project_euler_inputs.rb

@prob11_grid = [
       [8, 2, 22, 97, 38, 15, 00, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8],
       [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0],
       [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 03, 49, 13, 36, 65],
       [52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91],
       [22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80],
       [24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50],
       [32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70],
       [67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21],
       [24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72],
       [21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95],
       [78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 03, 80, 4, 62, 16, 14, 9, 53, 56, 92],
       [16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57],
       [86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58],
       [19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40],
       [4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66],
       [88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69],
       [4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36],
       [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16],
       [20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54],
       [1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48],
       ] 

@problem_13_numbers = [
       37107287533902102798797998220837590246510135740250,
       46376937677490009712648124896970078050417018260538,
       74324986199524741059474233309513058123726617309629,
       91942213363574161572522430563301811072406154908250,
       23067588207539346171171980310421047513778063246676,
       89261670696623633820136378418383684178734361726757,
       28112879812849979408065481931592621691275889832738,
       44274228917432520321923589422876796487670272189318,
       47451445736001306439091167216856844588711603153276,
       70386486105843025439939619828917593665686757934951,
       62176457141856560629502157223196586755079324193331,
       64906352462741904929101432445813822663347944758178,
       92575867718337217661963751590579239728245598838407,
       58203565325359399008402633568948830189458628227828,
       80181199384826282014278194139940567587151170094390,
       35398664372827112653829987240784473053190104293586,
       86515506006295864861532075273371959191420517255829,
       71693888707715466499115593487603532921714970056938,
       54370070576826684624621495650076471787294438377604,
       53282654108756828443191190634694037855217779295145,
       36123272525000296071075082563815656710885258350721,
       45876576172410976447339110607218265236877223636045,
       17423706905851860660448207621209813287860733969412,
       81142660418086830619328460811191061556940512689692,
       51934325451728388641918047049293215058642563049483,
       62467221648435076201727918039944693004732956340691,
       15732444386908125794514089057706229429197107928209,
       55037687525678773091862540744969844508330393682126,
       18336384825330154686196124348767681297534375946515,
       80386287592878490201521685554828717201219257766954,
       78182833757993103614740356856449095527097864797581,
       16726320100436897842553539920931837441497806860984,
       48403098129077791799088218795327364475675590848030,
       87086987551392711854517078544161852424320693150332,
       59959406895756536782107074926966537676326235447210,
       69793950679652694742597709739166693763042633987085,
       41052684708299085211399427365734116182760315001271,
       65378607361501080857009149939512557028198746004375,
       35829035317434717326932123578154982629742552737307,
       94953759765105305946966067683156574377167401875275,
       88902802571733229619176668713819931811048770190271,
       25267680276078003013678680992525463401061632866526,
       36270218540497705585629946580636237993140746255962,
       24074486908231174977792365466257246923322810917141,
       91430288197103288597806669760892938638285025333403,
       34413065578016127815921815005561868836468420090470,
       23053081172816430487623791969842487255036638784583,
       11487696932154902810424020138335124462181441773470,
       63783299490636259666498587618221225225512486764533,
       67720186971698544312419572409913959008952310058822,
       95548255300263520781532296796249481641953868218774,
       76085327132285723110424803456124867697064507995236,
       37774242535411291684276865538926205024910326572967,
       23701913275725675285653248258265463092207058596522,
       29798860272258331913126375147341994889534765745501,
       18495701454879288984856827726077713721403798879715,
       38298203783031473527721580348144513491373226651381,
       34829543829199918180278916522431027392251122869539,
       40957953066405232632538044100059654939159879593635,
       29746152185502371307642255121183693803580388584903,
       41698116222072977186158236678424689157993532961922,
       62467957194401269043877107275048102390895523597457,
       23189706772547915061505504953922979530901129967519,
       86188088225875314529584099251203829009407770775672,
       11306739708304724483816533873502340845647058077308,
       82959174767140363198008187129011875491310547126581,
       97623331044818386269515456334926366572897563400500,
       42846280183517070527831839425882145521227251250327,
       55121603546981200581762165212827652751691296897789,
       32238195734329339946437501907836945765883352399886,
       75506164965184775180738168837861091527357929701337,
       62177842752192623401942399639168044983993173312731,
       32924185707147349566916674687634660915035914677504,
       99518671430235219628894890102423325116913619626622,
       73267460800591547471830798392868535206946944540724,
       76841822524674417161514036427982273348055556214818,
       97142617910342598647204516893989422179826088076852,
       87783646182799346313767754307809363333018982642090,
       10848802521674670883215120185883543223812876952786,
       71329612474782464538636993009049310363619763878039,
       62184073572399794223406235393808339651327408011116,
       66627891981488087797941876876144230030984490851411,
       60661826293682836764744779239180335110989069790714,
       85786944089552990653640447425576083659976645795096,
       66024396409905389607120198219976047599490197230297,
       64913982680032973156037120041377903785566085089252,
       16730939319872750275468906903707539413042652315011,
       94809377245048795150954100921645863754710598436791,
       78639167021187492431995700641917969777599028300699,
       15368713711936614952811305876380278410754449733078,
       40789923115535562561142322423255033685442488917353,
       44889911501440648020369068063960672322193204149535,
       41503128880339536053299340368006977710650566631954,
       81234880673210146739058568557934581403627822703280,
       82616570773948327592232845941706525094512325230608,
       22918802058777319719839450180888072429661980811197,
       77158542502016545090413245809786882778948721859617,
       72107838435069186155435662884062257473692284509516,
       20849603980134001723930671666823555245252804609722,
       53503534226472524250874054075591789781264330331690]

@problem_18_triangle = [[75],
                        [95, 64],
                      [17, 47, 82],
                     [18, 35, 87, 10],
                   [20, 4, 82, 47, 65],
                  [19, 1, 23, 75, 3, 34],
                 [88, 2, 77, 73, 7, 63, 67],
               [99, 65, 4, 28, 6, 16, 70, 92],
            [41, 41, 26, 56, 83, 40, 80, 70, 33],
          [41, 48, 72, 33, 47, 32, 37, 16, 94, 29],
         [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14],
        [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57],
     [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48],
    [63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31],
  [04, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]]


@months = {
    'jan' => 31,
    'feb' => 28,
    'mar' => 31,
    'apr' => 30,
    'may' => 31,
    'jun' => 30,
    'july' => 31,
    'aug' => 31,
    'sept' => 30,
    'oct' => 31,
    'nov' => 30,
    'dec' => 31
  }

@letters = {
        'a' => 1,
        'b' => 2,
        'c' => 3,
        'd' => 4,
        'e' => 5,
        'f' => 6,
        'g' => 7,
        'h' => 8,
        'i' => 9,
        'j' => 10,
        'k' => 11,
        'l' => 12,
        'm' => 13,
        'n' => 14,
        'o' => 15,
        'p' => 16,
        'q' => 17,
        'r' => 18,
        's' => 19,
        't' => 20,
        'u' => 21,
        'v' => 22,
        'w' => 23,
        'x' => 24,
        'y' => 25,
        'z' => 26
          }

@factorials1_9 = {
  '1' => 1,
  '2' => 2,
  '3' => 6,
  '4' => 24,
  '5' => 120,
  '6' => 720,
  '7' => 5040,
  '8' => 40320,
  '9' => 352880,
  '0' => 1
}

@first_30_triangle_num = [1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465]

@card_map = {
  '1' => 1,
  '2' => 2,
  '3' => 3,
  '4' => 4,
  '5' => 5,
  '6' => 6,
  '7' => 7,
  '8' => 8,
  '9' => 9,
  'T' => 10,
  'J' => 11,
  'Q' => 12,
  'K' => 13,
  'A' => 14,
}

@suit_map = {
  'S' => 4,
  'H' => 3,
  'D' => 2,
  'C' => 1,
  }


@first_10000_pentagonal_numbers = {1=>1, 2=>5, 3=>12, 4=>22, 5=>35, 6=>51, 7=>70, 8=>92, 9=>117, 10=>145, 11=>176, 12=>210, 13=>247, 14=>287, 15=>330, 16=>376, 17=>425, 18=>477, 19=>532, 20=>590, 21=>651, 22=>715, 23=>782, 24=>852, 25=>925, 26=>1001, 27=>1080, 28=>1162, 29=>1247, 30=>1335, 31=>1426, 32=>1520, 33=>1617, 34=>1717, 35=>1820, 36=>1926, 37=>2035, 38=>2147, 39=>2262, 40=>2380, 41=>2501, 42=>2625, 43=>2752, 44=>2882, 45=>3015, 46=>3151, 47=>3290, 48=>3432, 49=>3577, 50=>3725, 51=>3876, 52=>4030, 53=>4187, 54=>4347, 55=>4510, 56=>4676, 57=>4845, 58=>5017, 59=>5192, 60=>5370, 61=>5551, 62=>5735, 63=>5922, 64=>6112, 65=>6305, 66=>6501, 67=>6700, 68=>6902, 69=>7107, 70=>7315, 71=>7526, 72=>7740, 73=>7957, 74=>8177, 75=>8400, 76=>8626, 77=>8855, 78=>9087, 79=>9322, 80=>9560, 81=>9801, 82=>10045, 83=>10292, 84=>10542, 85=>10795, 86=>11051, 87=>11310, 88=>11572, 89=>11837, 90=>12105, 91=>12376, 92=>12650, 93=>12927, 94=>13207, 95=>13490, 96=>13776, 97=>14065, 98=>14357, 99=>14652, 100=>14950, 101=>15251, 102=>15555, 103=>15862, 104=>16172, 105=>16485, 106=>16801, 107=>17120, 108=>17442, 109=>17767, 110=>18095, 111=>18426, 112=>18760, 113=>19097, 114=>19437, 115=>19780, 116=>20126, 117=>20475, 118=>20827, 119=>21182, 120=>21540, 121=>21901, 122=>22265, 123=>22632, 124=>23002, 125=>23375, 126=>23751, 127=>24130, 128=>24512, 129=>24897, 130=>25285, 131=>25676, 132=>26070, 133=>26467, 134=>26867, 135=>27270, 136=>27676, 137=>28085, 138=>28497, 139=>28912, 140=>29330, 141=>29751, 142=>30175, 143=>30602, 144=>31032, 145=>31465, 146=>31901, 147=>32340, 148=>32782, 149=>33227, 150=>33675, 151=>34126, 152=>34580, 153=>35037, 154=>35497, 155=>35960, 156=>36426, 157=>36895, 158=>37367, 159=>37842, 160=>38320, 161=>38801, 162=>39285, 163=>39772, 164=>40262, 165=>40755, 166=>41251, 167=>41750, 168=>42252, 169=>42757, 170=>43265, 171=>43776, 172=>44290, 173=>44807, 174=>45327, 175=>45850, 176=>46376, 177=>46905, 178=>47437, 179=>47972, 180=>48510, 181=>49051, 182=>49595, 183=>50142, 184=>50692, 185=>51245, 186=>51801, 187=>52360, 188=>52922, 189=>53487, 190=>54055, 191=>54626, 192=>55200, 193=>55777, 194=>56357, 195=>56940, 196=>57526, 197=>58115, 198=>58707, 199=>59302, 200=>59900, 201=>60501, 202=>61105, 203=>61712, 204=>62322, 205=>62935, 206=>63551, 207=>64170, 208=>64792, 209=>65417, 210=>66045, 211=>66676, 212=>67310, 213=>67947, 214=>68587, 215=>69230, 216=>69876, 217=>70525, 218=>71177, 219=>71832, 220=>72490, 221=>73151, 222=>73815, 223=>74482, 224=>75152, 225=>75825, 226=>76501, 227=>77180, 228=>77862, 229=>78547, 230=>79235, 231=>79926, 232=>80620, 233=>81317, 234=>82017, 235=>82720, 236=>83426, 237=>84135, 238=>84847, 239=>85562, 240=>86280, 241=>87001, 242=>87725, 243=>88452, 244=>89182, 245=>89915, 246=>90651, 247=>91390, 248=>92132, 249=>92877, 250=>93625, 251=>94376, 252=>95130, 253=>95887, 254=>96647, 255=>97410, 256=>98176, 257=>98945, 258=>99717, 259=>100492, 260=>101270, 261=>102051, 262=>102835, 263=>103622, 264=>104412, 265=>105205, 266=>106001, 267=>106800, 268=>107602, 269=>108407, 270=>109215, 271=>110026, 272=>110840, 273=>111657, 274=>112477, 275=>113300, 276=>114126, 277=>114955, 278=>115787, 279=>116622, 280=>117460, 281=>118301, 282=>119145, 283=>119992, 284=>120842, 285=>121695, 286=>122551, 287=>123410, 288=>124272, 289=>125137, 290=>126005, 291=>126876, 292=>127750, 293=>128627, 294=>129507, 295=>130390, 296=>131276, 297=>132165, 298=>133057, 299=>133952, 300=>134850, 301=>135751, 302=>136655, 303=>137562, 304=>138472, 305=>139385, 306=>140301, 307=>141220, 308=>142142, 309=>143067, 310=>143995, 311=>144926, 312=>145860, 313=>146797, 314=>147737, 315=>148680, 316=>149626, 317=>150575, 318=>151527, 319=>152482, 320=>153440, 321=>154401, 322=>155365, 323=>156332, 324=>157302, 325=>158275, 326=>159251, 327=>160230, 328=>161212, 329=>162197, 330=>163185, 331=>164176, 332=>165170, 333=>166167, 334=>167167, 335=>168170, 336=>169176, 337=>170185, 338=>171197, 339=>172212, 340=>173230, 341=>174251, 342=>175275, 343=>176302, 344=>177332, 345=>178365, 346=>179401, 347=>180440, 348=>181482, 349=>182527, 350=>183575, 351=>184626, 352=>185680, 353=>186737, 354=>187797, 355=>188860, 356=>189926, 357=>190995, 358=>192067, 359=>193142, 360=>194220, 361=>195301, 362=>196385, 363=>197472, 364=>198562, 365=>199655, 366=>200751, 367=>201850, 368=>202952, 369=>204057, 370=>205165, 371=>206276, 372=>207390, 373=>208507, 374=>209627, 375=>210750, 376=>211876, 377=>213005, 378=>214137, 379=>215272, 380=>216410, 381=>217551, 382=>218695, 383=>219842, 384=>220992, 385=>222145, 386=>223301, 387=>224460, 388=>225622, 389=>226787, 390=>227955, 391=>229126, 392=>230300, 393=>231477, 394=>232657, 395=>233840, 396=>235026, 397=>236215, 398=>237407, 399=>238602, 400=>239800, 401=>241001, 402=>242205, 403=>243412, 404=>244622, 405=>245835, 406=>247051, 407=>248270, 408=>249492, 409=>250717, 410=>251945, 411=>253176, 412=>254410, 413=>255647, 414=>256887, 415=>258130, 416=>259376, 417=>260625, 418=>261877, 419=>263132, 420=>264390, 421=>265651, 422=>266915, 423=>268182, 424=>269452, 425=>270725, 426=>272001, 427=>273280, 428=>274562, 429=>275847, 430=>277135, 431=>278426, 432=>279720, 433=>281017, 434=>282317, 435=>283620, 436=>284926, 437=>286235, 438=>287547, 439=>288862, 440=>290180, 441=>291501, 442=>292825, 443=>294152, 444=>295482, 445=>296815, 446=>298151, 447=>299490, 448=>300832, 449=>302177, 450=>303525, 451=>304876, 452=>306230, 453=>307587, 454=>308947, 455=>310310, 456=>311676, 457=>313045, 458=>314417, 459=>315792, 460=>317170, 461=>318551, 462=>319935, 463=>321322, 464=>322712, 465=>324105, 466=>325501, 467=>326900, 468=>328302, 469=>329707, 470=>331115, 471=>332526, 472=>333940, 473=>335357, 474=>336777, 475=>338200, 476=>339626, 477=>341055, 478=>342487, 479=>343922, 480=>345360, 481=>346801, 482=>348245, 483=>349692, 484=>351142, 485=>352595, 486=>354051, 487=>355510, 488=>356972, 489=>358437, 490=>359905, 491=>361376, 492=>362850, 493=>364327, 494=>365807, 495=>367290, 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@problem59_cypher = [79,59,12,2,79,35,8,28,20,2,3,68,8,9,68,45,0,12,9,67,68,4,7,5,23,27,1,21,79,85,78,79,85,71,38,10,71,27,12,2,79,6,2,8,13,9,1,13,9,8,68,19,7,1,71,56,11,21,11,68,6,3,22,2,14,0,30,79,1,31,6,23,19,10,0,73,79,44,2,79,19,6,28,68,16,6,16,15,79,35,8,11,72,71,14,10,3,79,12,2,79,19,6,28,68,32,0,0,73,79,86,71,39,1,71,24,5,20,79,13,9,79,16,15,10,68,5,10,3,14,1,10,14,1,3,71,24,13,19,7,68,32,0,0,73,79,87,71,39,1,71,12,22,2,14,16,2,11,68,2,25,1,21,22,16,15,6,10,0,79,16,15,10,22,2,79,13,20,65,68,41,0,16,15,6,10,0,79,1,31,6,23,19,28,68,19,7,5,19,79,12,2,79,0,14,11,10,64,27,68,10,14,15,2,65,68,83,79,40,14,9,1,71,6,16,20,10,8,1,79,19,6,28,68,14,1,68,15,6,9,75,79,5,9,11,68,19,7,13,20,79,8,14,9,1,71,8,13,17,10,23,71,3,13,0,7,16,71,27,11,71,10,18,2,29,29,8,1,1,73,79,81,71,59,12,2,79,8,14,8,12,19,79,23,15,6,10,2,28,68,19,7,22,8,26,3,15,79,16,15,10,68,3,14,22,12,1,1,20,28,72,71,14,10,3,79,16,15,10,68,3,14,22,12,1,1,20,28,68,4,14,10,71,1,1,17,10,22,71,10,28,19,6,10,0,26,13,20,7,68,14,27,74,71,89,68,32,0,0,71,28,1,9,27,68,45,0,12,9,79,16,15,10,68,37,14,20,19,6,23,19,79,83,71,27,11,71,27,1,11,3,68,2,25,1,21,22,11,9,10,68,6,13,11,18,27,68,19,7,1,71,3,13,0,7,16,71,28,11,71,27,12,6,27,68,2,25,1,21,22,11,9,10,68,10,6,3,15,27,68,5,10,8,14,10,18,2,79,6,2,12,5,18,28,1,71,0,2,71,7,13,20,79,16,2,28,16,14,2,11,9,22,74,71,87,68,45,0,12,9,79,12,14,2,23,2,3,2,71,24,5,20,79,10,8,27,68,19,7,1,71,3,13,0,7,16,92,79,12,2,79,19,6,28,68,8,1,8,30,79,5,71,24,13,19,1,1,20,28,68,19,0,68,19,7,1,71,3,13,0,7,16,73,79,93,71,59,12,2,79,11,9,10,68,16,7,11,71,6,23,71,27,12,2,79,16,21,26,1,71,3,13,0,7,16,75,79,19,15,0,68,0,6,18,2,28,68,11,6,3,15,27,68,19,0,68,2,25,1,21,22,11,9,10,72,71,24,5,20,79,3,8,6,10,0,79,16,8,79,7,8,2,1,71,6,10,19,0,68,19,7,1,71,24,11,21,3,0,73,79,85,87,79,38,18,27,68,6,3,16,15,0,17,0,7,68,19,7,1,71,24,11,21,3,0,71,24,5,20,79,9,6,11,1,71,27,12,21,0,17,0,7,68,15,6,9,75,79,16,15,10,68,16,0,22,11,11,68,3,6,0,9,72,16,71,29,1,4,0,3,9,6,30,2,79,12,14,2,68,16,7,1,9,79,12,2,79,7,6,2,1,73,79,85,86,79,33,17,10,10,71,6,10,71,7,13,20,79,11,16,1,68,11,14,10,3,79,5,9,11,68,6,2,11,9,8,68,15,6,23,71,0,19,9,79,20,2,0,20,11,10,72,71,7,1,71,24,5,20,79,10,8,27,68,6,12,7,2,31,16,2,11,74,71,94,86,71,45,17,19,79,16,8,79,5,11,3,68,16,7,11,71,13,1,11,6,1,17,10,0,71,7,13,10,79,5,9,11,68,6,12,7,2,31,16,2,11,68,15,6,9,75,79,12,2,79,3,6,25,1,71,27,12,2,79,22,14,8,12,19,79,16,8,79,6,2,12,11,10,10,68,4,7,13,11,11,22,2,1,68,8,9,68,32,0,0,73,79,85,84,79,48,15,10,29,71,14,22,2,79,22,2,13,11,21,1,69,71,59,12,14,28,68,14,28,68,9,0,16,71,14,68,23,7,29,20,6,7,6,3,68,5,6,22,19,7,68,21,10,23,18,3,16,14,1,3,71,9,22,8,2,68,15,26,9,6,1,68,23,14,23,20,6,11,9,79,11,21,79,20,11,14,10,75,79,16,15,6,23,71,29,1,5,6,22,19,7,68,4,0,9,2,28,68,1,29,11,10,79,35,8,11,74,86,91,68,52,0,68,19,7,1,71,56,11,21,11,68,5,10,7,6,2,1,71,7,17,10,14,10,71,14,10,3,79,8,14,25,1,3,79,12,2,29,1,71,0,10,71,10,5,21,27,12,71,14,9,8,1,3,71,26,23,73,79,44,2,79,19,6,28,68,1,26,8,11,79,11,1,79,17,9,9,5,14,3,13,9,8,68,11,0,18,2,79,5,9,11,68,1,14,13,19,7,2,18,3,10,2,28,23,73,79,37,9,11,68,16,10,68,15,14,18,2,79,23,2,10,10,71,7,13,20,79,3,11,0,22,30,67,68,19,7,1,71,8,8,8,29,29,71,0,2,71,27,12,2,79,11,9,3,29,71,60,11,9,79,11,1,79,16,15,10,68,33,14,16,15,10,22,73]


@problem81_matrix = [
                    [4445,2697,5115,718,2209,2212,654,4348,3079,6821,7668,3276,8874,4190,3785,2752,9473,7817,9137,496,7338,3434,7152,4355,4552,7917,7827,2460,2350,691,3514,5880,3145,7633,7199,3783,5066,7487,3285,1084,8985,760,872,8609,8051,1134,9536,5750,9716,9371,7619,5617,275,9721,2997,2698,1887,8825,6372,3014,2113,7122,7050,6775,5948,2758,1219,3539,348,7989,2735,9862,1263,8089,6401,9462,3168,2758,3748,5870],
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                    [9607,7385,521,6084,1364,8983,7623,1585,6935,8551,2574,8267,4781,3834,2764,2084,2669,4656,9343,7709,2203,9328,8004,6192,5856,3555,2260,5118,6504,1839,9227,1259,9451,1388,7909,5733,6968,8519,9973,1663,5315,7571,3035,4325,4283,2304,6438,3815,9213,9806,9536,196,5542,6907,2475,1159,5820,9075,9470,2179,9248,1828,4592,9167,3713,4640,47,3637,309,7344,6955,346,378,9044,8635,7466,5036,9515,6385,9230],
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                    [510,3556,5377,1406,5721,4946,2635,7847,4251,8293,8281,6351,4912,287,2870,3380,3948,5322,3840,4738,9563,1906,6298,3234,8959,1562,6297,8835,7861,239,6618,1322,2553,2213,5053,5446,4402,6500,5182,8585,6900,5756,9661,903,5186,7687,5998,7997,8081,8955,4835,6069,2621,1581,732,9564,1082,1853,5442,1342,520,1737,3703,5321,4793,2776,1508,1647,9101,2499,6891,4336,7012,3329,3212,1442,9993,3988,4930,7706],
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                    [3327,4030,7177,6336,9933,5296,2621,4785,2755,4832,2512,2118,2244,4407,2170,499,7532,9742,5051,7687,970,6924,3527,4694,5145,1306,2165,5940,2425,8910,3513,1909,6983,346,6377,4304,9330,7203,6605,3709,3346,970,369,9737,5811,4427,9939,3693,8436,5566,1977,3728,2399,3985,8303,2492,5366,9802,9193,7296,1033,5060,9144,2766,1151,7629,5169,5995,58,7619,7565,4208,1713,6279,3209,4908,9224,7409,1325,8540],
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                    [4420,1327,3560,2376,6260,2988,9537,4064,4829,8872,9598,3228,1792,7118,9962,9336,4368,9189,6857,1829,9863,6287,7303,7769,2707,8257,2391,2009,3975,4993,3068,9835,3427,341,8412,2134,4034,8511,6421,3041,9012,2983,7289,100,1355,7904,9186,6920,5856,2008,6545,8331,3655,5011,839,8041,9255,6524,3862,8788,62,7455,3513,5003,8413,3918,2076,7960,6108,3638,6999,3436,1441,4858,4181,1866,8731,7745,3744,1000],
                    [356,8296,8325,1058,1277,4743,3850,2388,6079,6462,2815,5620,8495,5378,75,4324,3441,9870,1113,165,1544,1179,2834,562,6176,2313,6836,8839,2986,9454,5199,6888,1927,5866,8760,320,1792,8296,7898,6121,7241,5886,5814,2815,8336,1576,4314,3109,2572,6011,2086,9061,9403,3947,5487,9731,7281,3159,1819,1334,3181,5844,5114,9898,4634,2531,4412,6430,4262,8482,4546,4555,6804,2607,9421,686,8649,8860,7794,6672],
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