136093790], [557838879, 13233874, 440494225, 933811687, 227080422, 374373869, 987994996, 283797552, 555632603, 308998715, 629629786, 145625439, 338271539, 213778798, 688057530, 690534315, 100835052, 288343201, 344958685, 344680675, 97253314, 689212893, 821673829, 268981477, 575017086, 222654930, 109170461, 951247166, 764478287, 166122843, 539807656, 881668337, 122175018, 127060960, 597290112, 237353320, 571877636, 268264318, 773194509, 334503664, 923042772, 226317194, 586433502, 829917071, 100178599, 490184183, 608849391, 429693898, 843183985, 467363691, 706596701, 747539641, 898572195, 952063689, 166564759, 406702243, 218807667, 237598717, 296609361, 243923655, 233702743, 912599774, 743050899, 755737659, 272784963, 408983901, 311858101, 838331890, 717895204, 455942438, 990613334, 162684442, 203982440, 120757778, 128281462, 389508786, 405562299, 414559129, 307388999, 67785830, 552271394, 646863814, 780196758, 116070569, 901586009, 829295478, 779060556, 873300599, 145261266, 800779377, 604794185, 13398867], [871093521, 912488088, 224875916, 696386094, 821653687, 6313114, 60955655, 565175670, 196270395, 463301180, 274527501, 502125047, 58625254, 889711356, 219165063, 157001954, 279085360, 541410255, 296287738, 467851345, 25566728, 302182190, 192130846, 385563685, 111211590, 220662471, 249868810, 128376717, 669763358, 535281136, 838939934, 17206591, 67105127, 858920518, 121797458, 827345602, 347166667, 630309247, 707135218, 351430069, 534808615, 374102532, 651854194, 885913924, 877150924, 228374687, 227603601, 241413705, 820479489, 333714708, 971429289, 129736363, 993917107, 368466635, 243244391, 407168421, 570620424, 768697011, 408201569, 18716639, 751022101, 717864055, 739401545, 852986577, 655474782, 592931306, 459911658, 243699826, 241774760, 352458179, 205698021, 24373747, 232649452, 558082507, 258940976, 791249523, 730269922, 188845661, 250481234, 878859875, 767483560, 334408550, 308829455, 938434005, 352019177, 932623730, 39307524, 263990159, 227850342, 84945151, 903250095, 161439233], [930276091, 601241748, 525339656, 804997449, 594384611, 644594572, 48753895, 917735611, 599560253, 484017953, 944507003, 388107469, 64269245, 534176022, 483240182, 750410906, 328958096, 485549534, 510504954, 392335219, 260019615, 914238513, 59363444, 461719915, 837613009, 633586304, 841758376, 321956059, 167343786, 655951177, 406902705, 103161428, 894662738, 607022266, 968200565, 667088598, 989166899, 772802990, 14256072, 308050281, 809009409, 471642472, 798890363, 34779234, 871228, 211217725, 894991623, 818989481, 698207275, 822714499, 622465720, 637531973, 313196613, 500739398, 553170920, 114616186, 942937824, 136551806, 507138602, 246260156, 216000142, 346786269, 598133145, 460239759, 840915604, 328255007, 852239542, 689479155, 412477523, 513514228, 265244273, 41835417, 308865927, 983799905, 633262523, 31954658, 70054476, 34539771, 663871241, 428855433, 73303537, 320806972, 579095177, 261043261, 476177155, 524488782, 264541109, 371868929, 690310800, 284787285, 86105794, 503880977], [819073190, 176020831, 575993065, 677092589, 655660178, 250349910, 71524719, 506612084, 38757278, 905469556, 687599387, 802870575, 986974684, 837305739, 219559192, 236501686, 153058914, 855075168, 82325807, 22355826, 105058827, 256392940, 955692231, 717044050, 456184015, 362882998, 133083128, 89944150, 817842875, 962020686, 109396370, 93567243, 997289956, 260451373, 794526132, 43473864, 412526941, 908591250, 869330572, 294578805, 758556229, 290012609, 796992362, 134377900, 89895262, 263660737, 957722899, 684195655, 145511494, 743300733, 18756623, 701345776, 873559866, 455509300, 788524763, 274340250, 750969924, 857501372, 546679600, 279002968, 89491046, 705433548, 685374492, 47673557, 175194398, 652444446, 486560844, 921139716, 735111778, 117080203, 372755241, 104914750, 870891487, 740182458, 768242077, 773570958, 200087268, 689733297, 19517186, 569069985, 130592008, 425628005, 154962417, 935904448, 481432834, 626858875, 203695148, 430126806, 439928135, 104404646, 860575561, 419538241], [374597921, 448164861, 554179849, 901584542, 732989798, 317864985, 159492603, 667941663, 996443046, 198932429, 284146415, 306596608, 543575860, 748540173, 323616607, 288185803, 538159363, 412144034, 660094212, 210172646, 916594278, 330255111, 172516462, 184102263, 386414915, 440162731, 264286655, 569140748, 392158093, 327233552, 121760335, 430746159, 467638608, 2695453, 661927177, 779702226, 847810951, 245243415, 695860450, 238610186, 487160872, 154989586, 802017162, 265168684, 933457074, 283248553, 990107747, 795072011, 255126940, 972105077, 769918567, 943918678, 437582397, 913509625, 753222482, 326066360, 282088327, 740638725, 689978736, 118524751, 405571316, 132731951, 645864822, 738755154, 682182896, 633784975, 371724380, 284881361, 740633410, 375877853, 792009049, 309395663, 181109113, 711984793, 55025864, 258967436, 576826688, 652141436, 596444506, 823574237, 471406033, 23837618, 213687593, 995767165, 635185261, 230010152, 554654806, 15151657, 5565473, 286960084, 273571245, 944502841], [511705171, 686309172, 75494002, 829413335, 98259726, 194324354, 324158915, 439231461, 889937134, 977554180, 711789533, 792221881, 508609494, 91203040, 303878291, 998236637, 870975117, 666930508, 23147238, 28483326, 530591400, 157742342, 26820295, 590806335, 640261602, 73634503, 283599519, 556205278, 697012717, 430526511, 633391848, 615908600, 121255631, 239390067, 209697228, 362376686, 349940361, 641365350, 833200718, 921245618, 586276876, 920555601, 744160794, 92555531, 286893597, 577217819, 41418423, 642555703, 930155100, 392092317, 881149842, 975389374, 564861408, 71338127, 709063405, 564679276, 556609428, 450076224, 759164012, 504572904, 443444301, 63255691, 105190685, 499795661, 56505531, 904201788, 41969614, 19369249, 678607079, 497514287, 830536098, 106008855, 618054788, 957739792, 145832861, 885211667, 352431424, 413065801, 176647358, 945055074, 369178570, 475141010, 575399963, 481183409, 851461246, 827122190, 648571738, 80180289, 184439119, 652269430, 951595388, 434888777], [901629031, 286701285, 455070843, 435855045, 297232889, 308242261, 974719554, 68979076, 379469489, 874756282, 310343555, 418488920, 425307452, 58891903, 390523008, 629826502, 573403019, 445996696, 714578195, 794685605, 548470777, 774521593, 751435837, 809336227, 888687308, 971800827, 817149612, 770538659, 482522661, 239282994, 283665861, 757210280, 489836697, 143403946, 701911802, 691295542, 89619966, 911593757, 591437447, 467236318, 408124656, 438062618, 380118903, 752593822, 325327913, 420540316, 739345184, 161563267, 177167464, 995462825, 188635742, 709955259, 924819564, 632538462, 631612930, 449832735, 25290004, 233333099, 296191261, 455242028, 253708472, 77579415, 412320353, 376828702, 200805392, 604915829, 537425434, 914360523, 74468195, 730487077, 449745651, 337841690, 15432210, 611929953, 617720840, 981380602, 153155458, 635621836, 528873893, 744093326, 134514615, 462130867, 597092869, 773809711, 958701653, 284499438, 445420629, 417017086, 148512489, 103051353, 622519902, 701349113], [988196094, 50900840, 363961029, 65503491, 876024738, 539138729, 838090782, 429214869, 603960205, 567228912, 322345405, 249354855, 962679136, 716857593, 807901571, 160126958, 684069122, 759967746, 161376962, 85960805, 78796841, 88759881, 152361946, 474951450, 548450084, 808432364, 281105891, 458772498, 480614697, 707309610, 75630539, 576456221, 126585735, 273321431, 856580023, 453722185, 829603293, 944641655, 239116947, 661491082, 811435257, 411114000, 63847674, 409295806, 691959429, 188146022, 425883610, 839688814, 330652579, 528947906, 324755105, 980972691, 888160115, 610277594, 366595839, 878658471, 798095748, 839670237, 600738827, 375561710, 281034831, 815930740, 5944206, 815870041, 303870999, 883335342, 679803206, 662702738, 96439163, 76012834, 584099789, 318486279, 559541683, 171335132, 318562810, 242015188, 461491903, 586410319, 346502077, 964778985, 173971552, 532514448, 466353857, 718879082, 306553701, 185478552, 173181713, 968903348, 302272336, 190678326, 455090086, 673138986], [365352423, 773296679, 983619425, 319738597, 566360385, 951964627, 498732601, 764943710, 283499379, 285188443, 809008885, 822211608, 771960554, 971195982, 991217436, 963511181, 82635047, 422167941, 41791332, 245646988, 260056238, 27661178, 682317212, 339264697, 58599370, 906564393, 458626560, 303825116, 796356502, 629876478, 622086281, 756115443, 367132041, 229939824, 491460821, 707931909, 503252295, 962131197, 892646903, 249635426, 561458950, 377406132, 879940379, 120595255, 144260982, 299494142, 563037715, 817981478, 202258347, 910456821, 309103374, 790328564, 949216190, 150823834, 80713334, 65990814, 968301507, 313526956, 426090367, 61092656, 794807634, 646458903, 245334448, 679415402, 760552715, 740369147, 387632515, 117910522, 474740511, 476566640, 21009488, 692266362, 765900467, 929095260, 206143541, 818893425, 701340228, 760469723, 674827346, 462240255, 216171254, 815076961, 844600407, 447724130, 220286056, 782485088, 76570304, 19437207, 736038405, 269909289, 778902773, 112164546], [434128700, 568777476, 437062660, 245308570, 668477913, 251131382, 234825654, 985607972, 105114476, 470424288, 624838268, 332169315, 48356657, 539514525, 246911323, 930328684, 514129549, 424984518, 488023760, 840692972, 427367282, 378938142, 260755607, 47377955, 198842850, 716072193, 876823376, 117099457, 243735857, 985493440, 482079889, 76983593, 578572692, 588516429, 105321286, 20416272, 918329457, 684273628, 567462278, 32694026, 398157595, 422778766, 233228718, 162679189, 877177337, 696258232, 669820812, 231689396, 485458926, 621515466, 634644961, 972903541, 263251684, 265093997, 414575246, 173701478, 332465185, 237276847, 982255956, 239182162, 470299092, 948000186, 762174444, 630924660, 539624288, 107593853, 460307536, 827755140, 168017343, 728456851, 954584019, 644211745, 65221261, 707837215, 899100099, 105782597, 905167376, 359438552, 136158559, 890112939, 32068309, 606986435, 91071771, 994990059, 441931752, 164951803, 98873006, 721814706, 959214200, 313166354, 961940701, 606843675], [502649296, 301571168, 524079706, 227561531, 570643364, 871776792, 697011136, 923518428, 822352070, 659828439, 938465325, 728055379, 502296915, 671121020, 886303324, 821337940, 933426648, 57137737, 760367108, 978695505, 223452052, 131201345, 626571063, 530967052, 928293111, 672599733, 865864740, 401223337, 827166862, 778807024, 992817212, 201643011, 905848875, 899680545, 797007076, 788520586, 387138249, 503721377, 554637723, 298141376, 227394822, 132437999, 633066816, 223259525, 281381106, 568034346, 841997802, 568423547, 630636880, 71811037, 428046332, 102698422, 543962818, 552767184, 420182748, 16902743, 944570314, 90624891, 780513377, 95278224, 982136371, 685397277, 604065961, 310305592, 514475340, 732895998, 42006205, 247151703, 665448698, 68986128, 955857666, 896127232, 106901139, 673440918, 835132840, 672840179, 184812769, 849544741, 744537224, 449273238, 997543773, 905395687, 574387474, 110679495, 483572864, 313725474, 98945697, 843463009, 981173145, 494061686, 338198691, 828244038], [503733420, 720136975, 325465684, 290394175, 620410074, 858458351, 870490369, 379849034, 501374255, 783912452, 691124589, 396349596, 900139408, 729679954, 858149797, 308193910, 75212388, 247379293, 425788229, 915551142, 321203156, 500387597, 553795029, 117860111, 645554748, 4278489, 798621151, 157367918, 443615250, 394638711, 134508652, 171817420, 586729282, 833454090, 42749497, 263258159, 693485203, 615960002, 718475937, 204118915, 795344800, 203423706, 519549015, 223726868, 587394062, 755796231, 164662817, 601347731, 386649651, 638190633, 387600447, 729758581, 569612764, 659240697, 889880211, 499536438, 124851862, 522090606, 193657147, 143006207, 894700751, 25322178, 313860525, 129473376, 302301138, 625168211, 169443864, 496982403, 356002325, 798107092, 225736970, 621965129, 719160123, 4435141, 934791482, 174157141, 322960060, 609423065, 61612618, 429410860, 546810139, 651716762, 671951, 635109005, 425673166, 282405771, 340898316, 395761027, 805216549, 822049076, 649191853, 741988766], [792583729, 678682212, 715187674, 757446729, 602532407, 370138593, 425736063, 478147513, 711158848, 693386382, 100155870, 297067750, 959103343, 150957178, 334919615, 374272499, 750979463, 326454683, 915843911, 755938635, 781216648, 999958636, 520868765, 70615214, 694980696, 54029985, 113544813, 322017818, 662265547, 699718659, 548165472, 338877913, 635726789, 890884851, 538601633, 302993738, 912254615, 399585995, 144199114, 751963906, 762390972, 407925294, 423413908, 262633178, 531616191, 966179931, 350849353, 170954539, 287011322, 559485228, 590191721, 550454511, 529795272, 992304425, 234056495, 630146100, 294384702, 382449378, 812404597, 818580953, 220857608, 152467619, 14585016, 776927891, 605539683, 494585172, 445757975, 299269509, 712321497, 727974895, 752935249, 518726668, 757511042, 8744423, 241284773, 570778740, 78606432, 679810032, 19251963, 381970208, 249964522, 512068115, 257963957, 177768912, 196260103, 535820553, 672021517, 408906293, 119560019, 117698177, 774837395, 368574129], [266888707, 226423766, 148532311, 709359127, 840147778, 259815654, 244156682, 410863572, 673541550, 467467100, 431688970, 648579763, 633234740, 480976553, 21723787, 179603443, 258959813, 80143891, 360292339, 683231983, 57191786, 295093995, 357739346, 958126635, 548766988, 865326330, 562931197, 14452305, 606520804, 542762858, 583303470, 821787929, 541268474, 47133449, 117499461, 231074481, 793497299, 765883606, 588221246, 856082418, 771731610, 368340306, 196947156, 738400708, 779149296, 337005719, 172519463, 541578413, 287095445, 557802705, 386304991, 408317528, 423160304, 171072218, 209535081, 183952551, 842835836, 175320320, 401054041, 628698350, 749787032, 97206172, 494822070, 889125513, 769411785, 897562593, 181484490, 916835095, 508228980, 561962802, 149878804, 649165727, 503443139, 696244559, 726933722, 596411184, 515761092, 857734528, 799854087, 598806130, 167921737, 338742666, 825967853, 522016036, 4066386, 550932943, 249423389, 470399952, 440809264, 195929639, 167675742, 718084690], [940487624, 526036122, 980390490, 526935692, 452753748, 307928921, 440625441, 738391302, 294645586, 952419368, 493233774, 255210563, 375328712, 150793886, 913261835, 589449012, 459759802, 234749399, 228470465, 450414814, 464093143, 122171677, 946272427, 925969524, 209121308, 24115324, 837481070, 463551317, 802101504, 599706617, 270625759, 980345330, 63297664, 578536215, 631027212, 949796886, 707428070, 647623166, 655996842, 646230320, 960583115, 738944569, 863428687, 842219586, 251713010, 468573665, 530928310, 133622591, 469714305, 157673464, 42042718, 152934768, 934247947, 165729753, 222413888, 971623629, 25072734, 214709226, 982769532, 667261554, 882380522, 229537277, 593448964, 104767936, 321310367, 607462519, 319519124, 521883758, 758360904, 354594098, 823286582, 161143324, 868776401, 166818544, 722740483, 165896150, 66194604, 19926930, 284503462, 848732921, 208703648, 69610972, 883468227, 497175811, 105098666, 929698282, 729823884, 537845774, 890134791, 347325155, 93374864, 312723756], [598317520, 711348655, 555686293, 333730172, 746093659, 423671283, 579689422, 596235793, 433980786, 940949583, 272796234, 51205278, 262232235, 909420695, 187602718, 512366562, 996513932, 760245383, 284302768, 253908126, 620803456, 877637199, 657101548, 38263373, 744583082, 968928546, 852272679, 123642188, 533509645, 122632558, 815380722, 287953445, 253682048, 814104622, 339359871, 947631977, 730358384, 147447858, 396793594, 365961041, 145560187, 264169555, 517598811, 90361302, 502647166, 795764936, 785226073, 671731768, 388990808, 682366420, 208945033, 211297457, 586271300, 673167753, 138705531, 499265881, 938960969, 557846144, 688847523, 173436838, 329421203, 857308082, 588339519, 46675519, 987918626, 500011234, 482821721, 778974127, 829617017, 817469571, 160804251, 803933649, 814508367, 699269226, 991012949, 272759185, 432456487, 916381451, 711146429, 331726864, 39818717, 454644975, 496031662, 318649620, 45661959, 331040719, 267345131, 602004658, 791800655, 706075667, 2075238, 849399218], [961332586, 404358188, 71135098, 284925146, 225370139, 886013219, 646955512, 446060588, 81189334, 854451793, 8672680, 658256762, 55508871, 230529668, 743397980, 900909552, 202737192, 618127768, 170236000, 655639085, 698718875, 64224271, 754475953, 127363478, 130071179, 582326068, 872768235, 267600355, 141663119, 477051356, 188856798, 966067348, 350702285, 997639832, 960520456, 59839522, 123312394, 794482924, 519174715, 674853324, 373077011, 597914376, 848282686, 354491573, 528302167, 366499564, 499602386, 914380372, 384046677, 181623283, 701038102, 339571632, 77134839, 440784415, 970850991, 128439810, 505045257, 912101486, 396988739, 437382988, 794586783, 929812536, 946527123, 45637991, 377058300, 113756821, 229289651, 60297162, 990145819, 913988546, 179518582, 292983739, 300021992, 345495486, 1919862, 293876620, 413002237, 774514004, 226183070, 603370064, 998406873, 159094579, 277665391, 284058154, 221268057, 496413397, 279184149, 741306189, 392416320, 699639148, 132334533, 556714189], [109096703, 758957495, 396626101, 769621653, 856817900, 596367846, 136724559, 336643356, 272497260, 213698976, 613167695, 752333245, 177087670, 592736494, 65833289, 818406692, 36431471, 808915672, 922997448, 984401627, 627114282, 520150178, 665629707, 855124102, 20806302, 793466893, 297022714, 874282470, 668752438, 145913788, 899613563, 836040584, 526347535, 79918734, 699889502, 24929368, 996008473, 935518791, 686203574, 839800223, 495999003, 951552160, 681507053, 581389845, 502400712, 750139484, 846283667, 967123601, 589868150, 63227338, 691381406, 169967480, 690541426, 95233762, 535412431, 683420846, 110332129, 779424685, 351829818, 772646724, 574805640, 958688828, 641090214, 964313682, 740534609, 160256047, 427848584, 722542168, 876140663, 560469354, 858066982, 722525323, 330127151, 628690123, 152145774, 114688147, 233664793, 665726603, 456904355, 218734575, 707411045, 845077595, 37168603, 342948609, 278932776, 506726502, 577589517, 120846145, 777374845, 525337444, 179454836, 620274176], [727505047, 263965986, 838133329, 685282207, 983461519, 412122695, 82893675, 637759255, 803898882, 836394035, 474225527, 219320631, 73534475, 9955760, 772606390, 342498836, 391314000, 113226985, 173547032, 468347645, 354077660, 651130045, 162091213, 695639813, 254785557, 663333694, 918603252, 28844270, 873702364, 54901200, 518233631, 18594501, 240222423, 812758324, 713589781, 728768274, 645944381, 990904991, 981328152, 946320864, 254434678, 371587636, 630744482, 175542978, 334672708, 743154510, 969432896, 107585350, 542727824, 385052638, 309413128, 516876205, 335669282, 40805093, 914601893, 994690609, 509225827, 268723637, 211432790, 936934016, 865289513, 67327954, 168610086, 783760204, 175564071, 269332840, 661641347, 201252574, 787089951, 288977184, 475431572, 840943178, 954844428, 72838866, 732065293, 839175538, 715149752, 669981331, 74677551, 721132440, 32392561, 959364114, 514011595, 798215761, 328924117, 155123112, 915634503, 328260773, 595601118, 252508302, 258867424, 306612306], [550710728, 126559349, 978582836, 428258783, 941311728, 943774886, 387142195, 226914189, 921009094, 404550834, 830440549, 612969836, 743351144, 785372827, 237685146, 930460440, 89634957, 292292061, 731702436, 364329010, 630082693, 936421727, 987117096, 283308606, 881919927, 875138922, 496041094, 209258942, 797419253, 9920595, 914183584, 624142032, 447589365, 91190306, 711786857, 963882279, 318244738, 753809915, 751689607, 409026285, 262076266, 945297845, 219039248, 730683858, 715620834, 925976773, 927520020, 76984968, 127013696, 585543789, 629336791, 193115071, 98091355, 128720792, 881177637, 480662203, 802575658, 59110710, 410562284, 863070757, 422139475, 891256361, 178430138, 522982876, 136073873, 206705270, 320022988, 132804582, 526440459, 666803543, 717620643, 184501489, 557624418, 151784561, 599105042, 767456753, 477784411, 705167119, 485023013, 310799460, 640522346, 532762879, 605706042, 953860031, 996941354, 701310357, 801583949, 143537260, 833467948, 564949953, 959892030, 529147665], [158208831, 805553043, 506410223, 20467475, 626050138, 845566736, 530010807, 72530149, 193826534, 145949220, 189778094, 302098784, 699737780, 51940708, 362829769, 28779330, 612253254, 568785319, 19651220, 9349614, 37596826, 25529000, 885538671, 919222758, 597984299, 52022891, 665606797, 453716047, 839727788, 548878201, 149020096, 421804460, 757160707, 393373994, 650222440, 921654379, 131567036, 936371630, 966127885, 730736821, 945078604, 968801154, 559975100, 291931722, 292552865, 787872863, 346011341, 632512197, 905549344, 333818365, 269009132, 455731470, 968212062, 917103169, 478779408, 715586892, 2895076, 382863032, 343603477, 686601272, 844154544, 602351826, 744594198, 826040548, 704163540, 482448788, 972689716, 115667706, 871180350, 271271648, 27429781, 861994778, 525407510, 823305215, 238465867, 22911624, 183072270, 965887351, 3694147, 990361617, 702027024, 450529552, 795475955, 928540928, 677630001, 378824096, 623136957, 943141442, 874334641, 608348631, 690920271, 521391934], [544761657, 890704805, 870123785, 380370395, 933933824, 151991782, 978322538, 187675367, 871074296, 23401503, 50279647, 182738354, 391070939, 626358160, 966240491, 989968311, 33408989, 890839672, 619023262, 781130182, 865863131, 664092493, 733646285, 972318076, 330952639, 202406730, 22963982, 8674196, 366966951, 147414372, 728872089, 988290836, 875208996, 992932051, 389600004, 410243430, 628829468, 712845911, 581536063, 605740220, 974607650, 962944185, 938415766, 247797606, 302281255, 430968266, 435884329, 365626430, 271089170, 607237622, 333925152, 84615898, 923526173, 168222842, 223757679, 609785427, 609130232, 285935999, 835641615, 141500571, 432392294, 386380627, 816602470, 737608488, 631005666, 258401972, 947133561, 902176287, 254370178, 576925095, 917352728, 369811019, 54530844, 166633209, 760882499, 670679334, 283522867, 921042862, 555776146, 212084650, 168005578, 83633534, 770586968, 362058712, 914474962, 888314000, 456346263, 263443399, 171572334, 643525717, 449775990, 300342366], [579862542, 433386143, 639415424, 83859862, 901481034, 825042745, 781532238, 414140904, 738604031, 679033451, 53397327, 188080321, 911825524, 533560655, 499123449, 585222396, 779924063, 106739260, 651038509, 226683794, 932637643, 344222571, 782980673, 636630282, 849176839, 469247807, 64165072, 196193266, 148269039, 489671475, 526231699, 895649667, 299677877, 686362595, 553268854, 681384553, 409928981, 344049557, 861058507, 199272978, 419214852, 416527246, 293549475, 376276340, 845432443, 662252005, 464127645, 263768915, 702271504, 399760342, 878037841, 576120627, 275193550, 641894176, 211793757, 720952723, 776499689, 314829794, 313053132, 578479313, 948840362, 623248910, 989124602, 647931378, 671941541, 199371445, 601531232, 306689460, 42671269, 127706821, 41994421, 938779580, 184888721, 59436388, 929989084, 838093701, 446497870, 541383612, 162553202, 713828454, 926180263, 290123842, 701398267, 723291936, 105995658, 917051130, 552745184, 334121726, 68443037, 654204114, 781677951, 462308060], [398631673, 695166826, 554954836, 10602753, 850039675, 746729321, 811688758, 62197686, 545807244, 226862519, 629251591, 870355245, 208119266, 894175587, 664656640, 436498663, 436107508, 980677671, 458260735, 905917303, 157748372, 111993939, 772193596, 313628319, 774542302, 588172244, 150297379, 963887535, 130271788, 277626951, 801437661, 782214331, 63280894, 374266394, 94698235, 158245881, 688139698, 174070474, 659543057, 843123947, 458883053, 910876713, 299659514, 532082882, 908066231, 385067915, 36215525, 613924058, 774281532, 892122156, 788609900, 210683414, 765699388, 337095547, 717684154, 434962449, 968027598, 611467154, 975467980, 111660630, 572194475, 746191889, 584985472, 964582505, 452242109, 992871951, 652351359, 94558195, 245258268, 12086508, 368023352, 590133545, 726044413, 79225484, 666836286, 819358868, 787229763, 69016490, 49623387, 529295526, 834205210, 342846991, 852152673, 181223844, 564100434, 710478905, 886587869, 848716040, 220173153, 180054508, 568235765, 726253220], [601120603, 62731464, 340203075, 294108336, 308014727, 295904282, 98773081, 205416541, 973953047, 38350597, 562838225, 998378036, 55438280, 129621432, 821797195, 938219856, 567692685, 254194634, 878440682, 251730454, 356255249, 481949672, 40418594, 158883940, 760641897, 18447368, 523476498, 94602698, 412991713, 117106907, 961081997, 196863029, 891027597, 4273203, 241462582, 147748577, 477369947, 500239774, 577483581, 36069392, 745750664, 838536211, 282014682, 51445572, 199868892, 239420770, 641224332, 319393176, 243465515, 739207632, 655946727, 283957238, 352830939, 988374640, 59619323, 898214490, 191946464, 756315887, 356349241, 680606112, 378535833, 756832198, 330371316, 418684008, 889462680, 861185998, 329049477, 817205828, 548331661, 735972277, 732734838, 319792188, 243963775, 883282098, 811993002, 416419225, 404928048, 181572782, 590204174, 567031717, 655153099, 115541, 417979124, 757307730, 273637216, 872451420, 233560799, 277324416, 243031825, 502800783, 987731355, 608522599], [24897571, 467838433, 863319357, 568924083, 877235296, 569147852, 882572801, 860378465, 588967122, 364018995, 338629357, 682897111, 324325335, 541358596, 498456561, 108047941, 786309728, 724826936, 62667547, 994225737, 197696653, 990011319, 157127165, 756562806, 970664728, 170363211, 723666594, 484448949, 290270184, 405714658, 900971172, 317912586, 449850755, 311235265, 32204810, 191877788, 626494149, 177409278, 689646521, 619996635, 244418195, 782078309, 297561758, 89458862, 859557479, 228743046, 467656626, 532250578, 674070541, 208221458, 132036792, 415790506, 256404572, 559981021, 343093530, 928898835, 712177145, 754089580, 794786258, 924676914, 215422027, 806794334, 533669837, 575777124, 910877347, 270518644, 772745836, 650988509, 57770266, 930562429, 216297890, 103412987, 45625771, 218007483, 650743134, 915254296, 668372189, 523886334, 609407708, 565560614, 999080034, 191376246, 474906103, 965405283, 360975569, 957269558, 7968339, 579370139, 339886359, 736710977, 933390570, 451483997], [350216812, 768715024, 480531199, 98842962, 991009597, 908720182, 968174561, 834351286, 982519948, 966958545, 961651153, 223437120, 115314145, 285078174, 188451441, 960209583, 679927422, 193785596, 601647188, 305624403, 79390928, 239805537, 319842883, 34568174, 492890557, 456595247, 391967333, 971021616, 468586778, 860692781, 789426743, 332237365, 6757750, 103396474, 623803113, 618931486, 4921988, 946694994, 740057680, 332860428, 281809676, 695503600, 458593510, 500601246, 829552102, 143581359, 673097899, 602165727, 639470035, 187377893, 598165587, 518796170, 907515733, 774746777, 815725138, 408054865, 290665178, 870172591, 977780983, 218777270, 354166473, 878991861, 105427005, 510487655, 145244753, 243875095, 262088151, 237080574, 832014912, 743245927, 403038263, 150945271, 228994954, 445725049, 107375604, 824691031, 495135427, 605268878, 756897901, 129997634, 26860963, 943393668, 900174962, 165149219, 446166101, 536214862, 877879423, 695095226, 373343181, 204808406, 227481697, 814499471], [243195117, 853823723, 651954779, 598022847, 554771392, 20367128, 663764167, 690402853, 667253007, 496913233, 520375585, 784000878, 295761528, 579436369, 167001054, 55360826, 785714691, 183436795, 582376051, 81844085, 723354541, 498621732, 731420077, 132081004, 82413744, 522608804, 172289543, 159378717, 417289197, 138533362, 490305562, 402271460, 237679146, 507468664, 913950306, 684312674, 331760493, 926514249, 362521484, 825500346, 196203101, 88727192, 938343892, 511336792, 342179477, 406341971, 500197971, 286241877, 844488188, 842836137, 385992248, 618345112, 235356043, 828504377, 135544416, 471732139, 686334589, 713793682, 274158683, 743763931, 582741484, 214982787, 911051201, 421777631, 206373143, 196336214, 412150285, 780401124, 194749818, 72945466, 564170866, 339439753, 306548942, 348491508, 746560843, 284752097, 547758502, 837702807, 108144314, 168823031, 669170237, 774839705, 911055386, 63537257, 14722866, 79293084, 945886410, 718517647, 396398170, 142580961, 175520755, 263910727], [34313333, 385936459, 978211438, 602838545, 122248779, 621795188, 335437136, 401873038, 218421113, 945464634, 949566742, 171447476, 890167961, 363876878, 781374858, 110671001, 205453887, 190914390, 591498783, 744380468, 525524645, 387087640, 26299466, 25832123, 311920865, 403709204, 275776110, 459885202, 4340640, 829898489, 910812348, 57851835, 838054467, 326621062, 335280379, 671855657, 468184796, 770482394, 942885755, 323086720, 245254482, 829253085, 192759164, 102721266, 538258808, 110668105, 980880121, 216400858, 825882779, 990913618, 233651627, 799834789, 740654975, 977905637, 359047497, 500010673, 152521362, 274284330, 780348176, 288949882, 788128519, 308502406, 304857404, 157541069, 648532603, 766787009, 798916627, 655107825, 675878070, 722848007, 521666741, 586937544, 183118112, 274408401, 453161223, 810449123, 962997084, 86578045, 740446981, 245123260, 356359175, 425821749, 264151102, 287218355, 62955569, 482227706, 307915797, 368086324, 762478915, 281247820, 563964097, 76954111], [710540397, 645209097, 434418301, 545400215, 105331631, 533984229, 157458165, 520871387, 683491889, 506489506, 579172467, 423983318, 358090058, 115410783, 574210413, 966053007, 665272405, 408192157, 461135766, 482600056, 463734374, 510903493, 983752709, 673627522, 202634480, 966954343, 999546300, 261697148, 59092139, 561425749, 931171374, 292131544, 615092390, 85381045, 931848139, 2294373, 348085532, 997063089, 919867354, 783776374, 935660625, 970402186, 222249891, 916075325, 952923508, 449137003, 367489632, 952770294, 929644268, 739944120, 11191883, 198981621, 775019739, 340044983, 806525516, 732743025, 599085931, 15520387, 223008637, 492760577, 328171320, 277954081, 949918902, 912357631, 300847255, 665562243, 943524823, 581790439, 71242538, 583074847, 739329004, 865443387, 804200988, 790306332, 343224593, 748104397, 637220382, 961287971, 333219248, 236698192, 244014719, 628081919, 507025221, 724649593, 437545288, 999168905, 624306214, 778356594, 536346060, 770515714, 253973477, 490064565], [718523852, 608412459, 952648195, 330970583, 486401280, 944955119, 454086407, 808020404, 854305829, 456201674, 930840991, 722767918, 206190500, 523888055, 305014789, 337062797, 727284548, 16579405, 634879508, 579591725, 541893510, 400596573, 196457774, 639369962, 324108152, 897494643, 114705937, 603190510, 241424205, 795583608, 443966994, 483094793, 512260124, 659065669, 110052971, 549144874, 930150515, 298312048, 897870177, 2109691, 893033285, 575568946, 819990539, 489552699, 669510559, 661795122, 923060353, 787310119, 782055700, 301856351, 177048909, 975088734, 558378049, 21853282, 747673564, 285808349, 887351283, 189389933, 925904490, 600206839, 21381753, 402589071, 620815606, 822194886, 473673312, 101843056, 809905374, 615158229, 326316794, 839621316, 366335783, 928557776, 245757317, 82979511, 757055121, 843278366, 787127372, 642349206, 102723236, 197775553, 498465702, 494734899, 261892827, 128439650, 830538665, 713854728, 996141411, 885823159, 434030107, 696153568, 455171442, 323846478], [334825523, 790057958, 506782920, 23736876, 233238572, 741588397, 372447822, 427007958, 847207752, 396018253, 342235763, 770815509, 677844184, 95268914, 72116561, 165152685, 164633031, 455036697, 207962828, 226450889, 256780152, 124533439, 747466488, 946026075, 372665239, 697279787, 83837547, 458041555, 238781055, 146526371, 633757782, 294491399, 654370896, 440206067, 770428333, 789101170, 774570732, 127555975, 715989450, 39682600, 479820681, 132094673, 850524394, 565595262, 964014201, 355659578, 737082843, 721798603, 670800174, 639519351, 737193908, 119234359, 417953881, 910676815, 510205349, 662464995, 511046250, 878027289, 83216663, 545693578, 764009769, 981891422, 959537332, 296325698, 70796939, 60142777, 181847810, 541775948, 734196944, 384799516, 459178251, 839012358, 304029155, 962105817, 997802144, 794209987, 860189083, 469362547, 42260468, 714920821, 412494791, 541715242, 338243509, 831011010, 247308900, 11412463, 344163352, 72314213, 605427924, 414523527, 704617107, 834016103], [666623647, 754410124, 108838815, 42784790, 515495468, 861652780, 823958908, 31019423, 163281051, 317663916, 889937957, 491943758, 142642000, 651411842, 928115437, 815384053, 995011295, 694637858, 338725151, 538589149, 657829852, 819149513, 568624944, 148443421, 566150252, 508153065, 628504898, 28701862, 634599994, 799738873, 251504506, 293167526, 558165937, 680453013, 738677886, 116790223, 630547329, 316274068, 706369495, 304516697, 701365004, 6095, 582899212, 410704200, 505074165, 501674188, 702488543, 681869865, 558939928, 671420547, 569826265, 197247944, 636919117, 745227846, 457704331, 635760449, 616236048, 935713444, 273349291, 297860723, 628459533, 776202960, 62570271, 849924133, 290152975, 428045451, 739182228, 592554520, 989992664, 553290970, 608349530, 631194960, 654460156, 879041052, 116125827, 704875649, 996852969, 220184883, 615664532, 302114546, 313906933, 377235812, 593817871, 602023329, 402802615, 941817315, 330285587, 269098807, 961182608, 964336873, 404500373, 323002833], [279542520, 210531514, 922844949, 23433134, 961211231, 118163681, 873691802, 268653867, 809035860, 850623804, 104116608, 529832322, 793292080, 971083609, 389760153, 609176981, 731284590, 700840124, 695290304, 637905000, 920759964, 48239368, 382865429, 282319529, 878803561, 387464005, 759360037, 753497716, 770615747, 465000453, 998299532, 620516557, 854977491, 613635589, 384455120, 796508293, 578480397, 282890673, 348507138, 312408572, 822377680, 614772746, 365144440, 991775874, 237943699, 933314212, 269238565, 630231968, 703562057, 218959054, 661925473, 402249239, 645859106, 754866250, 606833819, 657994362, 80940748, 325890551, 574215540, 516285220, 790642064, 992996712, 82403919, 574601030, 742158471, 147334987, 245922135, 939230128, 531905063, 642011292, 268653662, 63032436, 47535748, 45352430, 378949008, 7649965, 92339148, 689522685, 54076138, 567733748, 312558782, 920064689, 118584826, 655120106, 494215187, 197699741, 84316243, 245226073, 390904559, 675703357, 483040609, 245153476], [821792962, 999641065, 171255111, 814030185, 549099036, 447232385, 71230997, 470065859, 966434925, 583951535, 709101122, 716068935, 48167851, 761506383, 398479032, 525275778, 136726872, 630519278, 987749971, 17310333, 564766741, 870885683, 175023956, 840404987, 339572736, 899351930, 149557259, 190716490, 430686760, 813507016, 214311482, 341120583, 730047084, 396748324, 874484253, 685688576, 467099227, 752566966, 304823092, 138147014, 742346961, 762929860, 175160005, 467268976, 410945807, 992495297, 57259836, 960237478, 299058960, 863163360, 318225196, 845112422, 868017042, 331194337, 950720689, 658394699, 738827288, 917037065, 237701832, 754513052, 440067549, 899184497, 971543275, 648578627, 532100160, 286060096, 810652689, 26941742, 713205773, 591186908, 519972658, 552714661, 759427469, 706581387, 825942660, 356418239, 178501500, 654523082, 467103428, 101142405, 140291499, 105035233, 86805950, 552563716, 899426079, 117309413, 671051619, 516977308, 163559860, 998479121, 25460110, 862992769], [948725345, 360071298, 234016873, 403539581, 837657879, 323107587, 866141869, 803878695, 812895440, 898032129, 299492584, 20805053, 663971124, 523875966, 585670329, 139181293, 11147825, 41373968, 219551547, 19252342, 854710367, 353740845, 337170969, 112789597, 454470968, 737773491, 569429981, 932018183, 288984561, 170893393, 646092309, 560441114, 774034175, 48448396, 482039084, 892170717, 573597343, 757362014, 689887853, 858840305, 996282445, 765790913, 875837797, 824118880, 254501802, 998086361, 237928700, 223518446, 83292837, 665954010, 190672938, 831388634, 883043710, 158712936, 560469267, 837486876, 4502712, 416750181, 937507939, 637268097, 926605943, 997406734, 945528147, 492378740, 443804410, 667247285, 312077792, 618322076, 229967239, 293340977, 206725027, 253189566, 76873675, 548587113, 294751826, 904349174, 108641592, 938822597, 720069869, 876403667, 576572299, 947570523, 215665504, 302852325, 324416339, 680197550, 957558642, 922430068, 147871527, 495818333, 926145220, 25279822], [732770936, 675835994, 460357464, 356292217, 567365121, 69801840, 119767961, 668269421, 733425385, 907130077, 488943545, 759030094, 442942629, 136968166, 600575524, 421901228, 599610122, 646460524, 352972246, 789400214, 694452911, 624375124, 840959011, 264219300, 405166192, 991661227, 919139036, 594173906, 594684552, 525755153, 408714810, 340806064, 262696197, 359292942, 780248655, 348371980, 802370389, 18878101, 386516935, 502584112, 544388770, 215373583, 252388711, 630030254, 660524151, 666804009, 592624704, 471189772, 48110419, 204798640, 873775502, 712896077, 755672975, 51105433, 639038241, 724825533, 258244624, 724899556, 217377241, 952454991, 861410745, 879342928, 733159391, 326712327, 434765872, 995330300, 942144581, 746696303, 317394435, 505559916, 842715031, 822332718, 575325556, 505655658, 452895689, 837081708, 27993443, 778320842, 904975459, 867483289, 527951347, 972379371, 987586336, 72356057, 836409414, 769308297, 820790118, 576071008, 259506321, 261351696, 701539654, 576007240], [384670835, 531155356, 338809811, 327596982, 332694721, 894711511, 748673181, 55073437, 161942899, 69212239, 469572602, 179001337, 964466366, 785541605, 602907515, 295205705, 906736456, 256706839, 934422739, 243232725, 258856569, 67953322, 575093079, 255568115, 87767654, 810386652, 671234675, 968207404, 711323906, 226046958, 365186766, 8404243, 338605611, 672034348, 302910765, 910641947, 93917851, 769076392, 798960040, 706552626, 760668946, 905651275, 480039541, 12195176, 890825702, 802296603, 271032023, 363970216, 220227118, 740074630, 578955805, 703469933, 8815847, 71041166, 638690497, 133549837, 621071571, 849703175, 449584536, 931640326, 801821539, 903682409, 174218339, 941274483, 567137272, 685854289, 21135421, 403245288, 864164023, 779424254, 724471585, 796093412, 241359815, 938707833, 592657402, 38571325, 629544471, 388520512, 675095342, 278776115, 337603509, 748420789, 870187667, 72304849, 136500790, 844817528, 679243963, 199188734, 417136444, 746216158, 25189116, 932146500], [871690609, 329849226, 597870141, 580878145, 27757804, 124443110, 574895630, 151459370, 85597968, 821371622, 242864538, 554424589, 899125236, 502934028, 864916838, 300010169, 742081114, 967807465, 419444704, 90505838, 710395594, 820659411, 746134261, 617511090, 168680447, 865750838, 348145044, 790946083, 526983060, 412987362, 814381452, 876660445, 795177214, 677637057, 74519710, 910051385, 461365580, 430003498, 448750232, 368829861, 515327749, 673181417, 519826885, 14636438, 577564032, 298293916, 405941515, 235028194, 666285987, 633073069, 802562509, 677789102, 495461979, 976181430, 11221424, 783526497, 327174030, 956729691, 357408149, 617226562, 563718783, 402629938, 429268250, 199495757, 715579000, 833701789, 896938034, 301079116, 680391294, 964262577, 965691342, 584860398, 836230096, 165179324, 925064311, 653220456, 831219948, 698337840, 164149860, 285692355, 445844306, 340919227, 331053317, 150670458, 294512176, 527855660, 691902323, 325982616, 346922908, 203553266, 694385846, 178763674], [585278893, 591157114, 179855914, 35783717, 952122866, 83900788, 832079655, 99849770, 24320003, 782449263, 286450509, 618656992, 944870592, 418481408, 860038885, 980623254, 285405264, 469572965, 175252155, 923892950, 63980717, 978488741, 366139961, 228171332, 446633004, 137479954, 51575364, 162649744, 747882627, 85317361, 952532275, 151829619, 831415211, 61738743, 196467761, 286029840, 419506100, 834533865, 473673895, 141433719, 641258965, 799020278, 373791519, 524470599, 205516973, 764377691, 20636101, 368866218, 254279643, 150954734, 649136929, 595807217, 384704702, 448101779, 330764512, 151455895, 135543328, 856965829, 508365182, 385989424, 507432432, 940035000, 915886809, 467276805, 333944814, 158044910, 991862777, 637185399, 441617918, 104892545, 178490544, 657702035, 864414665, 787541126, 875832497, 485912027, 331772234, 783074162, 444898345, 289799485, 477802767, 589011524, 563347594, 878390557, 95498713, 655928320, 194295711, 229842941, 422420791, 591722183, 25378272, 587132798], [401750675, 925937877, 27261143, 40962017, 582561610, 67308895, 112501336, 765716447, 599395232, 121678435, 336812939, 875260670, 72140878, 451074610, 851764690, 175403998, 14510843, 862092518, 353893756, 499825259, 174254982, 705523461, 397075846, 937903354, 339762416, 400242513, 639654638, 602110445, 352656975, 185828633, 732951367, 678860316, 129752665, 710336994, 576415404, 681781018, 785688955, 975273919, 989900377, 542410461, 184827291, 590379873, 275501381, 531758274, 181151034, 670145138, 542368386, 36168087, 258984055, 745371532, 212578512, 865401838, 915898067, 75947262, 914503687, 660286456, 885689793, 869152014, 769203577, 496716199, 511899920, 475985088, 770521852, 603871066, 230584320, 65358029, 125612630, 859063038, 698826054, 358485106, 37499640, 187347588, 402118373, 265129900, 644155885, 705945245, 497074059, 274367666, 452953113, 161650657, 46502096, 466329460, 718236716, 600581253, 669430716, 483021094, 943270394, 22489942, 325250059, 902690613, 816909827, 910274064], [391127521, 372459004, 694316956, 605033021, 796787912, 467669729, 744547665, 963049841, 363834110, 39320555, 566466236, 9303157, 313454860, 890749783, 847638248, 731358037, 393910250, 765780986, 347460682, 558683315, 234110897, 951937611, 463576814, 318388175, 23087649, 354742747, 936273943, 181751497, 16526886, 379440733, 284011955, 408564239, 878916951, 293154290, 875435663, 398645080, 433899339, 994919051, 977254446, 960747978, 264527491, 855355769, 810867282, 563826786, 444462267, 15272306, 77717104, 918431526, 835629337, 996596466, 222038266, 401401546, 679011816, 207881562, 281864543, 36598384, 599078044, 514966071, 405259534, 106900080, 703727571, 628422528, 35175556, 505195747, 822865259, 836607620, 423728502, 331047944, 539819863, 619850598, 765832754, 806529958, 265255725, 437679643, 47407964, 122052969, 184890928, 939455206, 209078107, 616463487, 236731318, 895614585, 68857803, 671904192, 639000353, 743460658, 377660688, 131120366, 384632256, 741233505, 184981204, 499808371], [351457938, 321789529, 195400949, 35137505, 251345435, 236960352, 257530822, 884118977, 426612288, 942259456, 44796019, 664346970, 87730094, 717031354, 271818340, 263224293, 435202192, 585902450, 393960643, 664213755, 712357024, 150198459, 400635242, 998824320, 811862215, 736073286, 772861168, 834176104, 789762640, 681897266, 480189286, 864382806, 301313579, 850080988, 163621387, 242328389, 696585068, 588003721, 804148453, 792835909, 519342574, 344370469, 55047319, 79193734, 420315231, 983840788, 407102202, 954135730, 502053411, 771920723, 809841766, 411189817, 452001953, 411373352, 750426919, 894294636, 749489269, 953849923, 625693859, 453858673, 10919482, 449135263, 354626068, 367443497, 245736980, 995536124, 453351677, 335088645, 799175761, 895849634, 619256088, 317149564, 636248735, 698864912, 281953843, 562564562, 119607410, 592981528, 129351351, 642507697, 425141847, 30174932, 596086983, 944456897, 314300045, 841048868, 142467795, 250661503, 983525503, 635966107, 873551267, 765712584], [438144056, 270291764, 74415321, 61431320, 934736287, 971602125, 531874243, 490188802, 208483074, 537146231, 103644506, 164192309, 137803148, 248869556, 108848085, 884399677, 66071427, 721368888, 761268872, 513339786, 686850741, 773120123, 28222509, 32259457, 187702577, 339323349, 679800761, 215885501, 154224544, 913575797, 231467378, 341541639, 613755129, 463741580, 592999477, 591780991, 686269173, 329958331, 615191837, 197835710, 78222350, 714561080, 220206966, 3235139, 622738418, 750442797, 804529235, 493564648, 989211227, 540170210, 133601630, 828956219, 703340029, 226843622, 550799120, 750824682, 564253020, 895925109, 442344873, 873825345, 815342794, 367275328, 680505777, 640754223, 449384483, 551055143, 665080438, 247047289, 113207423, 572816642, 142155444, 276542557, 999498580, 208007474, 201650258, 734215265, 207305164, 928052513, 534688721, 227065579, 329429803, 959001823, 831871526, 391788164, 299561494, 721905139, 656046511, 766352159, 308655318, 697088559, 842382533, 623627552], [66859358, 317618869, 409231919, 852988441, 851698844, 983349325, 111541235, 687356674, 430244802, 665398389, 40444129, 965684949, 210917619, 626999204, 874049989, 635699969, 153801423, 139781844, 922347623, 569796795, 729888516, 84611137, 316150296, 617974337, 816634942, 624256609, 802549725, 452190669, 323767559, 922126473, 304272264, 25676129, 500093239, 169456535, 598135532, 930951125, 109661902, 726474218, 630336546, 922768646, 874840242, 506608455, 272414037, 194352100, 60873733, 476743545, 509191139, 58610166, 607088422, 278327609, 864135021, 384934721, 574579633, 827226364, 132026610, 557714840, 943492915, 420846616, 129936945, 551574558, 103036776, 379879671, 237933144, 86287995, 833624204, 667567479, 154726875, 326687668, 786749453, 147522769, 18540448, 513235618, 461509736, 240179953, 369998258, 895015549, 255753141, 815679450, 660338404, 714734170, 221904990, 944741098, 770072649, 117442802, 416290142, 760913479, 505927739, 82626526, 458470837, 105259360, 621658609, 755312547], [998153875, 29324252, 51556036, 573811942, 167878269, 121494890, 20159597, 91493259, 387139816, 319156304, 384278185, 89815450, 250082333, 838490037, 968511272, 212209127, 87213282, 680976410, 999582438, 177509676, 334298040, 641776312, 633373587, 984155828, 654748834, 564484973, 400833722, 277563127, 34684297, 152576820, 152147270, 781291525, 901482672, 122848358, 718555100, 466067332, 980176480, 901663231, 402711702, 920416308, 357406636, 403658220, 606724334, 625469975, 172683367, 726452166, 34587007, 750380229, 802527057, 499176265, 995585578, 900357392, 265823076, 261318416, 725697243, 24545805, 697498215, 2861680, 527145039, 484798918, 413004901, 435006082, 470084229, 183371666, 842521321, 102680061, 415200836, 663520747, 708224758, 25622958, 102743904, 872799589, 979319317, 234882579, 197351800, 264611464, 376907005, 829447189, 254276797, 407154727, 396006443, 632611124, 846801476, 157015193, 981581174, 582501735, 194282310, 820191505, 717123132, 60910292, 807359487, 579471480], [689408, 955713035, 234557967, 617838614, 756278961, 357408426, 968040756, 330310261, 68017391, 16073718, 923500754, 616521783, 918761735, 819565891, 54277210, 516546447, 415830693, 115321797, 16140801, 868025401, 323208723, 219764934, 778622009, 584840724, 362934654, 399118743, 79766090, 441835318, 497038236, 975461573, 272955584, 849785788, 901260262, 379559727, 655553698, 116363787, 474583932, 695517247, 928926877, 415448947, 478595107, 982790834, 893088283, 581116417, 791779294, 541375691, 652805915, 327686074, 698663097, 860692193, 809727037, 618409680, 270650397, 114516813, 320862410, 227698768, 83481147, 973971679, 317775257, 876028110, 225463793, 240005204, 118500379, 927308040, 277135748, 827981705, 880720653, 822054779, 984682085, 36475938, 489807909, 442115374, 220148160, 329062856, 404665504, 880217096, 182121108, 539569203, 524881293, 690129772, 388118359, 287093136, 808425985, 690682466, 502355110, 751290764, 387225827, 748796361, 349628959, 67078825, 45789053, 611965776], [485748142, 497259101, 575494463, 409935625, 942762441, 377223104, 95789380, 453333675, 362986755, 347312170, 424702316, 79444092, 39017023, 592999572, 421807429, 789727643, 960587653, 119901425, 847343086, 307868341, 669044939, 421423130, 789175373, 13735470, 782646028, 139617541, 11648302, 97931900, 411614386, 10483299, 584596106, 988884294, 142954177, 362909584, 493064702, 130951073, 279660378, 968636702, 344137295, 287406805, 301212740, 114959305, 92836590, 727894215, 729329223, 555598245, 313220698, 851466092, 609445262, 921503887, 573986605, 896530939, 838916279, 41904975, 419577993, 850577913, 508882503, 873258277, 731330256, 664644524, 907713433, 57535658, 761042664, 645140328, 700449605, 559070511, 913032142, 237146588, 649576263, 309376600, 268825674, 200943745, 462850589, 823112664, 214181958, 407675442, 490090317, 756093043, 577674115, 662319473, 847436218, 343847689, 569580820, 643208858, 845662796, 443294623, 684563873, 48833239, 32019534, 657006841, 302299648, 301184984], [405813109, 580221316, 509767551, 774116240, 200975909, 216733312, 142822170, 585884465, 693137731, 799210472, 586661834, 333627163, 759108551, 665813496, 242727273, 607598614, 459412472, 36488817, 402754453, 109832210, 603625708, 68087274, 486311134, 792121024, 991893725, 185498225, 468077149, 303106852, 134886184, 493618815, 206050295, 614354774, 835815244, 487038994, 239159119, 141440061, 49022156, 251206434, 949625314, 115951811, 425550720, 682156651, 615543173, 700731847, 229842697, 408200953, 295972260, 590198159, 182896328, 726880695, 979787350, 20004304, 992276328, 64107948, 70678921, 203773273, 758879293, 46720910, 598316013, 963453971, 269119757, 783125927, 590983061, 45351430, 364969715, 42737796, 847342753, 263881455, 417418850, 976726381, 945522436, 187477011, 770345648, 807707916, 212227355, 724621013, 542833080, 905932121, 864483509, 503652118, 301912538, 925534898, 889978066, 886462840, 547129392, 960926162, 338487113, 869465261, 346343599, 213978365, 305627812, 861324385], [383932426, 569791734, 452753001, 942895742, 334373069, 251472809, 969684186, 125518158, 692535068, 48284972, 64932971, 858608059, 384106599, 103867405, 558459617, 888872830, 95981197, 389964377, 850134782, 532499795, 487824546, 253878457, 162520253, 994848181, 995580556, 987148116, 496315562, 435574816, 668032242, 981124867, 530374854, 74208959, 904792804, 75179875, 724735507, 183636053, 323005103, 857626642, 578604422, 553429655, 942658155, 194757887, 295602024, 688217030, 763894430, 291331835, 774838760, 783623995, 121982082, 960209944, 789149680, 490644219, 58982706, 226904725, 585411392, 756582580, 808934165, 114804860, 87876800, 685949032, 53392429, 147618749, 770278001, 826512451, 135874971, 838591361, 312711130, 415517330, 310534888, 748786407, 983253727, 29617900, 147733030, 148689938, 510488665, 570799835, 335242502, 315219723, 138041533, 481775007, 812980611, 927847627, 643132112, 358181218, 614369616, 906935822, 255538344, 144383146, 34181772, 899929056, 14096109, 34267820], [639754846, 305472543, 989818478, 868190507, 954717317, 173129108, 972746267, 691837051, 856585214, 77232437, 548318720, 896346464, 721154589, 349381865, 288145303, 352398315, 473123233, 159454367, 610055629, 213166852, 150154994, 159439135, 550490023, 524118880, 716102016, 910590381, 852534838, 364517047, 777797136, 219737664, 587739129, 509407334, 212614010, 250031109, 336747448, 398488476, 482614463, 481176748, 14435360, 949259897, 571933250, 697683051, 675247418, 252670066, 259158795, 660221811, 380946330, 89520744, 117417191, 959259062, 915273112, 994187922, 554026153, 391950022, 358271039, 892399298, 887592445, 193275729, 849964126, 567943201, 620370980, 347615743, 158579943, 551823149, 663755185, 664736395, 871709708, 667292699, 274919798, 919500064, 545989231, 618332903, 378640781, 90264990, 274070985, 543412146, 603550769, 182890251, 507116223, 826561703, 19297196, 791613181, 167482442, 290813477, 395406722, 655290416, 511661441, 980028939, 608342410, 65053581, 231329300, 311524162], [786683663, 325764610, 295422681, 587048937, 348348991, 918901474, 241013565, 872031705, 165132249, 657554725, 509790705, 274751179, 948485700, 500066226, 700245923, 966635683, 645120920, 609326301, 712891124, 495633152, 9909090, 565173467, 204096470, 186380104, 465072252, 243870042, 748454242, 351149854, 828603764, 539645233, 514932160, 831406184, 993452192, 696856928, 490919876, 861823209, 510844252, 259769647, 206267721, 619426055, 589443195, 365727491, 793429529, 879529174, 437206592, 839424146, 226955497, 119226072, 653471072, 493702326, 668723159, 115131579, 273390867, 823798726, 637094879, 118076945, 537662327, 494084526, 906646187, 531168838, 463633688, 111432997, 477797970, 999250854, 253680008, 511086691, 131144787, 663761817, 322657130, 164749410, 839435323, 68583026, 704288999, 459030904, 715255087, 199959920, 22233072, 4283269, 127624500, 324598014, 674623230, 591446436, 574279692, 662505395, 178019711, 745645060, 247080920, 486902247, 522750079, 439642688, 789422004, 661118057], [942687481, 515910565, 281451677, 25739892, 887515858, 572250694, 633966476, 858202039, 99564058, 483319005, 404088296, 356629415, 394488323, 428989444, 932799109, 328366939, 206236982, 788511718, 246769205, 811579549, 593095086, 820485181, 641655843, 684088383, 80148876, 315181162, 371685931, 893999643, 249120788, 993154235, 295589098, 625628684, 607165635, 668996468, 550481004, 146313607, 964728413, 143051128, 299839690, 545506865, 458503195, 356854682, 755057557, 177068630, 897130705, 204005137, 518450074, 881001555, 528144316, 790885627, 156858516, 978356233, 781042946, 809941795, 270563027, 745494437, 881730082, 460861023, 167190404, 219165866, 835798866, 799941485, 693298301, 355991735, 234719512, 617148900, 163237416, 725936601, 346903009, 246611713, 235887320, 478673095, 568134030, 611534730, 214655568, 877281629, 863843803, 698475389, 254316815, 670491847, 720094027, 320581075, 750864884, 36504097, 274961662, 194129912, 497089215, 5463344, 192615421, 868581817, 75876883, 766303149], [124497515, 160453627, 716125379, 598987533, 534749293, 728010068, 200683130, 112956835, 584678804, 991685877, 914861150, 255066512, 427811532, 2509918, 192667485, 158841789, 953854328, 241035169, 312433695, 214565311, 890165858, 441971587, 756851118, 947070099, 311169294, 985264717, 479816217, 551487019, 952765427, 33558528, 659179297, 497501724, 758641311, 142066350, 324057598, 322585574, 72012712, 851296355, 784845725, 998938498, 584907562, 429073995, 45788603, 558441713, 159790398, 40183485, 435233684, 702416094, 525700512, 14703525, 144033602, 997103623, 38795198, 20134470, 314197897, 856852992, 316182300, 46083141, 175949086, 213500249, 248164304, 997933156, 189109312, 173642612, 933522726, 480304706, 581026542, 637209717, 651447341, 811821670, 560973521, 638992728, 399848187, 986326551, 548337091, 240415860, 811378340, 332983140, 923007412, 913546978, 193620734, 387135206, 790624555, 757307286, 724861919, 594038993, 366465970, 654660601, 603039076, 623203005, 393921792, 888651377], [835564981, 391439957, 1657718, 528349747, 163988483, 976554216, 726340842, 130588960, 690086358, 519968079, 911122723, 692560254, 893987790, 140134954, 435059687, 168828277, 544841533, 441730703, 671928103, 525517209, 667729080, 283755170, 279641296, 518458402, 178267563, 281042509, 229473254, 121032978, 527656820, 503229450, 41712019, 958623179, 851518585, 446669718, 267038879, 937625368, 990224109, 496526360, 702153830, 471026573, 306673183, 445815799, 496055948, 41161324, 202763250, 602104576, 570234136, 333060754, 743474925, 983071620, 460565736, 851100806, 660009564, 395241167, 579371369, 486356099, 159172770, 223462897, 543401406, 496646824, 619468774, 755789726, 910139348, 432588167, 433163209, 782841533, 374678291, 683004139, 722565144, 324446756, 823110648, 585561699, 184364972, 672943269, 184775257, 428004163, 261729654, 168343295, 365362584, 724680767, 511046435, 580728965, 490477774, 17378399, 150284982, 344982994, 187847203, 915285241, 789841191, 496650980, 434975378, 982789800], [157672194, 357636099, 940310413, 476337842, 694503346, 440777162, 56195995, 244340472, 307726494, 541109503, 615002928, 158656103, 356599916, 957029720, 442748972, 545819154, 275514593, 838761370, 367995471, 343718615, 508885463, 327866823, 411074852, 594263247, 119131099, 609558236, 962763228, 195833355, 4996026, 46103513, 696668220, 965560842, 383482421, 366796161, 633484028, 895090784, 794838451, 795435971, 762801898, 840334346, 249497610, 876197888, 814295831, 35062001, 608844617, 328680732, 933859682, 467020729, 397675788, 768327550, 346888815, 285115024, 936884038, 847469191, 205867246, 509535569, 78631783, 592204981, 363436617, 731937629, 94895981, 923874051, 71035780, 91337837, 428271675, 366270996, 152039720, 174107887, 53741826, 543909576, 428988568, 263993861, 954464500, 387144252, 453925452, 128647285, 90415654, 518889164, 867941352, 371295659, 556919251, 657532643, 934365934, 222011448, 383260638, 639952498, 332731907, 581665477, 399665757, 478814433, 440313061, 149183926], [782649766, 905341688, 435789355, 315111253, 718643742, 395961359, 805394923, 793500427, 544378250, 832429966, 6226150, 513095332, 641545211, 632956527, 662712930, 533534573, 808315564, 980724511, 164749216, 444938954, 950416627, 36976676, 293411283, 186327836, 623134542, 823976833, 879494236, 319593595, 402081218, 172805344, 405355214, 947071349, 965141564, 567292156, 167821356, 344310753, 88039925, 254846303, 159230456, 749460035, 469324397, 685613559, 997108516, 823817152, 98212199, 592620223, 969404165, 67926692, 182917493, 169900294, 374968394, 599735173, 284730077, 705433161, 396192116, 620900947, 61767423, 474242291, 31837483, 573726710, 470777807, 787741988, 120300674, 559796243, 827296433, 915188701, 293803453, 455537296, 159104764, 178805817, 269044205, 503203561, 583533389, 517250426, 383610443, 504738496, 40489459, 507052858, 417613900, 63808720, 594385713, 587583289, 403415125, 759230753, 6529563, 641668161, 654098826, 461253305, 236966723, 422669800, 648900868, 657416249], [780446732, 548243125, 440811411, 443135150, 267006084, 841003862, 126831629, 605189567, 70173661, 721763417, 620978029, 61091777, 457621908, 974188048, 246619762, 439393942, 908479729, 919761452, 474161626, 661141527, 971743610, 946060710, 496794272, 114525693, 716518812, 827053554, 986515804, 676024163, 771367314, 259574854, 580894427, 182062149, 443779674, 91360796, 248002940, 637206986, 312831682, 374089993, 778798049, 191027414, 431709952, 561230937, 203208115, 468314396, 396315487, 368449210, 593229833, 576354743, 706585556, 798148043, 85242159, 819676628, 384470444, 808775162, 758324924, 943361569, 57938758, 661299395, 473684544, 781200675, 702626429, 206853619, 319933871, 662940660, 871855550, 41944516, 535296256, 770891416, 425055440, 141460368, 593978733, 303478715, 422234759, 535208941, 624879099, 461198597, 816766251, 829385996, 750374528, 6930307, 123436946, 305363160, 253372879, 703332419, 727628036, 548813844, 637450019, 845739952, 651297380, 437821221, 663275056, 704697609], [464922121, 980653391, 176527600, 651889049, 958458506, 324720879, 236055244, 199601114, 212517891, 696397160, 334589896, 718469941, 613556639, 152415715, 919282212, 756217442, 71262029, 170474309, 590461183, 605738096, 526126726, 667033628, 878539369, 999259763, 767232562, 953911601, 654886979, 702914494, 48933949, 194490705, 407088522, 491592086, 725693336, 238148502, 739449661, 501542149, 86668807, 764991908, 350744382, 845783667, 267557294, 234502066, 962475891, 415215474, 136804405, 167460823, 366276620, 805668310, 82781229, 436301922, 356803695, 459409164, 498299627, 959325206, 703505930, 547287422, 707065823, 791404837, 42178483, 545719993, 124205997, 207737609, 576935141, 516114942, 140392087, 847250242, 188420400, 468430970, 874962079, 372383324, 435230343, 636387116, 380597627, 394018853, 58348524, 975733098, 735445944, 417919182, 330813882, 711041333, 496624433, 399855571, 823166391, 264121822, 461618550, 296206773, 219932581, 688793703, 627409447, 88717733, 397445975, 679569295], [950685142, 672665264, 871054751, 34940042, 981211572, 332772747, 844794093, 341939199, 169391524, 402513880, 659104211, 932136997, 205047891, 735832865, 29375792, 251219925, 690549344, 168998874, 240955108, 414724671, 7531371, 982153682, 172539997, 228125938, 602349154, 383784174, 179976022, 587271917, 801359846, 406405938, 991710963, 162188382, 88017904, 187880343, 454904965, 10292985, 171436222, 209271588, 144170223, 923815492, 4880729, 349018901, 123119986, 221179650, 814961289, 661743433, 320653102, 332299289, 943148144, 962123687, 175083786, 328078477, 52202139, 621606732, 21457255, 428906082, 233575106, 733284799, 221726226, 63781033, 346842481, 646559678, 449842748, 71992700, 457435497, 687616864, 595373138, 853331755, 280654962, 242511003, 577426048, 187807908, 968430473, 800714617, 4353491, 817366352, 236480125, 883904708, 393181860, 913106774, 156567266, 757622589, 372254347, 513058867, 767490430, 445622185, 2281737, 343404558, 473978237, 966973974, 571658410, 38044445], [37032513, 838105721, 271807367, 800209117, 797276420, 812521087, 926840334, 989032756, 624617757, 596118489, 565794968, 306014663, 421768657, 56531256, 463876987, 23198254, 309577295, 592172889, 18451995, 946705690, 606569886, 111516430, 397995678, 437192871, 111394411, 490527481, 329910992, 652514521, 385754697, 500776060, 89949219, 491459896, 578944342, 486796142, 992768238, 491384826, 280628995, 558733837, 370449351, 722645454, 812341607, 998600931, 762271404, 234031170, 98017980, 131479449, 845875218, 172571448, 593129598, 289983294, 970952793, 176570679, 589778076, 692595547, 279767883, 733876242, 329141766, 218587031, 855671096, 314792521, 169758229, 289118443, 44213273, 41698431, 756475113, 268408629, 525216651, 168946481, 481273945, 507055547, 260335118, 455948822, 737438901, 598711660, 199343493, 715268857, 777644, 666499654, 172449506, 499582255, 465953499, 508825809, 547492068, 74775910, 199442474, 782821009, 137724827, 174115123, 66142472, 32905259, 467730698, 424059545], [209689619, 485782455, 608393374, 870915157, 915627938, 945802347, 394071938, 423694307, 492264309, 969395590, 176425628, 970744602, 262386087, 897295653, 976553557, 520812660, 307213044, 810305134, 651539391, 29861766, 839533163, 904616119, 803266009, 156496158, 914446571, 174938709, 5308666, 87921455, 635428020, 478268995, 804892122, 659540107, 112586150, 479770137, 327085614, 821124028, 325768440, 82107550, 853991289, 681631382, 182948441, 469842791, 110502833, 251037578, 612048334, 455758150, 159624553, 972805459, 12703039, 742982494, 275230446, 969017992, 627049031, 281157162, 546650616, 965303582, 260334771, 555749880, 796460833, 294652968, 966462196, 766266933, 17039066, 570858771, 635288948, 856603069, 208685831, 222703153, 243901451, 402789874, 652400992, 8858650, 907731610, 211868472, 952496116, 839796840, 642800984, 500079833, 255647717, 776565018, 46958191, 453660642, 605201811, 804265532, 466632398, 308533385, 132625227, 789480598, 149789556, 77962374, 839322333, 99704642], [92913524, 80873306, 286316579, 119385240, 14209508, 40306977, 370047940, 299318809, 752123299, 950793337, 298915086, 136144614, 898409914, 769803608, 276009319, 525026878, 475283444, 939558306, 847342912, 584073752, 219743724, 648740469, 274556400, 887362961, 330318591, 946903345, 960116153, 164412199, 720514751, 712796331, 311847960, 185077779, 674653454, 274502738, 921342830, 782643511, 137318711, 608097166, 493518131, 352437394, 388097601, 474548297, 555840381, 234377151, 508355479, 300412115, 897065311, 994375135, 258336491, 503764143, 352110400, 689891608, 265784181, 152388091, 114346186, 292483760, 41877988, 623254108, 591744126, 662783190, 570693021, 255595195, 766162177, 468226734, 195264370, 504854475, 988802669, 133472440, 913418951, 316884918, 713304176, 917491073, 222115022, 746378928, 952716796, 84753201, 612053215, 811335740, 563475571, 863598740, 798723515, 829544226, 513100057, 864658501, 819501000, 364605478, 912456546, 155080722, 403610914, 819568067, 611889807, 920199882], [618371531, 118851452, 423031185, 952714262, 287328190, 171400937, 311174167, 922747095, 628219145, 296434556, 823775636, 554854030, 110520401, 667637432, 91661163, 136177490, 879708369, 610241295, 293197341, 728711630, 984136775, 506904227, 187440200, 536464259, 17648471, 875400176, 881610909, 591516127, 651338901, 971608493, 997810519, 643020090, 420199297, 278100195, 196256649, 884664028, 701580472, 44095726, 953394465, 369943909, 304178730, 980998191, 85651945, 584135334, 245314991, 18325506, 681742095, 794617846, 397158397, 132823318, 424152233, 348064574, 902195724, 67237494, 353471343, 130557009, 823753654, 385260658, 483925461, 816069488, 280104753, 19588742, 521077960, 929697582, 236799975, 299718302, 512534009, 952525541, 700406055, 898025826, 840024678, 926649964, 973229858, 123440631, 174634820, 949007159, 479000557, 730178063, 459344656, 745504563, 853766684, 177422747, 250441843, 98112409, 992204275, 762102322, 742322587, 380280749, 583268073, 335819612, 505499706, 339545634], [541413248, 172069523, 960037235, 301404113, 572097694, 833713836, 64009439, 793852186, 213032966, 859436437, 968910218, 645268257, 749769064, 552888823, 277137569, 44391067, 647016835, 294524765, 754691017, 17612104, 158582012, 184588736, 581174268, 937243737, 800302952, 107358194, 253848018, 52390417, 20359072, 804867633, 933408306, 136993094, 600943865, 890750238, 95741135, 944741907, 644667566, 169434301, 154261140, 773253618, 991059267, 998079347, 6575218, 535585520, 274656584, 127451742, 709012709, 597670615, 810137777, 372856459, 612030411, 196169897, 580686820, 750569034, 119146207, 516551267, 431263792, 193730996, 286992049, 668977045, 159530174, 517682390, 324724081, 652639201, 671789000, 58731810, 115454546, 986066289, 450346445, 303155298, 159135999, 202174540, 875339502, 207143945, 182375597, 494519842, 235009567, 468020316, 243888443, 450164426, 380505401, 247395642, 255100348, 50230301, 297021977, 136042033, 437283956, 317048057, 180862085, 236743357, 441054555, 310555854], [592624000, 74635926, 716394176, 144605275, 545158009, 869012442, 183800190, 589478766, 177262090, 723372310, 983886711, 106235963, 951490020, 574428351, 518711773, 132506715, 564564796, 104659974, 495272435, 328394308, 740896089, 940134718, 294111110, 666593656, 880805918, 40398474, 437311997, 934437668, 693303252, 612951192, 957922578, 609458358, 750138245, 845995699, 489792992, 815889649, 334584663, 937410242, 305594264, 453191604, 93126998, 317556814, 443967873, 734054817, 166356238, 733587921, 498411068, 702306271, 195513818, 86648904, 131108414, 665518384, 53768788, 929659384, 974890363, 290552593, 196265354, 402720447, 938000183, 350387689, 84410336, 243946606, 31176494, 142513755, 154663376, 327779877, 298029541, 218998368, 387649299, 651590356, 188622430, 646193192, 746937621, 943606317, 543366107, 615538444, 148805720, 160034190, 467420865, 635681816, 436661973, 664289751, 565262284, 894604422, 74659904, 225218365, 736432295, 501135907, 824975739, 383234887, 173077161, 663201648], [924348474, 324659362, 178239979, 382308264, 593473348, 908924162, 26290042, 423462825, 100422990, 468973637, 865278758, 902323825, 191442454, 131216551, 440051056, 197835201, 405019622, 715351062, 881765408, 239817079, 704642723, 165274591, 489142287, 346556677, 739884342, 124963867, 132882799, 586556092, 821852839, 509160592, 869130753, 758165413, 235401673, 796031469, 717275476, 45720846, 809095493, 3581477, 784234261, 538149691, 436851947, 357024314, 519600082, 159041943, 234930947, 961435190, 375994987, 371032685, 378404262, 71680588, 625395214, 994025913, 715195753, 552344488, 254768824, 442480726, 164226405, 251416114, 576568336, 633513240, 198196445, 307358256, 316363376, 431718724, 67403129, 511970524, 48226892, 1729680, 608667414, 391533361, 19752676, 689561763, 850864796, 731831120, 424114660, 4943778, 974793230, 836872535, 933282895, 884986520, 235462325, 500959142, 756276016, 831896252, 303353598, 429343865, 661315615, 773735063, 863871862, 626601955, 497908919, 658996302], [705485359, 571212531, 643079342, 625013346, 129192431, 126226221, 177912619, 853645124, 620392229, 555722940, 271107464, 762921963, 165512501, 702743301, 425390338, 597171819, 108791567, 133881967, 251401622, 930626669, 461810730, 778045047, 141062613, 293358188, 362502513, 248336476, 544969712, 17364458, 153046284, 964240317, 75769965, 240731412, 346341537, 741184971, 486865275, 860311327, 729465481, 86612279, 561775394, 386363370, 885186816, 141971310, 676565123, 38068322, 139648537, 103742704, 824327254, 849412867, 886741632, 45711845, 97974618, 253101728, 155103010, 688463220, 797845712, 739638618, 676795596, 423309224, 552524266, 437220072, 807742079, 304861212, 20000138, 53636534, 992944014, 75804573, 660411110, 38557126, 532230363, 959520870, 234894610, 500176339, 38089799, 496019016, 192834798, 232742664, 240591381, 953256436, 352478478, 369990115, 327353818, 86060636, 226357895, 73248305, 107264956, 822702099, 976627987, 385134629, 346276171, 360293525, 996097979, 489094607], [810424797, 440834907, 566657234, 181158859, 124202637, 270383191, 527553222, 771727120, 297015874, 410371415, 603246194, 48718386, 23425337, 916292208, 925266572, 873361182, 508410593, 741790728, 51813971, 333384852, 774562260, 825062402, 676527299, 462655841, 58182889, 652605890, 22016057, 750426189, 785723094, 406794683, 819864557, 590478803, 506735634, 341145141, 404304879, 312924929, 638732260, 147647323, 475542101, 413248105, 710546805, 453953357, 51328285, 327555232, 645284915, 743889455, 406264203, 590053168, 769653631, 543496854, 963303244, 746898590, 907065114, 186884111, 475606818, 247717917, 67216544, 872069213, 718215760, 964328042, 706040014, 970142289, 763839185, 420279344, 586038476, 404905004, 553266721, 5228652, 709280849, 902186633, 834233112, 521254813, 260561110, 34648260, 656096560, 77342207, 487983607, 341127361, 720250739, 175643559, 774266853, 524428625, 375368521, 558550284, 930068123, 365794819, 647985626, 793426943, 54237186, 711613460, 335736941, 398848507], [932385571, 287022762, 761843108, 196725094, 14087654, 970092786, 521441836, 475785278, 364049576, 438560613, 389585022, 684786533, 238007502, 791352725, 76830801, 15134796, 211575688, 896048184, 579601931, 765950760, 157917389, 695224298, 418879789, 136150753, 888955778, 561645411, 981020724, 838307279, 163246593, 304790750, 805266757, 169372241, 108967172, 345259866, 204913927, 187350635, 890731095, 236013965, 101719460, 183137322, 756001758, 749548224, 261701795, 72803578, 866576573, 410887658, 228903714, 515810492, 866676673, 958600262, 174934136, 161630438, 674276473, 895074675, 477170876, 57305414, 701093280, 263857086, 584492961, 475266682, 571706927, 503603187, 714088661, 422187116, 398316512, 284084564, 370792352, 644244852, 740433118, 332244988, 523368955, 897245888, 2383248, 554110679, 809925739, 428100026, 547297919, 654896560, 675339848, 242439992, 89252198, 211203148, 27075453, 683809111, 666529471, 829980147, 432921927, 469293110, 169728816, 706951579, 691521973, 791930870], [208015398, 206987850, 290952340, 131287320, 250844234, 955508000, 516912935, 204376287, 539401114, 622468146, 895658353, 73889386, 195612142, 740773069, 955785119, 399276347, 827704847, 347530186, 813752902, 65263762, 55334787, 446864415, 560789977, 763190754, 370504732, 377192837, 685855927, 725458475, 560465991, 100825808, 894026068, 972640394, 865305409, 744185366, 287743845, 975024986, 956850810, 871314426, 251180425, 671616157, 215692676, 268911619, 151218903, 531086954, 553339861, 594718219, 762307308, 625563976, 43870865, 300096952, 672734515, 497338946, 449627475, 136708765, 781073202, 380450607, 963913720, 607541213, 805231002, 236467618, 842539501, 79486427, 393412855, 454598538, 873777136, 187543755, 755522060, 748072965, 965875303, 515188466, 335401577, 361435659, 357565599, 461799222, 551410707, 994417845, 7149352, 228076566, 920740545, 515697227, 443920612, 313291759, 104870178, 788980624, 42571565, 856705043, 568850452, 861893509, 178982597, 712294119, 422955129, 142483190], [711969081, 713258772, 368595062, 18417136, 995115296, 105238085, 486794227, 893756062, 245464377, 668124453, 641523511, 875904462, 323869050, 28017360, 366565435, 494612852, 624136219, 969048466, 976924932, 910621284, 526312389, 177662147, 763446251, 576885783, 695647339, 617157929, 293942905, 154042196, 70852187, 888254317, 894928141, 79085383, 403517567, 398990877, 874928058, 537835939, 55601801, 823460377, 590060026, 962633741, 637668444, 937809753, 839620777, 94867985, 711601440, 21982180, 893961581, 267105270, 209147338, 854954352, 766140241, 159300676, 984084801, 275593987, 888573716, 41912536, 328522700, 707104386, 195373582, 270447318, 511351920, 148178965, 738399963, 197080852, 697215059, 859330954, 411457964, 852046723, 190423722, 456267113, 565264547, 640438508, 950435724, 948017464, 717811591, 567167344, 176456846, 811170547, 198596143, 116072343, 958895578, 649085202, 267521318, 251640098, 146699256, 360949344, 610965105, 528574913, 529422763, 906088352, 557620959, 491298787], [973483103, 828624270, 177699068, 550666590, 180117680, 850287022, 516389279, 951915122, 183140131, 182992197, 420883229, 207570249, 2584980, 686656006, 666502269, 554244726, 332737175, 433150268, 21316781, 872674153, 222767450, 180662074, 452997473, 294876642, 582456031, 705356600, 860455901, 182186237, 998016321, 825243130, 430147705, 526164156, 335306959, 918970195, 516029285, 425273440, 307012396, 608066299, 971946067, 422053452, 89078490, 357196877, 484858510, 857279805, 249594624, 286463343, 475401311, 101511635, 638717288, 704864588, 329537941, 908862754, 940030704, 707984697, 336026251, 143759075, 79940103, 101958412, 455465225, 665901167, 795060623, 979257972, 332524956, 667172685, 177317155, 108784114, 107115381, 703676134, 756681767, 759249989, 886298679, 426114478, 167196031, 549294845, 977130221, 310419608, 376578621, 820004152, 344938021, 298503716, 346900512, 906052227, 606189382, 706119011, 349688949, 65180034, 268034791, 19565983, 114102092, 270154478, 54729781, 304473734], [406557649, 615317014, 385250862, 411134308, 369304204, 472680040, 991341089, 362875963, 508688062, 2477327, 757319866, 458387824, 918119400, 564600696, 630354091, 755301745, 750269215, 867776979, 687223708, 500363644, 915799424, 265815486, 791243422, 283517885, 730178330, 441538275, 734120392, 433891827, 19260901, 714850200, 420107118, 253209915, 767572544, 787266016, 483221219, 786991987, 1420087, 473139236, 187355912, 806075310, 584265697, 571770834, 341734112, 509793480, 13556848, 302147812, 806753658, 256323557, 510290612, 969046595, 104610274, 978743751, 690307819, 164315677, 281488553, 582289453, 244189637, 584228551, 810265665, 428064745, 665563520, 455465468, 710004465, 90875318, 944506825, 835042816, 303221269, 515265793, 424095212, 583950290, 814985456, 906578361, 412070217, 296273518, 480158396, 18946622, 105226467, 990454638, 173286454, 700771709, 253077793, 489918500, 765106682, 66283793, 416554363, 485894969, 348345579, 113332290, 314119299, 418732992, 837834165, 57247847], [108705557, 792598705, 651178682, 154056096, 965228060, 703426452, 203791049, 7693436, 987363722, 525977894, 493507754, 546940673, 868384022, 5855187, 906291704, 551084832, 797568383, 549902487, 316390754, 873454634, 892613842, 97345912, 343583241, 83123181, 31769897, 252885106, 877595823, 286899839, 671640257, 37065337, 182531588, 232537954, 87844971, 599400875, 612424073, 55265530, 117312725, 740413120, 966626217, 574516279, 182365827, 681697631, 405348068, 872372525, 833718920, 249111875, 248999083, 884944451, 33057434, 440480834, 310772466, 800223169, 555803059, 313946477, 814790142, 335671787, 225529957, 48696591, 159300226, 103345753, 382698894, 562255903, 91928976, 781840033, 817620525, 449187758, 83889530, 802190369, 916597936, 949056925, 453166436, 499763418, 38101314, 56077774, 212591122, 502474482, 694301056, 567960078, 514667802, 553721972, 158547505, 989372272, 725061472, 703050601, 361801966, 702400028, 828438085, 556084222, 899747914, 490592069, 502524847, 393063023], [656508380, 991411164, 25498897, 236523984, 274471788, 933857656, 745281065, 486916153, 619458263, 205313195, 99905802, 452760177, 912260939, 363481408, 35089781, 253824251, 943666970, 297429318, 881263022, 632709079, 866935831, 569136892, 545604016, 681762247, 642676532, 159738667, 372941361, 704104986, 109178017, 31746188, 223233539, 965112920, 773497635, 125266763, 618530051, 821976692, 162819183, 713672781, 960241167, 248752838, 102918355, 546016150, 239622737, 307991085, 409042979, 728944760, 661585185, 603084228, 800768350, 74272005, 116350248, 117181863, 317334779, 428453698, 311066047, 316233680, 814095948, 271677708, 718029898, 691276518, 695428658, 373745673, 912671103, 952421400, 843541222, 225777872, 95316962, 181520003, 198292010, 617879942, 609296694, 909306943, 388817544, 330165103, 945623729, 904642768, 864860831, 374772051, 98583310, 516532758, 31235588, 343389802, 312034014, 84715912, 367242159, 363905295, 225158889, 386822886, 263047288, 483862906, 248714587, 994160841], [699335348, 664503198, 235539547, 756754075, 578685797, 73636355, 489633833, 229759678, 260821250, 285649404, 441974490, 319312278, 69563347, 352430697, 695994878, 798020858, 759041549, 576832629, 142873607, 933117765, 107500560, 898058303, 63647117, 836708650, 6438308, 895530829, 277156164, 512472423, 447255871, 379438496, 245744618, 49569487, 727712165, 288157754, 651008424, 901393424, 166013200, 200986226, 545946207, 790009703, 232718299, 238749717, 101075900, 879385180, 875174835, 871598225, 260485836, 260121272, 907998548, 691067981, 98387140, 629817892, 46188496, 326361500, 587658811, 35898024, 483861808, 431350580, 978086, 637275690, 389386794, 747692692, 795599251, 594741820, 854560727, 357679996, 296120011, 585604914, 486540610, 16259249, 115938866, 622899815, 271963754, 411430980, 389579194, 89241005, 246499638, 999343300, 12442111, 92530752, 395011519, 874053693, 174150891, 748529659, 152065961, 382986186, 910241117, 986506628, 290060732, 214981284, 633880158, 442989049], [189155475, 246319175, 980469007, 226453256, 834794611, 47575039, 871355451, 571632192, 965966933, 29334624, 4588514, 464049993, 84441412, 623808445, 888545115, 585111979, 574432047, 126787845, 325293891, 514268351, 262660894, 72569703, 960161023, 220428731, 494653303, 379900602, 722814409, 909165399, 711676745, 48650717, 810443704, 710467385, 920206085, 4759622, 344810670, 633042350, 646386485, 742349514, 414272210, 13835768, 722326828, 486005327, 722531895, 122344108, 706183642, 325896861, 422389461, 290346147, 38915100, 554335170, 673062974, 391745816, 894222894, 940330523, 552097149, 207002615, 300051184, 86236139, 459650443, 933545545, 970707861, 741673827, 292584777, 901632773, 775059225, 943843540, 383898686, 733006795, 358736860, 288447281, 967039453, 256473262, 753222368, 945236735, 743203588, 178829949, 169232251, 959098735, 589369796, 478017981, 614767393, 642225362, 323024600, 979279497, 552988884, 223693524, 313184493, 200568417, 921174339, 138772720, 882066801, 980790026], [51711056, 337529550, 151344097, 490906463, 90952147, 221868393, 655581303, 498566476, 949691348, 304134661, 768380328, 84210461, 849847760, 765274244, 316654295, 446820820, 616003706, 502675132, 450184090, 270911378, 441034370, 586159834, 161950302, 460294062, 853174445, 3742148, 670292824, 881389205, 279051935, 542380376, 936995078, 211485895, 514074833, 582758636, 119319252, 441713173, 696051941, 217468499, 19180611, 423048511, 767728613, 125201009, 616196320, 64717280, 771867248, 361810285, 919626150, 190912298, 756370418, 112644079, 818979257, 98755375, 744258053, 257428428, 137291327, 783115077, 18614661, 390912236, 372971289, 568749571, 374865221, 12121895, 249307558, 558020805, 606502051, 89375127, 946175954, 534507443, 92449083, 806159277, 910413037, 706050018, 756628895, 392491061, 772008245, 120343642, 405779237, 283748459, 612040322, 781094302, 54434714, 434494719, 199989606, 659580695, 224724900, 752967908, 477064118, 99972267, 68485843, 566824498, 588947836, 178370774], [488230199, 726360324, 865151122, 247756165, 170123869, 712601318, 983087346, 612108589, 875837916, 7109089, 751659513, 153742700, 48135347, 380667554, 200928626, 847220669, 359509458, 946724991, 577449856, 454808114, 554114317, 303579569, 235617424, 59193083, 438455373, 896405644, 549189541, 398693954, 282113593, 856394822, 54422100, 433252258, 942192443, 476759462, 473753198, 235782058, 204537170, 627571983, 323361463, 10543674, 788808718, 605649141, 672988670, 238390924, 197376581, 535620753, 620278161, 982285958, 90053139, 693143395, 223770999, 555211491, 783073964, 504870507, 751562444, 709458203, 174248627, 993284573, 451924701, 615037742, 418443626, 783629001, 275707396, 947171737, 426150463, 961274701, 53891570, 940535544, 620644297, 127637971, 592791382, 201668567, 514726755, 64015207, 560124198, 281280464, 273826617, 786770640, 807154507, 249241405, 619578485, 593748284, 411003605, 88116416, 105880854, 644933213, 580941029, 684095347, 722805108, 813150311, 564494962, 312424048], [348201166, 867526543, 108696304, 469085915, 515886620, 826606916, 102497399, 771776598, 772519626, 336846947, 554059977, 155529885, 808029398, 529135940, 733276151, 562600883, 948652546, 787577865, 840509823, 966530159, 590710586, 895871967, 496226750, 346145626, 276919362, 506248719, 717847335, 801274834, 615401332, 285299973, 976162788, 768420474, 761153406, 486648994, 548560764, 967010763, 420179986, 265171187, 218644026, 479978815, 715762807, 403477500, 644805088, 439477552, 937067903, 814170022, 152361209, 172668870, 331150253, 41673191, 875510378, 825370676, 952895245, 904486493, 503196334, 404243469, 910150502, 968596058, 323168164, 472847375, 913731268, 537556648, 602697310, 729898659, 218438733, 475655446, 437585272, 568041076, 331237190, 317208118, 984726920, 771781261, 334884630, 753746726, 604224253, 186660330, 311396483, 588707789, 76572483, 551996024, 285763070, 519670000, 888319679, 632449590, 636591837, 133935657, 967439510, 704373248, 87731540, 640446460, 390326984, 418506649]])) + +test7 :: Test +test7 = TestCase (assertEqual "for (maximumScore [[310076548, 764126805, 485388059, 987528751, 437560592, 997825191, 515523887, 62578341, 251436316, 763663045, 352002813, 589371022, 838236324, 662659028, 805162197, 826595352, 806582107, 329585108, 158109325, 652056160, 545600678, 259713482, 713354123, 458595692, 986027609, 785628709, 261185623, 719256557, 588289241, 750163159, 846538612, 292027067, 966840310, 968455810, 21481500, 485050387, 82734919, 66493717, 673437962, 287363129, 342834119, 412567189, 267404789, 286243776, 688609100, 328747644, 427755667, 985607240, 776976506, 707058481, 789417999, 805337232], [249844905, 422872898, 703456496, 882110397, 589476351, 500269527, 266150671, 837539771, 320295046, 960332496, 202699874, 107446805, 654090267, 970732445, 49411055, 277348427, 814808576, 390231757, 348559104, 574396436, 67676854, 423911769, 749321123, 796902455, 200917110, 305720994, 66658236, 277656039, 997538477, 116475385, 915849527, 378458971, 468354504, 296294579, 417427016, 47496, 223315310, 499136059, 507551056, 622937208, 17212718, 228111996, 70551858, 273705530, 10191643, 978069796, 755197423, 648159910, 356548942, 936085274, 625197622, 832242364], [463542462, 587108158, 138360853, 53931199, 906890500, 592332229, 657781873, 764015389, 590556, 190988231, 425668346, 241620526, 543586434, 362267881, 961880340, 637906303, 509876468, 903994285, 692551413, 659045556, 344468807, 844154580, 236288361, 31994947, 761699573, 767957245, 591585619, 651982732, 348168937, 612082749, 989606214, 639541290, 955931493, 524897499, 122826017, 120086501, 122279692, 264727946, 66275389, 542289201, 748397169, 729152621, 291385341, 817214343, 250607420, 103795479, 641704787, 647784848, 235340368, 811499095, 309778281, 681178265], [812267468, 93670665, 938725740, 432342391, 840991079, 724392545, 325347128, 371979361, 531175701, 371810490, 624796159, 905549241, 854325619, 298213982, 38207019, 809414313, 86960662, 936805820, 596017253, 13353804, 407143420, 363384666, 14010276, 732357492, 546999634, 406356622, 136220005, 421648448, 438994135, 308346287, 622187575, 814328155, 187689247, 254176607, 23724175, 686329010, 916135288, 884022352, 852160899, 516829783, 843948430, 205471754, 772917254, 646723672, 497672814, 261270878, 566050837, 178891368, 401144610, 879413398, 695752544, 100294478], [985593843, 19019148, 386742639, 287131008, 935830170, 267960783, 549129560, 79456352, 50602488, 60541012, 468685467, 931978553, 274324171, 634668627, 201785555, 39237271, 953002644, 393216262, 340099924, 626951236, 65561059, 392753104, 978639431, 889366656, 83119209, 188354067, 715269239, 445985517, 303869611, 61555882, 912542538, 133120934, 686362246, 965961756, 548455668, 34774094, 852512667, 73091004, 61682419, 289331955, 924173810, 800161179, 153612210, 148638249, 686624972, 273511504, 160379748, 777819228, 134000969, 373708223, 892031765, 866527358], [457454677, 653037344, 266375407, 845322328, 905033886, 320839936, 369891119, 397452015, 679437877, 491827644, 705565742, 502949402, 505136316, 231748414, 590112187, 486721588, 247399304, 161777707, 553121963, 742536612, 682238785, 398778225, 705000602, 439775525, 137910153, 997441139, 479094036, 297215884, 767389899, 189186835, 130467634, 453772502, 893296043, 115816030, 58067675, 340075223, 880660443, 676371411, 180476628, 22409276, 333621897, 532970053, 439603357, 365833480, 921539395, 562505640, 174625197, 653702209, 594487932, 457129315, 836789088, 37515390], [838461392, 900587260, 982728845, 430476770, 514440055, 644057843, 832999604, 850217247, 35213335, 370582527, 498648122, 13080883, 349771954, 155175165, 753852466, 506980429, 162661259, 554779600, 564439449, 229023057, 606621411, 699847406, 189363752, 841331262, 436679676, 251201219, 514029627, 256165581, 295579057, 269262552, 796005836, 425962695, 82213235, 188953841, 282103138, 417766519, 110229666, 906019474, 947476475, 910303455, 293733581, 146933042, 836935628, 596825008, 859524801, 334793575, 510409815, 12297254, 835840669, 204988326, 30498570, 688226921], [70925426, 736376634, 93052084, 534495366, 258925497, 425992174, 396231326, 30520032, 236950892, 658941413, 666987684, 166843410, 901684650, 402909635, 444666745, 763068248, 918245655, 872550802, 972056507, 284629859, 259767067, 762509783, 308332088, 211500650, 404501725, 954857817, 11298468, 330039345, 942757272, 39182635, 189626207, 770124777, 316487684, 787981335, 519932763, 104996189, 297958819, 653369130, 722659555, 459111482, 320544450, 842541904, 477084724, 843967589, 612695504, 756764864, 191292537, 303276509, 467638434, 871153317, 261195390, 220940389], [878297855, 556436901, 217041040, 961384835, 948122207, 389002401, 504161918, 628928513, 939212252, 669388922, 861195851, 359292178, 458107119, 75570901, 320219183, 956425033, 223963977, 342261675, 780862423, 586602788, 824753044, 700257776, 560029495, 512156121, 328676421, 17123992, 541598776, 824245345, 809246040, 349699414, 959063937, 380019100, 660168057, 826453249, 442279576, 11685932, 629400, 475681185, 57364798, 847907531, 251037668, 268540958, 870816824, 814579162, 922024244, 660959029, 61628108, 51462504, 343011781, 905483171, 701411977, 941533250], [29490754, 708669728, 577016828, 517063080, 947592345, 867514727, 996151169, 286667700, 103594489, 156406952, 254222225, 401545607, 886985752, 934819975, 510474958, 242151921, 755134119, 604968173, 906920476, 227144970, 53118028, 571185807, 533886326, 938405769, 527536714, 784571315, 60400677, 897559617, 645532245, 641718011, 97818622, 804581417, 277488146, 604079204, 173184510, 331594740, 240552141, 617526141, 445290650, 117084900, 49663532, 136335893, 185355521, 565922189, 553768232, 435312585, 728255937, 938871170, 226329689, 824869545, 527239209, 584109102], [295873314, 207691215, 606689754, 993932793, 32251143, 778381814, 62651905, 85027681, 125536461, 828847120, 740357913, 553768799, 425639950, 990245078, 115859652, 904702248, 579405295, 204295699, 981363010, 375149233, 82846341, 176599534, 626106236, 173357937, 793070857, 839851098, 676848060, 707585233, 567286819, 732008859, 921143325, 706394014, 529248046, 314291721, 908955997, 591397258, 178842726, 917150667, 342236059, 218123795, 701643273, 826359041, 639993820, 391407215, 3436873, 513827670, 106163762, 516278618, 749574640, 512664897, 525211363, 506136121], [890022914, 98923839, 998024834, 825594631, 867440512, 954060221, 133503633, 127057442, 614818034, 461789121, 155744265, 657209465, 402450742, 210991341, 181726931, 664855393, 588017747, 759815930, 352134331, 86093643, 739466699, 103960658, 434471019, 993899435, 140339442, 558005514, 708245270, 902368878, 344704883, 576132, 136166734, 608536624, 754572579, 478369988, 999988665, 600114971, 445357727, 319068755, 58952593, 826455090, 287471507, 163849289, 119245869, 256662159, 629466502, 247592356, 535272131, 764294912, 526314402, 153260199, 579646626, 491175200], [907659743, 143608852, 533347077, 885492862, 547228200, 878173929, 470157762, 501095703, 837331634, 499770827, 883467090, 588690242, 627064815, 130691706, 725211125, 701672623, 53326323, 430055003, 199678975, 854778075, 149519813, 348955533, 592688486, 220613194, 573302602, 967918845, 454531183, 476036594, 760858957, 698495708, 779966664, 380573973, 762001677, 926314258, 790437870, 621759934, 93920318, 225417413, 220457864, 911845737, 277457925, 263957832, 893571653, 774712038, 184855857, 934376519, 664932435, 480981100, 582949523, 581287960, 957655463, 951195620], [71185398, 751495286, 308908619, 18081414, 417921709, 579821236, 954556674, 865006284, 990833865, 351927737, 131519949, 910138727, 552071606, 740553949, 824892954, 263351956, 987464175, 70182944, 121051038, 179732419, 795566078, 228182766, 529348044, 361362709, 914097112, 819189435, 602613406, 72394080, 875131228, 280701101, 362343453, 609043152, 623752839, 694755087, 761736050, 208752167, 96313604, 790653653, 810513011, 10198216, 523603783, 755680241, 233347630, 293889067, 706851870, 918740640, 62742159, 161663310, 732465242, 208014007, 958823876, 592624149], [65618935, 675005634, 723815559, 16997909, 381463610, 996396507, 274073620, 693770012, 825818935, 363601847, 807825302, 370259367, 851238061, 159348271, 169283472, 337975031, 495410300, 863287726, 76158588, 465197909, 523725766, 366344396, 296280954, 315735924, 302008225, 852357876, 701212338, 358620562, 837987271, 281490667, 755583126, 158365218, 211411030, 429336293, 951971763, 548087459, 931444156, 884154066, 531938721, 51396317, 671950886, 733937038, 810806422, 195313485, 93504195, 279134208, 866167317, 507789709, 657994522, 250302350, 504552373, 457297907], [402772773, 790799819, 925366321, 957837961, 227285725, 655305220, 307512187, 896989088, 868283414, 445461471, 371011167, 147523683, 499202047, 675996660, 397750579, 414570442, 471592905, 17297380, 17062994, 928877330, 841712653, 25178278, 396272481, 270777383, 267172216, 114615456, 920185362, 4229789, 413563464, 944690766, 560565398, 249770528, 1063196, 19007354, 411461738, 800353417, 478090135, 242922376, 359047971, 242879243, 676124091, 264040202, 559424540, 235561916, 804046772, 726163439, 927274240, 879624326, 305111630, 887023100, 780877681, 27033341], [102356513, 993598859, 840630617, 461534456, 202464707, 795280084, 394651269, 281562803, 136057185, 241706276, 848096339, 477949310, 29460405, 232651320, 987793393, 433782803, 688387106, 697279719, 364571194, 74666579, 496990201, 905563193, 741261085, 739481372, 431553866, 293880313, 686100649, 349139875, 968529791, 602849308, 91556886, 894826183, 512036094, 536804221, 372670986, 897288975, 56176788, 456148635, 46273345, 592414045, 618411068, 815570848, 387529319, 143085926, 342407639, 510796676, 432532561, 537769125, 160714077, 39080734, 402275797, 921250019], [794538259, 667639197, 501613458, 510021308, 547864017, 2985219, 79928085, 514156233, 155150733, 462427810, 755015797, 185348814, 683311675, 888919262, 466931994, 784359559, 197279270, 890848287, 464420293, 835805848, 708853755, 297899503, 842113401, 674854981, 556336099, 485329638, 816616466, 867764882, 608775987, 663806260, 355976908, 655116687, 993217237, 238364358, 217897863, 332608903, 803940381, 331436819, 743853278, 240577151, 816090280, 779342635, 661042821, 218681463, 934327603, 293937318, 181937500, 179066385, 741848761, 272156929, 851556910, 388846192], [599240084, 48559203, 20452351, 960631459, 448710721, 433601833, 238129977, 963059529, 412646209, 713060434, 762392494, 909507356, 971011779, 216965449, 826237915, 755211829, 768018229, 662643928, 679592696, 928897037, 220767371, 669585258, 40847345, 559900801, 820851105, 633479429, 66960261, 931353191, 620763499, 996431668, 527380062, 423490293, 942439267, 225579592, 93195462, 960784241, 47114666, 353613077, 696382291, 730896119, 726677435, 478630552, 585653158, 235321358, 782083791, 278605268, 238675577, 109303051, 689824010, 330219292, 711973103, 985982556], [80864647, 632354637, 661102044, 43860041, 775941063, 580865340, 195956769, 200993194, 346580249, 879281512, 902016981, 496030641, 682304333, 977846430, 257513904, 298564206, 680075463, 19190514, 434766619, 912150469, 313271458, 753661208, 287274945, 642505871, 148684477, 35781323, 152731180, 452263213, 238212188, 475026402, 920711473, 995116863, 787813024, 572948528, 538676602, 850513643, 194229391, 43696039, 39762957, 441505475, 80872655, 154739586, 387153286, 123391520, 470058710, 939370443, 667910282, 919141273, 696715911, 943970122, 773086987, 923920370], [481317920, 768267657, 151675053, 178465925, 231339522, 762567665, 281528374, 884063712, 675039138, 724470218, 634379250, 584310567, 234872175, 805238901, 676466122, 558960375, 860762486, 865058812, 225173971, 787432955, 77985600, 645431712, 266679345, 393306089, 212975766, 111485511, 904089388, 530288296, 115175331, 484474337, 434634511, 973237386, 237590990, 565068461, 986930287, 486223084, 831954895, 474833222, 883265257, 695700, 150158234, 818776084, 328036482, 549476380, 838346006, 774501127, 145667377, 306165237, 137817641, 372583520, 419811019, 534001253], [650411145, 332894867, 17929945, 755895930, 498330859, 92675917, 871659300, 511740994, 691809708, 64019421, 531041760, 131959052, 507470126, 183958277, 540963698, 438586288, 24908971, 839278303, 395560925, 215660676, 571364195, 235966507, 116918765, 572975884, 386502594, 797346207, 30949516, 36362525, 830540720, 694498038, 552616683, 98548145, 551992073, 444363399, 125467987, 943660500, 872536416, 450584342, 716380532, 288230350, 715500932, 182749100, 715215359, 258435398, 186096418, 676189277, 361369945, 168870260, 671118092, 363548942, 789441766, 836666947], [825451250, 414772520, 196191999, 142916044, 278540815, 533165146, 527066786, 242293066, 269429082, 25941238, 672344307, 250274837, 799194674, 306108843, 141110847, 540828277, 695450111, 287034172, 441220808, 588448149, 236952079, 291385797, 887300856, 536037694, 198519241, 254351571, 155302494, 726773475, 774802134, 86970565, 296530701, 719277521, 477298192, 839609165, 583594077, 616941870, 521220368, 644973825, 56909524, 107203503, 132713720, 50346038, 836930740, 829619153, 633492857, 910303694, 486842974, 78828240, 90991608, 725979499, 676347979, 791940749], [993743115, 561010481, 563895133, 770064016, 918783235, 54756788, 833762465, 449099159, 292564153, 296743667, 587713587, 946965021, 485590061, 495498026, 253288573, 849956678, 780888558, 389653831, 892758062, 989737775, 496956051, 532067604, 918633671, 833457223, 76343350, 820941784, 833530358, 553012948, 946475597, 677541238, 459842620, 961167561, 765899066, 7309020, 441817763, 931240052, 980206975, 391572467, 112991140, 953281120, 415533331, 193706123, 762670675, 931833906, 128691542, 271152636, 241474412, 839095021, 630982341, 510365217, 63096602, 439890026], [559443219, 978130807, 685399667, 777008923, 841986302, 602994986, 155116048, 7252236, 921294114, 776254540, 924307404, 774432268, 62354403, 737598299, 107302292, 25147323, 502939525, 522236698, 636808262, 678993871, 7634494, 605308595, 251118893, 619311700, 914978421, 411605558, 41634160, 500215248, 417096718, 858829699, 505946542, 587621425, 896438664, 213714294, 848029140, 970665718, 669485337, 103262422, 815678732, 673184557, 558586884, 907212058, 751366850, 755565507, 471810834, 730655813, 372850682, 625653324, 994108723, 939221252, 374605507, 183162938], [209514501, 377697278, 131621819, 94536453, 459000571, 314935732, 380375622, 286169802, 904290459, 305418409, 492601403, 268775682, 759818002, 483191721, 67243675, 733583350, 165498722, 375216058, 203500628, 74319608, 281836296, 666098085, 521220841, 184198736, 906278553, 724580270, 905019907, 950750723, 65153851, 92522483, 99431660, 103203360, 752616207, 49943810, 147621524, 915678733, 818920537, 142894412, 6472898, 786779367, 45284956, 371365984, 248816649, 402861785, 91747389, 32226549, 750181600, 396372714, 457518155, 694695325, 603002265, 229520576], [38498169, 271441462, 220993231, 70281196, 833347238, 396186800, 124322911, 228447378, 839466874, 926557255, 14822465, 76276903, 178984699, 895474205, 498348213, 466518900, 292210127, 686327450, 702537160, 935337170, 879292531, 221025258, 238519686, 227080473, 651043333, 860579762, 280209232, 384078953, 790524548, 626100611, 701987365, 3193915, 162794358, 325401076, 380314329, 891648797, 630724476, 457342765, 994736940, 281063860, 237466803, 609091740, 234569117, 590603511, 523022291, 132358105, 645514416, 346666578, 434663119, 135696211, 642016348, 726973030], [324713057, 580825434, 447284710, 318156215, 358932874, 695817626, 332337093, 262443454, 463585124, 69380541, 530578564, 690723630, 623307617, 868932739, 106650989, 614103989, 153760269, 397735167, 924142994, 321057101, 667994777, 501388043, 691256339, 604579305, 805867172, 987961173, 105708277, 217862750, 264847027, 228251910, 650465518, 218406166, 931663231, 885931541, 932498548, 690728991, 95010854, 930134249, 354733432, 203626557, 915798369, 855446693, 664031006, 534747681, 742636104, 453954655, 992597908, 628289261, 375379136, 718906403, 805057853, 617728903], [78393288, 689120379, 95840243, 113383796, 274523905, 255318487, 844938633, 475359560, 742535669, 38758788, 760304151, 408345572, 946524031, 778098799, 212746968, 100102898, 258635979, 483271757, 329270313, 177149039, 804318164, 353471949, 243551605, 518561761, 879205386, 884800870, 257874928, 736080249, 711997660, 615402210, 735933593, 236415384, 729957520, 327424210, 85244504, 31918769, 15706512, 41543636, 906823511, 463949604, 465404789, 287387268, 704865068, 27672661, 254151812, 372561159, 871031305, 748011677, 674685667, 146685721, 516497915, 216342886], [734214941, 508092566, 983829638, 434666945, 223308949, 879324264, 986231486, 679918219, 617588827, 719795180, 21253741, 365740428, 878297549, 952301794, 547925030, 730409738, 650271277, 837769673, 287348243, 202335907, 214083926, 776562291, 336071635, 706560127, 485518890, 383135490, 638996170, 740313422, 974946598, 950099865, 892846570, 49348923, 53699490, 968656272, 460133574, 778901130, 82771643, 11614359, 545829667, 744422054, 1140005, 182397048, 650783978, 978194090, 785975979, 442134527, 918364826, 587096095, 552015395, 394720680, 596677113, 343284061], [697712567, 662822590, 786815734, 698977195, 958047250, 264479879, 171266671, 161025591, 855621628, 914000715, 709048754, 850593747, 183804995, 270946938, 229155360, 636978642, 549414812, 151179786, 19734462, 4798215, 91724148, 36081129, 492532359, 734837730, 667825739, 846548, 20235857, 460515730, 348926942, 514935227, 68300844, 36581210, 326369023, 121862214, 55007590, 432079954, 30125905, 909055771, 948729172, 993741931, 36533353, 424873979, 308793064, 500055632, 655026165, 738034235, 234573950, 240437214, 395979134, 942618339, 830228784, 826458210], [758435178, 771288250, 388740030, 906627520, 895125003, 764287120, 706187504, 515075958, 209230821, 283648454, 791914315, 124133760, 961285683, 929084294, 543935361, 570106092, 185201107, 287807693, 434145103, 11071996, 984071114, 977180505, 207862169, 383483093, 30117232, 144656162, 946732442, 16067459, 900862330, 757753465, 229079906, 16132151, 333314808, 333265392, 387897304, 532175917, 695711167, 901839195, 66599198, 792932476, 518390237, 770922830, 761385209, 189493709, 777556985, 486433505, 979051338, 103572731, 879141059, 689335396, 788370421, 728346934], [703197063, 398522196, 529674934, 586031447, 589629137, 799715370, 367951265, 201082632, 751978864, 990329482, 380568832, 97875395, 825277651, 298779181, 585413367, 290653745, 307835142, 210888123, 555578981, 842680548, 496391547, 300084142, 254329724, 387744632, 167220889, 973859249, 432826443, 596436687, 327356876, 375758745, 59972924, 168552937, 603499615, 411816661, 92040171, 431502797, 199813780, 61041472, 106198020, 911482696, 657541306, 824411402, 2197297, 127042168, 82248640, 1316086, 411276330, 147327090, 50262843, 522991988, 464921464, 337250106], [213731549, 190549251, 274952704, 161263646, 588184190, 863451123, 793926580, 952248578, 409567428, 554727620, 755341894, 750273345, 918050568, 980042967, 452645962, 253351039, 614331169, 379368211, 825268530, 90077696, 796450190, 240115332, 888138640, 553583180, 914347020, 204478395, 34508118, 7418709, 291769478, 677239415, 265053199, 717772032, 107848376, 533014422, 510600400, 283592290, 834580486, 705163060, 844332208, 64555529, 207456786, 811005501, 312438887, 511540442, 258866001, 690648351, 275445515, 128414888, 769351845, 796736990, 615664119, 522347057], [828377144, 208876549, 302210308, 55616512, 441068961, 354384488, 663194241, 49484919, 922245254, 297459762, 864870369, 9799309, 54243849, 512349080, 981829701, 600538854, 381579507, 308680188, 249073421, 92346454, 310388257, 969692679, 270864599, 925126126, 205364942, 298762551, 947244097, 20346600, 134485903, 256068575, 602939738, 78476541, 465715795, 793020429, 415233057, 297867883, 19819993, 572430813, 608656608, 186830265, 156391811, 259758540, 616368064, 48626327, 585846828, 344805272, 172308886, 296628936, 886489653, 936520838, 391880554, 657954140], [547605303, 632265828, 912494298, 427388701, 581556135, 784398370, 969720452, 357011739, 172490534, 890309723, 539848714, 216794252, 324870015, 389690720, 800806970, 69388404, 201591815, 917627205, 106145988, 447890857, 851273759, 15857320, 511083343, 590503649, 112236703, 481475608, 688454972, 903948165, 486506851, 402036548, 661093306, 715058537, 126183498, 105099739, 36535302, 468376961, 655740473, 592185849, 601029877, 841393393, 160343414, 193852084, 158942100, 809100960, 790094631, 250287380, 741768383, 703080165, 683885062, 174359315, 230376171, 974723316], [599655897, 245230203, 272987001, 438611010, 782067084, 678511305, 167580674, 607369678, 863595249, 582362573, 914283518, 698285346, 806180261, 735111256, 355397066, 934334925, 525309217, 896580643, 320610957, 433345009, 660957632, 475257771, 805940526, 241136063, 298776670, 395239074, 279351793, 598268836, 481992940, 561693051, 642529528, 337141205, 474435672, 369088716, 441503577, 864314440, 237764650, 193787307, 313241209, 504766016, 644533193, 316127496, 68726715, 91426797, 949279217, 844434599, 642256246, 484244173, 131326835, 323345957, 89313876, 363811383], [547282305, 631790237, 209371116, 457107078, 158168813, 957274509, 792027998, 824383987, 360971596, 178654604, 782434915, 737841337, 706287012, 289613594, 772957889, 775688114, 118252751, 975580319, 909910564, 446579707, 391165628, 261199167, 557391509, 281250016, 709431384, 685175770, 793311756, 854679522, 538542028, 891897119, 890716371, 691259961, 55248751, 99865802, 996030938, 166001992, 439821113, 843365243, 563981478, 681598168, 910633214, 605315753, 983184818, 935324387, 154059850, 442513536, 239565452, 884457599, 256439862, 718891833, 833968995, 142322018], [553749394, 157933777, 112645738, 6410872, 84914905, 296570458, 963986612, 672648461, 16079970, 165514532, 334200828, 260797023, 769079940, 383531989, 107519262, 531178698, 834286211, 264021125, 564839565, 765170035, 71784471, 933186855, 239673314, 243909345, 991245695, 185417129, 515992789, 164392433, 584288262, 8538716, 957057795, 45608161, 654494744, 757163719, 422323443, 710120480, 196519157, 745039862, 325712121, 81529656, 916104325, 277083421, 444908348, 88781558, 87749496, 436618383, 440724084, 784942032, 890535599, 499271290, 983605128, 827414337], [420094859, 384335397, 426892468, 422385332, 363364411, 92819867, 851678704, 750322663, 880097682, 699949558, 642066166, 952335817, 499338030, 991708067, 85110901, 51561610, 162540184, 812528438, 826608456, 505651282, 503497813, 704026500, 88284623, 207601412, 593691622, 558111338, 641272728, 805737333, 387482947, 170427463, 616345102, 896917162, 929972804, 593486552, 796853918, 246740863, 130304742, 467523500, 182195600, 849677767, 176746385, 141861929, 604027341, 916675224, 858736800, 182575635, 956718827, 130635141, 512392006, 351515453, 781490216, 433303928], [829079720, 695887598, 609988068, 120265922, 351215876, 961847731, 328751340, 885891277, 177016744, 110620728, 546237404, 382407244, 844661866, 475161973, 833620809, 697092413, 386654550, 397863170, 684461541, 828583911, 959666972, 351591563, 730335887, 246038882, 146218152, 645091972, 247392140, 414246923, 545069796, 193951937, 213683894, 129818437, 73165027, 439833705, 466338590, 394659684, 776902495, 727555172, 965616070, 707599770, 909089622, 400714506, 528812665, 321741255, 467241820, 823720235, 163857041, 876667644, 837118807, 757802844, 745754183, 658748158], [615171878, 108197588, 343493146, 460200993, 986865242, 344550337, 659026767, 722937170, 256252307, 54625780, 595435902, 723772172, 577690323, 442305100, 880513440, 680238301, 614821094, 202703746, 600342838, 921217180, 840966245, 831440830, 60618218, 508063394, 520132858, 635931016, 607163501, 896186397, 414107369, 870381373, 484382444, 299761290, 338050805, 217199759, 505374762, 987210416, 18895786, 610756788, 867362823, 436027139, 247650500, 767333120, 263716935, 20758830, 931431146, 378274787, 34044036, 294006198, 747111392, 783921840, 810020156, 451335769], [151608445, 558449053, 52428757, 360796135, 435388029, 188448483, 355628549, 356782937, 200049622, 531931422, 162873662, 551182839, 999600464, 128927358, 85066411, 917205419, 899427338, 681632174, 276656489, 840681294, 627269955, 394068453, 310219491, 259184441, 216545694, 9057400, 164352537, 157449722, 981185393, 493920255, 819219315, 918845860, 78573867, 771118322, 579291223, 559452937, 448671806, 383701304, 956576630, 808575730, 988716155, 532209763, 580582571, 73637971, 282841995, 133005572, 449428185, 97154391, 585711870, 656776976, 473548035, 344695702], [332380779, 127786975, 431481932, 438076981, 687492012, 7766857, 884588151, 58973818, 965232645, 372745012, 719626890, 253235061, 828657439, 432955767, 478643609, 312838643, 350107434, 885263505, 298165357, 243714376, 796438197, 492555494, 587123511, 751141068, 635393548, 389337022, 491834824, 796550990, 102546073, 724311819, 963505380, 145456861, 560974967, 419220972, 682918989, 405832730, 730920728, 47867027, 479144801, 272836107, 456437812, 834829862, 815931206, 605860186, 326069750, 272632575, 586588459, 829502901, 887709227, 632006011, 792396777, 497321651], [280015165, 15606471, 989634938, 646612232, 356260252, 922645728, 766577595, 487509362, 324158805, 688606085, 98187229, 576780265, 295762831, 942202921, 893683047, 441562158, 17367909, 494318998, 497446794, 971815150, 249031219, 822055915, 679023785, 982555106, 728772243, 136776055, 466663922, 127790410, 657355489, 699291040, 410366371, 492175406, 6892829, 578798330, 349088405, 808022758, 376362109, 948090174, 503131847, 981048194, 411701614, 580487556, 394387964, 687414240, 464881486, 842770583, 599789699, 637000797, 807404475, 708509842, 61628810, 917206800], [742835343, 628024335, 812418913, 2607327, 171077480, 621526211, 925482990, 345555057, 879982295, 198320594, 281226990, 92369258, 928304573, 542745699, 30192234, 625813493, 261861794, 71100449, 298678291, 856039927, 31847786, 148724118, 832166256, 400724673, 388797557, 610127364, 765949302, 660148712, 477976698, 986519381, 327317430, 489350566, 104395349, 161017988, 707607183, 998302125, 296457903, 748800086, 10760152, 160333163, 797321194, 302241842, 987573847, 254109576, 829511621, 204755165, 512471935, 510954602, 140779549, 379316033, 213423476, 991188275], [100794726, 923917129, 17729862, 836890516, 125375170, 643947524, 574903691, 694025215, 458043634, 855561526, 631282086, 429595394, 401612442, 985421961, 450430308, 251635242, 980887403, 520607162, 806798020, 620480451, 780406678, 764961407, 655803204, 317612129, 2934713, 19924482, 830715638, 309307169, 944692645, 615414876, 467239925, 904726823, 897779487, 619947845, 150577233, 972184462, 929601116, 831709791, 643482852, 803306705, 588747861, 27128790, 667815609, 400033662, 444476817, 906110779, 36713358, 404616818, 890850067, 399118266, 554631232, 641754838], [387572939, 786585937, 671418561, 439419122, 386639208, 831529147, 639833203, 346342584, 372334439, 804402989, 389657968, 895842716, 145129903, 897071997, 825332338, 115793743, 112701892, 34652092, 20640284, 377888509, 726859582, 432160678, 341839826, 297249216, 475936761, 92151881, 16605281, 832793590, 470555938, 149567806, 350691776, 214613953, 184126976, 773430425, 357792163, 350665100, 402708014, 405285098, 742499773, 368120124, 332220691, 4298808, 658929692, 342913255, 821627880, 156042005, 373521474, 374487673, 417843044, 229807853, 134673644, 691272429], [512729584, 577853142, 165539306, 452450562, 175413973, 794549977, 324673114, 367849751, 911443420, 333541133, 799601990, 986658189, 776335771, 605996847, 263057292, 517173832, 152526038, 456709493, 476641022, 747352700, 175171060, 674705328, 893417217, 778601285, 390247107, 706947489, 398937281, 681540878, 789155810, 405069599, 219662431, 21293526, 16676401, 93567698, 217797340, 262116250, 121449553, 647988133, 893108346, 299880775, 953148258, 326562709, 950665006, 880678914, 612489112, 975797262, 869138453, 751024414, 813927650, 424246303, 737651007, 759396545], [723900700, 127720337, 404009941, 139083402, 206749689, 649755795, 600140279, 456140553, 485467797, 61990734, 454111139, 859121457, 987709903, 375068306, 561772373, 39292831, 982235975, 954568036, 605166405, 565546282, 225910651, 189410931, 984508079, 525866415, 824227064, 831736840, 772663240, 248887286, 907409006, 787863728, 154924102, 289128527, 739081407, 324777637, 585917873, 109676371, 392853578, 917287962, 889772014, 268114974, 467278752, 522431398, 348541363, 605607561, 184587007, 107961117, 743503853, 552258201, 550906300, 756037744, 846229543, 451615785], [103080947, 282570055, 448369000, 822442766, 906241565, 90941491, 890532551, 277482880, 24813491, 699111338, 822002563, 4912856, 992714668, 50208800, 772589989, 966364118, 362789714, 297524218, 209252834, 104869537, 932448109, 707430027, 510697204, 895053714, 90338051, 750310735, 421710704, 69994281, 768292398, 818327478, 367118049, 795550284, 825215653, 719342318, 201903195, 332082463, 384839902, 731660371, 18816522, 700098121, 192578080, 407700682, 655971751, 489607456, 742038712, 416600636, 761397525, 145313765, 500815559, 74251431, 197775035, 428547271], [217781609, 573883486, 96448195, 348290938, 474525550, 364566358, 217813973, 473267689, 782028708, 504158346, 567044406, 695672581, 662938501, 904240917, 119492563, 809539293, 527674176, 92638948, 875919893, 567966874, 835929625, 958096128, 166399193, 49855919, 476260091, 526166842, 535713661, 473849025, 667126642, 146124324, 107602485, 851389697, 997524546, 347369242, 128209766, 258216260, 867903469, 33550366, 863991052, 980775877, 631199338, 688342207, 498201778, 891132221, 989284088, 622195155, 886072570, 132268353, 112055655, 638568246, 716354434, 136679916]])," 895928341175 (maximumScore [[310076548, 764126805, 485388059, 987528751, 437560592, 997825191, 515523887, 62578341, 251436316, 763663045, 352002813, 589371022, 838236324, 662659028, 805162197, 826595352, 806582107, 329585108, 158109325, 652056160, 545600678, 259713482, 713354123, 458595692, 986027609, 785628709, 261185623, 719256557, 588289241, 750163159, 846538612, 292027067, 966840310, 968455810, 21481500, 485050387, 82734919, 66493717, 673437962, 287363129, 342834119, 412567189, 267404789, 286243776, 688609100, 328747644, 427755667, 985607240, 776976506, 707058481, 789417999, 805337232], [249844905, 422872898, 703456496, 882110397, 589476351, 500269527, 266150671, 837539771, 320295046, 960332496, 202699874, 107446805, 654090267, 970732445, 49411055, 277348427, 814808576, 390231757, 348559104, 574396436, 67676854, 423911769, 749321123, 796902455, 200917110, 305720994, 66658236, 277656039, 997538477, 116475385, 915849527, 378458971, 468354504, 296294579, 417427016, 47496, 223315310, 499136059, 507551056, 622937208, 17212718, 228111996, 70551858, 273705530, 10191643, 978069796, 755197423, 648159910, 356548942, 936085274, 625197622, 832242364], [463542462, 587108158, 138360853, 53931199, 906890500, 592332229, 657781873, 764015389, 590556, 190988231, 425668346, 241620526, 543586434, 362267881, 961880340, 637906303, 509876468, 903994285, 692551413, 659045556, 344468807, 844154580, 236288361, 31994947, 761699573, 767957245, 591585619, 651982732, 348168937, 612082749, 989606214, 639541290, 955931493, 524897499, 122826017, 120086501, 122279692, 264727946, 66275389, 542289201, 748397169, 729152621, 291385341, 817214343, 250607420, 103795479, 641704787, 647784848, 235340368, 811499095, 309778281, 681178265], [812267468, 93670665, 938725740, 432342391, 840991079, 724392545, 325347128, 371979361, 531175701, 371810490, 624796159, 905549241, 854325619, 298213982, 38207019, 809414313, 86960662, 936805820, 596017253, 13353804, 407143420, 363384666, 14010276, 732357492, 546999634, 406356622, 136220005, 421648448, 438994135, 308346287, 622187575, 814328155, 187689247, 254176607, 23724175, 686329010, 916135288, 884022352, 852160899, 516829783, 843948430, 205471754, 772917254, 646723672, 497672814, 261270878, 566050837, 178891368, 401144610, 879413398, 695752544, 100294478], [985593843, 19019148, 386742639, 287131008, 935830170, 267960783, 549129560, 79456352, 50602488, 60541012, 468685467, 931978553, 274324171, 634668627, 201785555, 39237271, 953002644, 393216262, 340099924, 626951236, 65561059, 392753104, 978639431, 889366656, 83119209, 188354067, 715269239, 445985517, 303869611, 61555882, 912542538, 133120934, 686362246, 965961756, 548455668, 34774094, 852512667, 73091004, 61682419, 289331955, 924173810, 800161179, 153612210, 148638249, 686624972, 273511504, 160379748, 777819228, 134000969, 373708223, 892031765, 866527358], [457454677, 653037344, 266375407, 845322328, 905033886, 320839936, 369891119, 397452015, 679437877, 491827644, 705565742, 502949402, 505136316, 231748414, 590112187, 486721588, 247399304, 161777707, 553121963, 742536612, 682238785, 398778225, 705000602, 439775525, 137910153, 997441139, 479094036, 297215884, 767389899, 189186835, 130467634, 453772502, 893296043, 115816030, 58067675, 340075223, 880660443, 676371411, 180476628, 22409276, 333621897, 532970053, 439603357, 365833480, 921539395, 562505640, 174625197, 653702209, 594487932, 457129315, 836789088, 37515390], [838461392, 900587260, 982728845, 430476770, 514440055, 644057843, 832999604, 850217247, 35213335, 370582527, 498648122, 13080883, 349771954, 155175165, 753852466, 506980429, 162661259, 554779600, 564439449, 229023057, 606621411, 699847406, 189363752, 841331262, 436679676, 251201219, 514029627, 256165581, 295579057, 269262552, 796005836, 425962695, 82213235, 188953841, 282103138, 417766519, 110229666, 906019474, 947476475, 910303455, 293733581, 146933042, 836935628, 596825008, 859524801, 334793575, 510409815, 12297254, 835840669, 204988326, 30498570, 688226921], [70925426, 736376634, 93052084, 534495366, 258925497, 425992174, 396231326, 30520032, 236950892, 658941413, 666987684, 166843410, 901684650, 402909635, 444666745, 763068248, 918245655, 872550802, 972056507, 284629859, 259767067, 762509783, 308332088, 211500650, 404501725, 954857817, 11298468, 330039345, 942757272, 39182635, 189626207, 770124777, 316487684, 787981335, 519932763, 104996189, 297958819, 653369130, 722659555, 459111482, 320544450, 842541904, 477084724, 843967589, 612695504, 756764864, 191292537, 303276509, 467638434, 871153317, 261195390, 220940389], [878297855, 556436901, 217041040, 961384835, 948122207, 389002401, 504161918, 628928513, 939212252, 669388922, 861195851, 359292178, 458107119, 75570901, 320219183, 956425033, 223963977, 342261675, 780862423, 586602788, 824753044, 700257776, 560029495, 512156121, 328676421, 17123992, 541598776, 824245345, 809246040, 349699414, 959063937, 380019100, 660168057, 826453249, 442279576, 11685932, 629400, 475681185, 57364798, 847907531, 251037668, 268540958, 870816824, 814579162, 922024244, 660959029, 61628108, 51462504, 343011781, 905483171, 701411977, 941533250], [29490754, 708669728, 577016828, 517063080, 947592345, 867514727, 996151169, 286667700, 103594489, 156406952, 254222225, 401545607, 886985752, 934819975, 510474958, 242151921, 755134119, 604968173, 906920476, 227144970, 53118028, 571185807, 533886326, 938405769, 527536714, 784571315, 60400677, 897559617, 645532245, 641718011, 97818622, 804581417, 277488146, 604079204, 173184510, 331594740, 240552141, 617526141, 445290650, 117084900, 49663532, 136335893, 185355521, 565922189, 553768232, 435312585, 728255937, 938871170, 226329689, 824869545, 527239209, 584109102], [295873314, 207691215, 606689754, 993932793, 32251143, 778381814, 62651905, 85027681, 125536461, 828847120, 740357913, 553768799, 425639950, 990245078, 115859652, 904702248, 579405295, 204295699, 981363010, 375149233, 82846341, 176599534, 626106236, 173357937, 793070857, 839851098, 676848060, 707585233, 567286819, 732008859, 921143325, 706394014, 529248046, 314291721, 908955997, 591397258, 178842726, 917150667, 342236059, 218123795, 701643273, 826359041, 639993820, 391407215, 3436873, 513827670, 106163762, 516278618, 749574640, 512664897, 525211363, 506136121], [890022914, 98923839, 998024834, 825594631, 867440512, 954060221, 133503633, 127057442, 614818034, 461789121, 155744265, 657209465, 402450742, 210991341, 181726931, 664855393, 588017747, 759815930, 352134331, 86093643, 739466699, 103960658, 434471019, 993899435, 140339442, 558005514, 708245270, 902368878, 344704883, 576132, 136166734, 608536624, 754572579, 478369988, 999988665, 600114971, 445357727, 319068755, 58952593, 826455090, 287471507, 163849289, 119245869, 256662159, 629466502, 247592356, 535272131, 764294912, 526314402, 153260199, 579646626, 491175200], [907659743, 143608852, 533347077, 885492862, 547228200, 878173929, 470157762, 501095703, 837331634, 499770827, 883467090, 588690242, 627064815, 130691706, 725211125, 701672623, 53326323, 430055003, 199678975, 854778075, 149519813, 348955533, 592688486, 220613194, 573302602, 967918845, 454531183, 476036594, 760858957, 698495708, 779966664, 380573973, 762001677, 926314258, 790437870, 621759934, 93920318, 225417413, 220457864, 911845737, 277457925, 263957832, 893571653, 774712038, 184855857, 934376519, 664932435, 480981100, 582949523, 581287960, 957655463, 951195620], [71185398, 751495286, 308908619, 18081414, 417921709, 579821236, 954556674, 865006284, 990833865, 351927737, 131519949, 910138727, 552071606, 740553949, 824892954, 263351956, 987464175, 70182944, 121051038, 179732419, 795566078, 228182766, 529348044, 361362709, 914097112, 819189435, 602613406, 72394080, 875131228, 280701101, 362343453, 609043152, 623752839, 694755087, 761736050, 208752167, 96313604, 790653653, 810513011, 10198216, 523603783, 755680241, 233347630, 293889067, 706851870, 918740640, 62742159, 161663310, 732465242, 208014007, 958823876, 592624149], [65618935, 675005634, 723815559, 16997909, 381463610, 996396507, 274073620, 693770012, 825818935, 363601847, 807825302, 370259367, 851238061, 159348271, 169283472, 337975031, 495410300, 863287726, 76158588, 465197909, 523725766, 366344396, 296280954, 315735924, 302008225, 852357876, 701212338, 358620562, 837987271, 281490667, 755583126, 158365218, 211411030, 429336293, 951971763, 548087459, 931444156, 884154066, 531938721, 51396317, 671950886, 733937038, 810806422, 195313485, 93504195, 279134208, 866167317, 507789709, 657994522, 250302350, 504552373, 457297907], [402772773, 790799819, 925366321, 957837961, 227285725, 655305220, 307512187, 896989088, 868283414, 445461471, 371011167, 147523683, 499202047, 675996660, 397750579, 414570442, 471592905, 17297380, 17062994, 928877330, 841712653, 25178278, 396272481, 270777383, 267172216, 114615456, 920185362, 4229789, 413563464, 944690766, 560565398, 249770528, 1063196, 19007354, 411461738, 800353417, 478090135, 242922376, 359047971, 242879243, 676124091, 264040202, 559424540, 235561916, 804046772, 726163439, 927274240, 879624326, 305111630, 887023100, 780877681, 27033341], [102356513, 993598859, 840630617, 461534456, 202464707, 795280084, 394651269, 281562803, 136057185, 241706276, 848096339, 477949310, 29460405, 232651320, 987793393, 433782803, 688387106, 697279719, 364571194, 74666579, 496990201, 905563193, 741261085, 739481372, 431553866, 293880313, 686100649, 349139875, 968529791, 602849308, 91556886, 894826183, 512036094, 536804221, 372670986, 897288975, 56176788, 456148635, 46273345, 592414045, 618411068, 815570848, 387529319, 143085926, 342407639, 510796676, 432532561, 537769125, 160714077, 39080734, 402275797, 921250019], [794538259, 667639197, 501613458, 510021308, 547864017, 2985219, 79928085, 514156233, 155150733, 462427810, 755015797, 185348814, 683311675, 888919262, 466931994, 784359559, 197279270, 890848287, 464420293, 835805848, 708853755, 297899503, 842113401, 674854981, 556336099, 485329638, 816616466, 867764882, 608775987, 663806260, 355976908, 655116687, 993217237, 238364358, 217897863, 332608903, 803940381, 331436819, 743853278, 240577151, 816090280, 779342635, 661042821, 218681463, 934327603, 293937318, 181937500, 179066385, 741848761, 272156929, 851556910, 388846192], [599240084, 48559203, 20452351, 960631459, 448710721, 433601833, 238129977, 963059529, 412646209, 713060434, 762392494, 909507356, 971011779, 216965449, 826237915, 755211829, 768018229, 662643928, 679592696, 928897037, 220767371, 669585258, 40847345, 559900801, 820851105, 633479429, 66960261, 931353191, 620763499, 996431668, 527380062, 423490293, 942439267, 225579592, 93195462, 960784241, 47114666, 353613077, 696382291, 730896119, 726677435, 478630552, 585653158, 235321358, 782083791, 278605268, 238675577, 109303051, 689824010, 330219292, 711973103, 985982556], [80864647, 632354637, 661102044, 43860041, 775941063, 580865340, 195956769, 200993194, 346580249, 879281512, 902016981, 496030641, 682304333, 977846430, 257513904, 298564206, 680075463, 19190514, 434766619, 912150469, 313271458, 753661208, 287274945, 642505871, 148684477, 35781323, 152731180, 452263213, 238212188, 475026402, 920711473, 995116863, 787813024, 572948528, 538676602, 850513643, 194229391, 43696039, 39762957, 441505475, 80872655, 154739586, 387153286, 123391520, 470058710, 939370443, 667910282, 919141273, 696715911, 943970122, 773086987, 923920370], [481317920, 768267657, 151675053, 178465925, 231339522, 762567665, 281528374, 884063712, 675039138, 724470218, 634379250, 584310567, 234872175, 805238901, 676466122, 558960375, 860762486, 865058812, 225173971, 787432955, 77985600, 645431712, 266679345, 393306089, 212975766, 111485511, 904089388, 530288296, 115175331, 484474337, 434634511, 973237386, 237590990, 565068461, 986930287, 486223084, 831954895, 474833222, 883265257, 695700, 150158234, 818776084, 328036482, 549476380, 838346006, 774501127, 145667377, 306165237, 137817641, 372583520, 419811019, 534001253], [650411145, 332894867, 17929945, 755895930, 498330859, 92675917, 871659300, 511740994, 691809708, 64019421, 531041760, 131959052, 507470126, 183958277, 540963698, 438586288, 24908971, 839278303, 395560925, 215660676, 571364195, 235966507, 116918765, 572975884, 386502594, 797346207, 30949516, 36362525, 830540720, 694498038, 552616683, 98548145, 551992073, 444363399, 125467987, 943660500, 872536416, 450584342, 716380532, 288230350, 715500932, 182749100, 715215359, 258435398, 186096418, 676189277, 361369945, 168870260, 671118092, 363548942, 789441766, 836666947], [825451250, 414772520, 196191999, 142916044, 278540815, 533165146, 527066786, 242293066, 269429082, 25941238, 672344307, 250274837, 799194674, 306108843, 141110847, 540828277, 695450111, 287034172, 441220808, 588448149, 236952079, 291385797, 887300856, 536037694, 198519241, 254351571, 155302494, 726773475, 774802134, 86970565, 296530701, 719277521, 477298192, 839609165, 583594077, 616941870, 521220368, 644973825, 56909524, 107203503, 132713720, 50346038, 836930740, 829619153, 633492857, 910303694, 486842974, 78828240, 90991608, 725979499, 676347979, 791940749], [993743115, 561010481, 563895133, 770064016, 918783235, 54756788, 833762465, 449099159, 292564153, 296743667, 587713587, 946965021, 485590061, 495498026, 253288573, 849956678, 780888558, 389653831, 892758062, 989737775, 496956051, 532067604, 918633671, 833457223, 76343350, 820941784, 833530358, 553012948, 946475597, 677541238, 459842620, 961167561, 765899066, 7309020, 441817763, 931240052, 980206975, 391572467, 112991140, 953281120, 415533331, 193706123, 762670675, 931833906, 128691542, 271152636, 241474412, 839095021, 630982341, 510365217, 63096602, 439890026], [559443219, 978130807, 685399667, 777008923, 841986302, 602994986, 155116048, 7252236, 921294114, 776254540, 924307404, 774432268, 62354403, 737598299, 107302292, 25147323, 502939525, 522236698, 636808262, 678993871, 7634494, 605308595, 251118893, 619311700, 914978421, 411605558, 41634160, 500215248, 417096718, 858829699, 505946542, 587621425, 896438664, 213714294, 848029140, 970665718, 669485337, 103262422, 815678732, 673184557, 558586884, 907212058, 751366850, 755565507, 471810834, 730655813, 372850682, 625653324, 994108723, 939221252, 374605507, 183162938], [209514501, 377697278, 131621819, 94536453, 459000571, 314935732, 380375622, 286169802, 904290459, 305418409, 492601403, 268775682, 759818002, 483191721, 67243675, 733583350, 165498722, 375216058, 203500628, 74319608, 281836296, 666098085, 521220841, 184198736, 906278553, 724580270, 905019907, 950750723, 65153851, 92522483, 99431660, 103203360, 752616207, 49943810, 147621524, 915678733, 818920537, 142894412, 6472898, 786779367, 45284956, 371365984, 248816649, 402861785, 91747389, 32226549, 750181600, 396372714, 457518155, 694695325, 603002265, 229520576], [38498169, 271441462, 220993231, 70281196, 833347238, 396186800, 124322911, 228447378, 839466874, 926557255, 14822465, 76276903, 178984699, 895474205, 498348213, 466518900, 292210127, 686327450, 702537160, 935337170, 879292531, 221025258, 238519686, 227080473, 651043333, 860579762, 280209232, 384078953, 790524548, 626100611, 701987365, 3193915, 162794358, 325401076, 380314329, 891648797, 630724476, 457342765, 994736940, 281063860, 237466803, 609091740, 234569117, 590603511, 523022291, 132358105, 645514416, 346666578, 434663119, 135696211, 642016348, 726973030], [324713057, 580825434, 447284710, 318156215, 358932874, 695817626, 332337093, 262443454, 463585124, 69380541, 530578564, 690723630, 623307617, 868932739, 106650989, 614103989, 153760269, 397735167, 924142994, 321057101, 667994777, 501388043, 691256339, 604579305, 805867172, 987961173, 105708277, 217862750, 264847027, 228251910, 650465518, 218406166, 931663231, 885931541, 932498548, 690728991, 95010854, 930134249, 354733432, 203626557, 915798369, 855446693, 664031006, 534747681, 742636104, 453954655, 992597908, 628289261, 375379136, 718906403, 805057853, 617728903], [78393288, 689120379, 95840243, 113383796, 274523905, 255318487, 844938633, 475359560, 742535669, 38758788, 760304151, 408345572, 946524031, 778098799, 212746968, 100102898, 258635979, 483271757, 329270313, 177149039, 804318164, 353471949, 243551605, 518561761, 879205386, 884800870, 257874928, 736080249, 711997660, 615402210, 735933593, 236415384, 729957520, 327424210, 85244504, 31918769, 15706512, 41543636, 906823511, 463949604, 465404789, 287387268, 704865068, 27672661, 254151812, 372561159, 871031305, 748011677, 674685667, 146685721, 516497915, 216342886], [734214941, 508092566, 983829638, 434666945, 223308949, 879324264, 986231486, 679918219, 617588827, 719795180, 21253741, 365740428, 878297549, 952301794, 547925030, 730409738, 650271277, 837769673, 287348243, 202335907, 214083926, 776562291, 336071635, 706560127, 485518890, 383135490, 638996170, 740313422, 974946598, 950099865, 892846570, 49348923, 53699490, 968656272, 460133574, 778901130, 82771643, 11614359, 545829667, 744422054, 1140005, 182397048, 650783978, 978194090, 785975979, 442134527, 918364826, 587096095, 552015395, 394720680, 596677113, 343284061], [697712567, 662822590, 786815734, 698977195, 958047250, 264479879, 171266671, 161025591, 855621628, 914000715, 709048754, 850593747, 183804995, 270946938, 229155360, 636978642, 549414812, 151179786, 19734462, 4798215, 91724148, 36081129, 492532359, 734837730, 667825739, 846548, 20235857, 460515730, 348926942, 514935227, 68300844, 36581210, 326369023, 121862214, 55007590, 432079954, 30125905, 909055771, 948729172, 993741931, 36533353, 424873979, 308793064, 500055632, 655026165, 738034235, 234573950, 240437214, 395979134, 942618339, 830228784, 826458210], [758435178, 771288250, 388740030, 906627520, 895125003, 764287120, 706187504, 515075958, 209230821, 283648454, 791914315, 124133760, 961285683, 929084294, 543935361, 570106092, 185201107, 287807693, 434145103, 11071996, 984071114, 977180505, 207862169, 383483093, 30117232, 144656162, 946732442, 16067459, 900862330, 757753465, 229079906, 16132151, 333314808, 333265392, 387897304, 532175917, 695711167, 901839195, 66599198, 792932476, 518390237, 770922830, 761385209, 189493709, 777556985, 486433505, 979051338, 103572731, 879141059, 689335396, 788370421, 728346934], [703197063, 398522196, 529674934, 586031447, 589629137, 799715370, 367951265, 201082632, 751978864, 990329482, 380568832, 97875395, 825277651, 298779181, 585413367, 290653745, 307835142, 210888123, 555578981, 842680548, 496391547, 300084142, 254329724, 387744632, 167220889, 973859249, 432826443, 596436687, 327356876, 375758745, 59972924, 168552937, 603499615, 411816661, 92040171, 431502797, 199813780, 61041472, 106198020, 911482696, 657541306, 824411402, 2197297, 127042168, 82248640, 1316086, 411276330, 147327090, 50262843, 522991988, 464921464, 337250106], [213731549, 190549251, 274952704, 161263646, 588184190, 863451123, 793926580, 952248578, 409567428, 554727620, 755341894, 750273345, 918050568, 980042967, 452645962, 253351039, 614331169, 379368211, 825268530, 90077696, 796450190, 240115332, 888138640, 553583180, 914347020, 204478395, 34508118, 7418709, 291769478, 677239415, 265053199, 717772032, 107848376, 533014422, 510600400, 283592290, 834580486, 705163060, 844332208, 64555529, 207456786, 811005501, 312438887, 511540442, 258866001, 690648351, 275445515, 128414888, 769351845, 796736990, 615664119, 522347057], [828377144, 208876549, 302210308, 55616512, 441068961, 354384488, 663194241, 49484919, 922245254, 297459762, 864870369, 9799309, 54243849, 512349080, 981829701, 600538854, 381579507, 308680188, 249073421, 92346454, 310388257, 969692679, 270864599, 925126126, 205364942, 298762551, 947244097, 20346600, 134485903, 256068575, 602939738, 78476541, 465715795, 793020429, 415233057, 297867883, 19819993, 572430813, 608656608, 186830265, 156391811, 259758540, 616368064, 48626327, 585846828, 344805272, 172308886, 296628936, 886489653, 936520838, 391880554, 657954140], [547605303, 632265828, 912494298, 427388701, 581556135, 784398370, 969720452, 357011739, 172490534, 890309723, 539848714, 216794252, 324870015, 389690720, 800806970, 69388404, 201591815, 917627205, 106145988, 447890857, 851273759, 15857320, 511083343, 590503649, 112236703, 481475608, 688454972, 903948165, 486506851, 402036548, 661093306, 715058537, 126183498, 105099739, 36535302, 468376961, 655740473, 592185849, 601029877, 841393393, 160343414, 193852084, 158942100, 809100960, 790094631, 250287380, 741768383, 703080165, 683885062, 174359315, 230376171, 974723316], [599655897, 245230203, 272987001, 438611010, 782067084, 678511305, 167580674, 607369678, 863595249, 582362573, 914283518, 698285346, 806180261, 735111256, 355397066, 934334925, 525309217, 896580643, 320610957, 433345009, 660957632, 475257771, 805940526, 241136063, 298776670, 395239074, 279351793, 598268836, 481992940, 561693051, 642529528, 337141205, 474435672, 369088716, 441503577, 864314440, 237764650, 193787307, 313241209, 504766016, 644533193, 316127496, 68726715, 91426797, 949279217, 844434599, 642256246, 484244173, 131326835, 323345957, 89313876, 363811383], [547282305, 631790237, 209371116, 457107078, 158168813, 957274509, 792027998, 824383987, 360971596, 178654604, 782434915, 737841337, 706287012, 289613594, 772957889, 775688114, 118252751, 975580319, 909910564, 446579707, 391165628, 261199167, 557391509, 281250016, 709431384, 685175770, 793311756, 854679522, 538542028, 891897119, 890716371, 691259961, 55248751, 99865802, 996030938, 166001992, 439821113, 843365243, 563981478, 681598168, 910633214, 605315753, 983184818, 935324387, 154059850, 442513536, 239565452, 884457599, 256439862, 718891833, 833968995, 142322018], [553749394, 157933777, 112645738, 6410872, 84914905, 296570458, 963986612, 672648461, 16079970, 165514532, 334200828, 260797023, 769079940, 383531989, 107519262, 531178698, 834286211, 264021125, 564839565, 765170035, 71784471, 933186855, 239673314, 243909345, 991245695, 185417129, 515992789, 164392433, 584288262, 8538716, 957057795, 45608161, 654494744, 757163719, 422323443, 710120480, 196519157, 745039862, 325712121, 81529656, 916104325, 277083421, 444908348, 88781558, 87749496, 436618383, 440724084, 784942032, 890535599, 499271290, 983605128, 827414337], [420094859, 384335397, 426892468, 422385332, 363364411, 92819867, 851678704, 750322663, 880097682, 699949558, 642066166, 952335817, 499338030, 991708067, 85110901, 51561610, 162540184, 812528438, 826608456, 505651282, 503497813, 704026500, 88284623, 207601412, 593691622, 558111338, 641272728, 805737333, 387482947, 170427463, 616345102, 896917162, 929972804, 593486552, 796853918, 246740863, 130304742, 467523500, 182195600, 849677767, 176746385, 141861929, 604027341, 916675224, 858736800, 182575635, 956718827, 130635141, 512392006, 351515453, 781490216, 433303928], [829079720, 695887598, 609988068, 120265922, 351215876, 961847731, 328751340, 885891277, 177016744, 110620728, 546237404, 382407244, 844661866, 475161973, 833620809, 697092413, 386654550, 397863170, 684461541, 828583911, 959666972, 351591563, 730335887, 246038882, 146218152, 645091972, 247392140, 414246923, 545069796, 193951937, 213683894, 129818437, 73165027, 439833705, 466338590, 394659684, 776902495, 727555172, 965616070, 707599770, 909089622, 400714506, 528812665, 321741255, 467241820, 823720235, 163857041, 876667644, 837118807, 757802844, 745754183, 658748158], [615171878, 108197588, 343493146, 460200993, 986865242, 344550337, 659026767, 722937170, 256252307, 54625780, 595435902, 723772172, 577690323, 442305100, 880513440, 680238301, 614821094, 202703746, 600342838, 921217180, 840966245, 831440830, 60618218, 508063394, 520132858, 635931016, 607163501, 896186397, 414107369, 870381373, 484382444, 299761290, 338050805, 217199759, 505374762, 987210416, 18895786, 610756788, 867362823, 436027139, 247650500, 767333120, 263716935, 20758830, 931431146, 378274787, 34044036, 294006198, 747111392, 783921840, 810020156, 451335769], [151608445, 558449053, 52428757, 360796135, 435388029, 188448483, 355628549, 356782937, 200049622, 531931422, 162873662, 551182839, 999600464, 128927358, 85066411, 917205419, 899427338, 681632174, 276656489, 840681294, 627269955, 394068453, 310219491, 259184441, 216545694, 9057400, 164352537, 157449722, 981185393, 493920255, 819219315, 918845860, 78573867, 771118322, 579291223, 559452937, 448671806, 383701304, 956576630, 808575730, 988716155, 532209763, 580582571, 73637971, 282841995, 133005572, 449428185, 97154391, 585711870, 656776976, 473548035, 344695702], [332380779, 127786975, 431481932, 438076981, 687492012, 7766857, 884588151, 58973818, 965232645, 372745012, 719626890, 253235061, 828657439, 432955767, 478643609, 312838643, 350107434, 885263505, 298165357, 243714376, 796438197, 492555494, 587123511, 751141068, 635393548, 389337022, 491834824, 796550990, 102546073, 724311819, 963505380, 145456861, 560974967, 419220972, 682918989, 405832730, 730920728, 47867027, 479144801, 272836107, 456437812, 834829862, 815931206, 605860186, 326069750, 272632575, 586588459, 829502901, 887709227, 632006011, 792396777, 497321651], [280015165, 15606471, 989634938, 646612232, 356260252, 922645728, 766577595, 487509362, 324158805, 688606085, 98187229, 576780265, 295762831, 942202921, 893683047, 441562158, 17367909, 494318998, 497446794, 971815150, 249031219, 822055915, 679023785, 982555106, 728772243, 136776055, 466663922, 127790410, 657355489, 699291040, 410366371, 492175406, 6892829, 578798330, 349088405, 808022758, 376362109, 948090174, 503131847, 981048194, 411701614, 580487556, 394387964, 687414240, 464881486, 842770583, 599789699, 637000797, 807404475, 708509842, 61628810, 917206800], [742835343, 628024335, 812418913, 2607327, 171077480, 621526211, 925482990, 345555057, 879982295, 198320594, 281226990, 92369258, 928304573, 542745699, 30192234, 625813493, 261861794, 71100449, 298678291, 856039927, 31847786, 148724118, 832166256, 400724673, 388797557, 610127364, 765949302, 660148712, 477976698, 986519381, 327317430, 489350566, 104395349, 161017988, 707607183, 998302125, 296457903, 748800086, 10760152, 160333163, 797321194, 302241842, 987573847, 254109576, 829511621, 204755165, 512471935, 510954602, 140779549, 379316033, 213423476, 991188275], [100794726, 923917129, 17729862, 836890516, 125375170, 643947524, 574903691, 694025215, 458043634, 855561526, 631282086, 429595394, 401612442, 985421961, 450430308, 251635242, 980887403, 520607162, 806798020, 620480451, 780406678, 764961407, 655803204, 317612129, 2934713, 19924482, 830715638, 309307169, 944692645, 615414876, 467239925, 904726823, 897779487, 619947845, 150577233, 972184462, 929601116, 831709791, 643482852, 803306705, 588747861, 27128790, 667815609, 400033662, 444476817, 906110779, 36713358, 404616818, 890850067, 399118266, 554631232, 641754838], [387572939, 786585937, 671418561, 439419122, 386639208, 831529147, 639833203, 346342584, 372334439, 804402989, 389657968, 895842716, 145129903, 897071997, 825332338, 115793743, 112701892, 34652092, 20640284, 377888509, 726859582, 432160678, 341839826, 297249216, 475936761, 92151881, 16605281, 832793590, 470555938, 149567806, 350691776, 214613953, 184126976, 773430425, 357792163, 350665100, 402708014, 405285098, 742499773, 368120124, 332220691, 4298808, 658929692, 342913255, 821627880, 156042005, 373521474, 374487673, 417843044, 229807853, 134673644, 691272429], [512729584, 577853142, 165539306, 452450562, 175413973, 794549977, 324673114, 367849751, 911443420, 333541133, 799601990, 986658189, 776335771, 605996847, 263057292, 517173832, 152526038, 456709493, 476641022, 747352700, 175171060, 674705328, 893417217, 778601285, 390247107, 706947489, 398937281, 681540878, 789155810, 405069599, 219662431, 21293526, 16676401, 93567698, 217797340, 262116250, 121449553, 647988133, 893108346, 299880775, 953148258, 326562709, 950665006, 880678914, 612489112, 975797262, 869138453, 751024414, 813927650, 424246303, 737651007, 759396545], [723900700, 127720337, 404009941, 139083402, 206749689, 649755795, 600140279, 456140553, 485467797, 61990734, 454111139, 859121457, 987709903, 375068306, 561772373, 39292831, 982235975, 954568036, 605166405, 565546282, 225910651, 189410931, 984508079, 525866415, 824227064, 831736840, 772663240, 248887286, 907409006, 787863728, 154924102, 289128527, 739081407, 324777637, 585917873, 109676371, 392853578, 917287962, 889772014, 268114974, 467278752, 522431398, 348541363, 605607561, 184587007, 107961117, 743503853, 552258201, 550906300, 756037744, 846229543, 451615785], [103080947, 282570055, 448369000, 822442766, 906241565, 90941491, 890532551, 277482880, 24813491, 699111338, 822002563, 4912856, 992714668, 50208800, 772589989, 966364118, 362789714, 297524218, 209252834, 104869537, 932448109, 707430027, 510697204, 895053714, 90338051, 750310735, 421710704, 69994281, 768292398, 818327478, 367118049, 795550284, 825215653, 719342318, 201903195, 332082463, 384839902, 731660371, 18816522, 700098121, 192578080, 407700682, 655971751, 489607456, 742038712, 416600636, 761397525, 145313765, 500815559, 74251431, 197775035, 428547271], [217781609, 573883486, 96448195, 348290938, 474525550, 364566358, 217813973, 473267689, 782028708, 504158346, 567044406, 695672581, 662938501, 904240917, 119492563, 809539293, 527674176, 92638948, 875919893, 567966874, 835929625, 958096128, 166399193, 49855919, 476260091, 526166842, 535713661, 473849025, 667126642, 146124324, 107602485, 851389697, 997524546, 347369242, 128209766, 258216260, 867903469, 33550366, 863991052, 980775877, 631199338, 688342207, 498201778, 891132221, 989284088, 622195155, 886072570, 132268353, 112055655, 638568246, 716354434, 136679916]])) + + +-- Grouping test cases +tests :: Test +tests = TestList [TestLabel "Test1" test1, TestLabel "Test2" test2, TestLabel "Test3" test3, TestLabel "Test4" test4, TestLabel "Test5" test5, TestLabel "Test6" test6] + +-- Running the tests +main :: IO Counts +main = runTestTT tests