TopCoder Statistics - Problem Statement

Problem Statement

Alice and Bob have n bags, each containing some, possibly zero, positive integers: ones, twos, threes, and fours. They play a game using these bags. Alice goes first, and then they alternate turns. In one turn, a player first selects exactly one of the bags. Then she or he removes some non-empty subset of numbers whose sum is divisible by four. Whoever is not able to make a move, loses.

The number of ones, twos, threes and fours in bag number i is a[i], b[i], c[i] and d[i], respectively. For each of the 2^n - 1 non-empty subsets of bags, consider the game played with only these bags. Determine how many of these games are won by Alice if they both play optimally.

Definition

Class:: BagsOfNumbers
Method:: wonByAlice
Parameters:: int, long[], long[], long[], long[]
Returns:: long
Method signature:: long wonByAlice(int n, long[] a, long[] b, long[] c, long[] d)
(be sure your method is public)

Constraints

n will be between 1 and 50, inclusive.
The arrays a, b, c and d will have exactly n elements each.
Each element of each array will be an integer between 0 and 1018, inclusive.

Examples

2

{13,13}

{12,12}

{25,25}

{9,9}

Returns: 2

When there is only single bag, Alice can win by removing all integers in it (their sum is 148, which is divisible by four). When playing with both bags, Bob can simply mirror Alice's moves to win.
4

{3,4,1,7}

{2,2,6,9}

{1,0,7,7}

{3,2,1,1}

Returns: 15

Regardless of the choice of bags, Alice always wins.
4

{0,18,15,16 }

{3,14,8,18 }

{9,12,16,12 }

{0,10,6,7 }

Returns: 14

When bags 0, 1, and 3 are selected, Bob can force win.
10

{3,0,0,1,44,3,27,26,0,41 }

{0,26,0,1,0,0,6,7,1,9 }

{0,9,1,0,5,0,4,5,0,1 }

{0,0,0,0,1,0,3,2,0,0 }

Returns: 512
10

{27,100,0,2,11,0,1,35,0,13 }

{62,18,0,0,55,1,0,79,1,70 }

{71,35,2,0,74,0,0,86,0,22 }

{96,36,0,0,42,0,0,9,0,46 }

Returns: 768
10

{21,37,1,6,2,93,68,84,46,62 }

{16,81,81,65,96,4,61,29,42,19 }

{95,2,79,36,31,51,99,12,8,64 }

{87,11,84,16,10,57,78,0,21,12 }

Returns: 992
50

{872865760834107033,1,0,798802229356192672,0,946282688240620357,1,3,514619014619574191,0,228365712072324239,1,1,500339636036377724,430135673190650954,783006609861771362,893278173359089191,2,0,2,2,451711673732667570,0,1,3,608538632384772498,537567593875597049,1,73796265108460951,619065288107964660,0,775929351079995601,503300488685099644,614941235686914698,0,2,2,192800332382154715,874930001897173925,2,0,6810472719715716,653601057320296882,0,3,3,3,3,627647239126683494,3 }

{887342822978919219,0,0,821802878138317037,0,420375194658141699,0,0,491465377157014038,0,767009909182405454,0,0,592795272450606720,889770587386565344,466113669291578233,315796989364434079,0,0,0,0,864280235374979982,1,1,0,641405947061272533,786171599477482401,1,959373851357659050,582721851561643611,1,771524446501955069,197981279042015366,358993112077002049,0,0,0,787076015670899719,399216216222855681,0,1,904243737850527399,763734230978198215,1,0,0,0,0,36904675259456667,0 }

{637219151449044450,0,1,500577243270502457,0,369361885323369250,0,0,298362140472523628,0,749492622233828832,0,0,762852173191028813,947442733040944754,918570813647382003,961981216324280770,0,0,0,0,4324638892336275,1,0,0,397726729352734234,912519878518288317,0,868579188232779937,812579328728886334,1,548571748348196188,562881689887588193,335455102186194837,3,0,0,421783088449712198,741861319957077709,0,0,785934456767207752,843543006264983763,0,0,0,0,0,523259445038548485,0 }

{393975111447701478,0,0,547742397871387654,0,809997643350718307,0,0,935618279144677896,0,791624932528568069,0,0,671411920182127327,529429594885964107,483822831278508045,465424897949867058,0,0,0,0,985465811442562094,0,0,0,762644648091091117,509385861957460117,0,781598405164100961,574972602688454299,0,542603954450347608,916590898225741719,948954135132595357,0,0,0,890193297497977238,559040728178941580,0,0,880063989075618759,450823666686903474,0,0,0,0,0,965968595542160613,0 }

Returns: 562949953421312
50

{416472535722643224,296212926521436323,59579047375959019,628544373724308582,417704238750609721,1,487679694963767686,982317738693887406,921384690204380217,533733082594785223,42666472738812692,395289856852251946,808850010025466277,194826695004456916,320495418080027450,199293091157784448,0,1,3,452112309618913335,278727658443537660,414758349128610297,671657973981789956,799114849748881291,585108252426392209,0,170843006538663124,128339190398485523,570938977938448308,3,928460634206584196,0,0,91096022565635043,0,0,232005079011123675,817068209362411947,2,218811966179687904,784869599546381098,0,664494203939463830,529249519296575754,303941460814671164,716131406626692576,87518269572739807,2,779938444487813302,163532720979609120 }

{28173709122910944,402348562684190118,58593165087612603,372006511012179256,650474692349588999,0,647735762869873400,53794051172059544,216099313405014006,362873153327326312,364719052733638309,43479305787711959,457284001964403130,860306635503208204,825508368174103218,719560728530901104,0,1,0,589574482353236415,360765084243051281,474004547396364054,11517781349589161,715424458147377048,14743262275533373,1,628363427471881053,743371766403603221,788577749447174052,0,284724791718295398,0,1,113591097599498024,1,0,194706652879792503,254985805760681089,0,294052178964087078,545062696176592536,0,153879946230482861,593537821653319438,856186199028087822,704306710251763950,569713830857557077,0,644183524084048561,109114604888823906 }

{350682049045781834,442951194383424951,864418317766058558,261278930235774105,590473876615106253,0,59282689408312319,829607975041287616,83657573667571867,677293377828874241,441984182072087929,14472022587020643,156063001021281320,538777489350701647,102425631815519123,37613047669197418,3,0,0,185115696376058900,336485260608174188,325809920465709654,161209774210159096,12685442723271687,445200425948879115,0,153321779939180479,94645948775440424,110301956836012431,0,49286065415568027,1,0,970539672099959366,1,1,428093214147515533,76564830903073526,0,76959075517974455,113083772456938697,1,319634631447411092,672725586984192281,769488290823097314,285352814776763991,730433680102577012,0,28148958523406721,295822249009869048 }

{177827148351770406,254412358144148926,661121193275329869,19945127014225707,2350138581649112,0,298234310741064605,56524199252152739,387345123468896508,200146907725649441,626351214353669419,657067998925993017,11141919373693935,77516421630555265,218786870504479652,121230250821428332,0,0,0,12391582764832343,85494072522000627,366157339463003233,264462958800361668,221479109419814853,71494659922198984,0,87159873303231393,313728990590174156,168734046137969039,0,147601570155753291,0,0,191291189879257924,0,0,572826201557502183,169860095229974384,0,529035745307731109,5482096310627494,0,76254175942557352,89319193747480470,102785372961798462,43283315108049353,255380095339199819,0,20855581571690413,307881268196637004 }

Returns: 844424930131968
50

{159433985310532367,505124862430648167,0,873065674186306534,685885126918360155,25211206751079129,800363918867078689,3,18820917535581907,865088170003905480,946908024996410495,862200442106622255,1,483996629424013523,0,776218465479437863,383013941268805541,159354460564013126,168623087800650079,105617050618708105,111916238622386314,698358544704860899,322692682321582965,165450852673343097,3,164836717079816359,667099318265341488,902623078026920971,336287657758900372,811674692509861014,796665554269072547,958493459307746264,625691051227125094,101570910242978823,22547928966672785,675186704690311998,170100930447553428,468077265498624422,668470020523244293,182300252382035272,235948510377993280,178227636003544828,616560892667943819,477127009088622233,792617601079695368,634982642814267627,368442409163998985,126476298139370010,116920565447942346,939283979674741981 }

{598622504010787224,555871508921790997,0,948011821920360213,130362788320281826,400718118256541719,356448071748111147,0,735021869412909112,882382981873400642,56674285485197386,617497322430958336,1,272330721214449230,1,304341890931350073,836529389320289015,10317461027431458,2545119198650023,696570866876120429,894882883316707343,820411827957139937,96502341686128335,3716729466307870,0,253355412872864297,392076551582680860,834049231395274968,284159502050183600,479685201400579287,96389185370184176,442970731563484935,256887130557795405,32587241188201191,66534948141827377,542269879492641231,323242068586506799,384993439418025045,108359302415022823,626317845308779457,953143690037695986,441652328444947,506351229296029110,442023700767200078,613237771375482225,366818348363933590,998206069494598117,33676845201527060,5797737428874655,15913522060801679 }

{904664522514871997,640708163055601150,2,103341924462210739,129604468286445373,100024681014500455,434831800540836834,0,255400669075716945,599225021883776304,328096855383901140,807606789505691550,0,218115199921922886,1,181037381258824931,554462017315646249,644519406636,1319703572529466,952183278162553758,829691706701706335,922714676414722058,822893735360040662,2020868084707092,0,270581209805888598,65485104779311680,769933513335263191,544782429739086567,466027914425437298,47997421404054210,377708094099904442,594552016592643578,21728690355651,6981864869142797,598068410487520860,545605053676335843,297535027128261760,888313705293201839,613695199453702282,195454108119880575,327479597979248,29612770975771101,135778798839636356,37636511614642010,71741731048704615,209446363808894336,230251467432240108,12745627094334180,688568077176270183 }

{535737084380665522,861944425451081261,0,411011183144261614,846933928893111427,936516321552471088,503421817798176340,0,99328566875626513,100978383944120292,6677406972871961,50786092126273014,0,760039038093006248,0,62801759223043535,336649301057016183,87443559771616,667163375160973,542316642851899479,985104731910903777,514247375887967015,711866567370367655,348543639025575,0,862839409299909841,105887263560339570,458770347293048052,14314255223658015,415578474147796341,234455150197098250,979516478027866402,948120526968701513,3382627931433564,944417639606621,790417943714323912,119207361454694304,12138050572831787,403179363074431317,604552771990287458,525711130091372467,61927740452487,88288781455670297,75686495717016268,11804687334050273,121853064330436969,432491546102706852,375546843939345671,3397042206872054,964702465380184795 }

Returns: 985162418487296
50

{703456052251052968,757222508583888850,368039513324378260,551315587181445077,769583962410723604,717230255266499366,156920478447541259,793248612624105660,499101252573777616,993483328678138924,42239765407087184,246500348622545937,958662346786403232,192588179771730680,64913990790212153,888599019406815466,312871832427373475,969391584042687967,901001625449897114,880403180344783309,109250512397032681,635339202115131707,259842532927642954,632646847356343974,467967199977950497,986801171985215603,889249274564463214,194052501699160999,337997099131165181,56453576339906304,277084496097038738,350813337881065263,694686328822263311,146350948435371464,590606840410780700,602151689711738505,41789441976324263,446397776016968067,421053496044754999,397363705436344722,120947721896236482,501048240810436425,292135564826082309,161744279628069549,138169104380016549,134429150744354474,65884384351663731,398012300718072423,3939212674712030,928593235247149669 }

{199459856233937516,528690158681279322,9782649059829555,746238662393736144,917532384858663981,935033185569277512,525846616188160229,190631996122594467,817324939293090418,808289188795778302,5853537847286943,144338781063404640,203505320868410565,216941045198220922,430619404867925559,442234026924171550,433783522841168093,374234110193558374,661762018780418225,2251187936430718,6927141563240948,3808929852019362,676374608902165348,553608550685243001,711655483455718084,162029340193230621,108943168659517060,802347449322332901,124878514960173298,625294158991604118,9762649733330948,973606132971399083,805535183271244894,888531996134731618,466449371883067183,992152865599050277,2541137643652287,286920405875249031,748498400842339562,437520494983822415,435499732918831,267650513027144043,24903600744241867,1882411324891730,665151625658465566,77343988528001568,935506557442014648,774169756861117700,508477674930289514,212272669203117408 }

{140806882970792396,71649111347479988,23990985418739151,507741128986690839,893363446470978810,100045301090916463,501958214298770743,904037782380161988,313312032463354731,338160540462628561,570744035673779,481706149996324961,694553768155105527,415047794957567832,326037438194232026,650721492292608225,502869078278604844,332808592802665638,955903023169286202,981105226218002431,3100192718486785,676803468176948679,432398028020402369,159983675430898088,60040777095290031,42871137098970476,529272530725297940,469246274936746191,974189060240079807,792854857094191783,3823372696082522,571650785772988259,94603167206720841,861436886782683212,839598778603816613,125715427219881751,20650635099984,994502825533396833,799271953465819755,164792114630038275,23762638971008966,307112081343798918,34938257681603212,772085060126038,425309064228141176,123759402002821,664244716390328317,825611458913881767,649037472616728060,552775023985552277 }

{383498012721913921,289020189523287240,3300359166199403,969876377133786618,602335426010914692,398662838144512,263591305283418476,880526743014243591,547184361981688677,890652814224265264,228174143167909,461906093618174319,570393148198803555,453787899995780593,488839912802880974,431736312707144484,785781294929624931,753655325736488383,117436215970436796,954926166084730640,10042682084550149,186734734321465243,721875489088474813,209743372374859158,251844401244033031,955737853202047270,716019047146907878,739785732505294649,803559853351909808,804844954489767012,11555341093340884,510984635835272843,74865246011366551,64956036788495664,975550940965460819,69560580520709944,2409525153106313,9390890626995472,906931335317469597,991031461622412696,40298659937552674,873622822516359978,1418913804989627,1187686139736102,773076261947913850,2095788513314578,81469370047403017,969633483168450479,350241910662486426,16828614385336891 }

Returns: 1090715534753792
50

{880088196615810288,61524286466716975,325882714778886605,503417612196608599,44835555254155611,187271202436676768,65203269509660367,910939715221101950,95328034936352785,722835809325462544,353867051106768087,922317527551377806,682472965824137688,228281443294862373,649395563453642623,30281614423624272,935501128500758816,228930307704828965,359174938583312448,346929886306100174,201298761834850314,642980128702828804,516153626865898445,54498616540012579,603232973472490645,686985997472506652,487954340906481539,143625444966737864,675471644707591666,190956351559946027,915615281659712358,654319145066168036,718713321427807181,283989228133009071,747247100894668399,738073510747200515,630098645940923325,197807341737171358,900355051327288428,26915977239879127,17128137621247994,472652474773844869,900408822669992255,404358609627430326,632918057339581,609648142634400713,219786911678794319,112482474896086790,10201500900361739,56976688888089874 }

{389423712592873099,330184641157599359,137898238714120228,1897001421886,850380296229150642,68731594209731934,50395758423720398,929421771091098503,149106095095918393,375900400251152843,547360057532978749,701464462390767707,496053938396195541,701399616099543954,302478159078856447,27435346690573650,916585559081093671,172172460356687802,47159442698762936,276709954839675484,65797228404450191,882508370595533805,546250416079372249,106694194564658839,13528794416730043,358503643935937989,238853477381386567,77565336595711067,139986198330389284,457470558070994557,496753452358382799,185667441654672479,378609683943380489,8482941317892653,593184383112978556,293206615081160311,445109321790170168,428667049361270083,441799925963205549,8484982102582321,925331051048325,360481456287915980,911550250225203272,812340311197514012,1315649098961263,3555210857776934,882967772515044599,435354838877160953,917661849397274003,663548597525804156 }

{799681275117876225,978053950048420018,233913027575286604,1480906736901,527671401711868315,102717717751824414,59772727820474532,25564937591350263,856078639886358601,612558316446828951,63456890951157528,745334955504187127,771718181729412235,75507359642137189,22815529336802052,715097584547021532,118278559133804430,53929510238616398,1827722982570989,222311847578584088,316938470169893,205789648439767756,190489411365017436,112127918825199569,21222431289470,562400085258543683,135693094252750359,85932108223327032,14018381678480631,919188300539156408,275377884367822393,66020742439724711,16222373672584248,11108958508312071,404336233546856532,194396705830799753,547034393895761190,901391029014828780,790553730807577565,22199519613014414,862389172765599,167046245922453617,379740928607509535,586845218985796809,220690381855242,13875845271758742,184261522442594196,47517941189746710,661828949161424530,403346840193960964 }

{963454244202474307,755312467121031723,182657010010370454,1210157058376,929797961792083800,697833678766014932,1361298261917091,73388318737179263,593140141401428098,97854594785005929,685771415830145187,989269888361104341,883924064022496962,754804189255732286,26424274703783288,146352246512548280,847568848196825028,55883677559198980,889742943748361,203684725345757138,956159227883218120,673249115484751828,649061199494134944,41416126943393524,13387942252933,972275054937371274,532766243817325326,192504468201976573,64078260511005181,930218740004520778,432799844190092424,25713514985340065,44080705523292643,4119044143115633,657895900146441886,947704019043910129,295570068193912328,562537913427261304,666417118257031791,143667801683533360,143742260644856,184749045390319051,116933563168548384,850414733894815850,262515045818182,20360893782906899,897341601835600152,916652263340487192,469571737110247599,668685824018186051 }

Returns: 1124800395214848
50

{889963900214924340,50880296595613988,2135545066830652,544895750727926760,278370410917200272,918691572716770788,635363959192851954,765317734141129534,357330599306101360,921450437607967604,656727410227380673,926216581183033764,371709791529678268,19120075250637573,938671935756281071,323755234252308364,200147772388446409,731407205342733785,777339252684238155,8100404182199758,240457409721299020,868799769963112055,283625512525026947,405592256676372818,708375499119139396,140953929834792965,671366663534353365,973838913856002699,614219439821673620,580398629889023410,873343158509497520,256224173172642853,461066360821119286,639818559551450644,728404230831835997,732367070036571971,844587092241441967,590271715959158122,937251709584370253,605225033183803222,710419018307805754,963859385330364724,347730850370313208,63563722789769946,588973742278207578,38798024298411638,202138846252093208,708049119879353662,17741032763599154,43337285917974373 }

{19882479750063151,902110588699028940,166125289332187141,234496405356413354,443562733430534488,907241123485695271,924963656855699893,72188646967295387,624450414317542343,888572351115789439,774674845339415568,178212329489769876,990631984358801987,794902978944140466,389255836187234200,674958794896974624,847857457469752772,902438403697199312,640092648683931762,882546231806941120,590233858144999745,158863235220951708,97818108713996839,503653056053517256,393382500578652794,270806815004608801,400855732512904028,618892476483609645,93142857555466994,283236308920451123,215334874429780,500788764175163148,697833071363375619,50165278328053613,635327258451192549,182697825557451154,641182111303618897,881394509897143047,895466121544544428,167995919493719592,558887770950000439,208998819313017915,279421435734874186,358440963267956316,369702521644336023,628334502703856124,118712208579062711,806466961526481229,360116924396613716,4461287267191935 }

{336874374641616881,530305530119997860,74993123398787141,456316458761160975,471734104525970375,764481389253632466,36668791753129744,374919629595355648,531341131098971572,519920912117045236,278492160338820030,11092035350955564,90276050243560015,435350321405805353,551056188372081094,174263426762490643,673891166964126210,398798051514839138,161104772778724480,623944328347129465,631140927873602641,712472032456009309,187475705987951174,114094364591854737,53596914040337632,244934608468259705,161997139939065811,932991527898988746,62310875626469321,714483585088216673,337461959961031055,29314565203633941,763028513938812696,28095087434962505,196926892473913540,175181332922679405,504268076992770178,497420476485686845,595306304544222733,922275960815840482,526158781451421487,541562042909182194,54213324404021249,719081516329226756,756148639542946,66096770506044864,671842032535597513,163518694210275139,592426339285709752,26378316333175302 }

{824200018410835481,346525301268612271,583439781779127654,561449055413097716,429518166275365271,999893393341721812,56638369537902823,256520994171454589,554804381488523940,370642692847429485,315440073390906412,93311182536206,664209048585724308,933218160839221989,242196154086940568,371596846786115028,274434989101947626,963839621078854528,460232101152929893,292405460579999187,435860660899112787,562721194039718559,594964989727640492,8982741882087053,588269689263529178,35558973768706827,984938453071114647,471092817912113213,564761992138064940,394582543151276033,754464904520170371,13323196939601452,28651320527554819,9347169221985280,70557849679194786,794007033482047933,924095927025125178,342408160486285395,276059088514937684,535668859230911841,752324497561649634,15783560028302472,580881367684786556,636091432449196459,43240587742218544,10280320759179456,774393586565199047,552682109688755559,86839451121616395,3806677742454770 }

Returns: 1125865547104256
50

{145165964023745796,319089139425301096,751617187658082313,703307994700068072,80001387012963819,561373610577228653,309326916490374991,103155071790377431,912313797936157596,857403731163619209,434542384832544267,135648001153548576,104973916017275131,581541658522152967,479817819643878799,799928472345630347,987627869502989023,787133833830312372,867288224837867098,522658718599156212,168934781081717273,74412897381699710,844975237110369588,9235549811520306,199368204760396649,897430741901170630,883971183305725763,958387874397440303,826390422691384605,486897832839675900,166469020081911303,327213954939832589,997209201322475517,895832137608314843,445720972981290065,344978152392623,603724008002489917,826632646740027432,695801348124033130,897519170116323055,29481191329486946,429509849889292828,426706343547220482,366933025799582389,519424736410040018,591704540705362050,949827757348015482,938167262394252147,556075983289960665,668903158954275066 }

{46218464294756060,599934134052608215,723233579767469518,9256844815177615,626600171363340989,828433937065772900,906444206526614327,347423538275852725,999205665385376050,207175327505484768,464865017177786072,643446817411496254,876981732445744009,950912353484940678,474744108201954401,61784598673247574,345124198550650625,455686818286526920,733190384507379784,181093544081615835,558119794692460010,681085858508678613,708593277360988810,532267765894081799,412937353204485183,278748707106042276,603022957769736298,43798859960584503,139473673981871491,215695227626753233,276652666345747295,763506352532003325,956809225428545388,173938529959512512,109232193778141280,67842069414764115,524825968839888672,777988597298871244,566332216734042529,3030663432730555,34477362756943831,209246910315071005,674681904887855788,69333888591673231,82053697798639602,870652711315310959,548301087037778620,294901623897312784,65610603726014300,455417849810207866 }

{356275963880979321,832073866644515993,84493816423729474,1090050856181289,44374964144973966,628561051060969227,114626942400986358,371160022750002980,688293091151113044,28629594409912418,875158162227745204,958065754338870472,766468672518200588,278768028743018863,903045404410258248,726170049811771743,118800235522414204,507502480560557955,934597009667841419,90499164473702187,337965649864891331,892028431678481930,543192407715397422,463713488503057926,15687282754402307,816289403221039417,980870520765021831,13186420984048049,95744079370105294,897091780079063642,889701267363389583,363425349702230140,45817992381528962,285310670061830586,267632745742673708,29266057850951,855814485972523218,371909891045622636,140616133065202185,205113231069821644,6444107058738273,994736933415169898,601665962613528644,105188342728100210,867863794760572235,55835955739254095,519980878820872878,947137241558873087,5372635092189194,391459375092600214 }

{934882100342013976,842297823154917852,625229411142045513,1055254858082331,32042987606773610,138407904646446991,783724118077229181,641410055567955699,441443051927662196,31274924415245913,320402826934873308,850844815782131091,556987159581427107,594034191098025697,374882241912130377,731143556324469678,16911027609472172,27320756889364060,795842791533428561,636910625845189511,678165760866633837,373708818946021271,400870244284961585,822866661994627020,94674196613384602,555981055714443291,950926869080380515,8122005655387195,21497473160167116,714204487788703023,46474655300525474,198045823635211592,435830939960083823,246179857120802963,65775647059391987,8152271614685955,449335220611023115,479754799897265957,126263257261469608,312708579906780908,13127444367720876,304942384447276702,622074532949419603,56710093671877425,86135897518898171,106284995662369663,438617465340001224,682648828809646776,6465964645843597,327544635777062460 }

Returns: 1125898833100800
50

{642106781762222431,408498908458977132,661897084694370831,732827607641219717,404679642317571062,769180110322559797,601982879792149126,740577229676005816,345138175653933168,763717683522647247,390851004429897307,380620070364392506,726176683285330847,505565482945616803,614095603024881643,138423800590668388,38726384802585567,116999245018122529,140303687223323101,788669303616102019,838208764716476690,431534688091422648,694455535781413877,624264242615866338,111730754014451729,620581523606810922,677161455086659228,920156310495752887,307122221399482056,861523187705708127,5789358195573029,375860525159687121,189072570585987549,69670520276335739,929184779973638957,337107063204837369,677356090996036465,409085717468708916,94637949460779672,101118001552324304,841673469669144197,372272509581927193,135539203601190445,218580534921898629,161848486458099872,263341848014239645,397881602361154667,322820587202193832,943708517581698119,519207902084657955 }

{386825491875168828,689223306349434612,302995105818553984,623696409514668246,630655093772820997,808784309078579957,268348571198170714,855909451236222611,22479739249621955,902962424074176105,628550230465022525,84655639200743410,674624827041779998,223577432608600597,863760520268982201,672590713154887327,693140117670378082,309201221168613452,8307355752945296,832530502044326754,24893269903523489,427565838108504867,924122049487837906,375281755868835023,131482931622948920,426237513600796460,207897991421802944,139799784272618,172860019775677959,991390293887158310,586145446194999802,690067558766741938,383056141991220548,934470500432611815,406840846059512955,25962139587366643,406809108641302030,201285825887054759,592667061380138337,984267809370392335,168990034261534340,18212208681793436,331545513889195144,447507190605809481,450295216647560515,583929381383687999,639093931550259609,227702077248110607,695146764576464355,5676790061084953 }

{563298491394883321,755657168475471275,478211757326076889,282766522126005056,144624860451102253,214545456269792970,784278048361168281,29192184113531345,447614493550143927,149222093389211020,163207537221967163,107605968966489828,927286965902959948,434907676308772927,779401733574031785,529438533517855429,725482104036060040,333202618875459866,20801117000460714,808881667295472451,673338164453943284,676516493589183294,75963692304574030,8729903077323362,947081508282527,674497776780399600,397640820840071589,519631252973727047,12746384448081697,517143236442420722,5361528153456476,639155313376459720,557912051332629695,568843418979903408,664543162734135694,3551971002009891,648989878078525433,237275544662685219,3112503398196093,674753392302101530,329294718091570448,437459001001641329,602368263488332377,7216823789035276,655504573440078028,337572023931252082,677520332378245784,717915106661422115,498913786102828230,221194221064449863 }

{99996803425412049,851857958597343166,492572731752992378,561760790308821367,939073371925113115,166186116344716829,715448953378270704,903708385357509279,853705175411656449,403964789820661005,41921132514014144,185242795452784333,770862487567291631,792133479585410099,768168637239641884,680397821461194260,801770551758825612,905618113139652793,1063595388323414,744065360433519028,378656364888281774,924432093273440323,394337253971588755,59844778963657504,61162480571627800,517926751711305597,700989931441414241,320128036454154054,780739191924630678,710899278193952137,481575278275941973,897168017231892669,90952908878687084,509708300483606013,394506295159036454,4145795553363440,562974467377797878,63439382807714306,83548595071112635,756094864847631618,390303878684127946,938346184401320343,378817952697674991,117696876502121013,116428576587942343,867563082379276305,107293387202219865,431587655229817058,224038600138782524,100980266989963838 }

Returns: 1125899905794048
50

{706806663396588729,501055407742441425,185182845091580005,125777002953163780,357000946975346195,920118084154650264,349089212029594146,771542657486956553,624123639645184643,927402370450557885,126093503459263670,282623189786771874,654332315174884034,44408879899713882,437541476108384879,221482025331312299,211913741635985713,590592295718653243,937475233689225335,401498983204187850,79812478545535325,17910671959306814,306550494018971003,825986628745770628,12513434199957269,976748363169222298,796798235093036077,899071193503857320,148328859812925360,422776715622374486,796008091431336468,703157177202251403,139745656197898065,278237083852608726,56604873965270682,418878815791213260,585837280476677707,918914643152024657,591422536692584068,762535316981860270,406103457330738257,202274529376207145,342984806597852923,383322264022385155,703947904889092712,405971825338966538,48804861434990357,644003487292415340,744949942488528130,503277921626145463 }

{744188220050489032,3240505476769798,1131147603055577,206641579292590506,489815693059439109,742876227903271592,41047040402475284,349503992472631567,591397263494638433,873398434525953876,904060098901414172,956558306227227382,374168340456917615,741809521683684661,386192511785891407,584183675148776020,401061923530126510,347732218918824960,854199966591085664,190298144399787348,217788874853144439,352138520496410024,304160881149776325,237145217896953066,730609983798238591,397677391550386640,459376129485293669,985459542793921126,679060872346651444,345232064142353425,700336158098522452,441900935752148768,406983489700133808,220707821329199965,645769264529344221,195908610973329757,71850831727023276,188322282434670281,954051990896736981,404595415945826063,126499547127180236,818972428840661152,18856882515613080,100702745519243781,643823557029549776,542696623894217966,690656863701324229,419075148876224044,759830644547671140,141953906823315107 }

{305573273590967388,901814420375779119,960307114605309612,913457694364216867,739151759340451639,680404775791725826,106133423411488037,932911256085693418,371495333622502049,733482352336245453,275414795113616907,546297385341913376,562921523334803881,306399968640869289,798978426365000369,234018279220763611,85993600499852764,187011582525592898,811713380861634783,901899301276873286,247700923344733377,147254596285986809,724790611950027773,168012093164349884,34031309186473991,180634156041657723,378694296657424773,829262948600744019,967190108735660298,319607252823263944,808677483822450027,7984901252676638,768589440649063564,83157198496452327,708235070063984345,749280592369652951,302957049153795181,29692129407383621,423781492887370914,402990089520177734,844603404178901990,52468537509964026,55721972324900139,13304485481376882,185998292693999791,822567120804207958,687959625716323014,960217943498889801,87611381211629453,898542126081416339 }

{429476272641757800,811016848560606540,249542183521308028,875739384397416146,486495287308124578,503143232001702728,227426394019478521,940527137502167515,557522781283309332,889982114468181029,14941343173728886,475647811714164025,713555810598758211,609609991957312853,680202696160367660,601806975240409884,110240415666872472,473597660744329170,243012920033778868,629578504918063351,846942474275742512,573392797239727879,311074133950311253,410638140827165955,571658853259955030,918477199059611755,209027566706679852,793188758652538251,251334454724196700,95540871745031080,951468376943334738,39133934854507221,690346692394900005,92307805614721327,201616510887129391,764431941340125604,178392065361541619,281520614315834804,754964676044948449,926893456526486153,891194850530190689,101765747004648394,13210948823448401,2981647600490653,528991474670751346,954091044253712529,567809577678924161,513761022191183235,113239425154304550,31427393999349279 }

Returns: 1125899906841600
50

{748886628180068908,673127496741360281,42861046531098502,650442630512376466,905266206878950690,890085120375724536,273586812897795160,997598045210254792,286966804753936835,129516923343168017,33475350701388901,159668076019369175,309798375202614120,587957139091642896,246922882175213767,402018570878262200,737536422049666294,949111539464741887,16391036784655806,982564366612987317,715554905548330051,589763897574817064,882026755823138021,129923812285919777,4176162173854145,964581903405838395,529952169406156122,239286761968803449,192757566045339228,581581349765346278,247790400119764977,179352836321114084,941828582466380790,76434265858585744,258539277549267771,488259675149587541,956444945947688169,567385219004197971,674861596533347547,410745503459649646,479382076243058137,970894191758006404,746411553104562875,104613947112823639,931750831849769905,383405197563276734,805641429597440793,485565505816882956,369854707989421521,770482387099483072 }

{87635436312963834,854189510839923074,358884305626157742,583318097989412411,76481854162048283,387103909922384716,9085968494493936,544196404647800247,958346139394834671,930301022034982946,880444758717066342,824416487541589880,754672958460468649,285844957737704083,265098174584419380,809367100738231131,495603902517494248,43942471243408476,860940859131961397,1019169510934067,867043160813418522,838700276214910416,47249391400957801,230297368666409703,774776226289838239,86124406800317481,510273654744319279,934185996740997817,530243542003171601,709590237595871892,185609509237212810,994800650061657302,481668552633460815,71831175818903958,176779897202828650,848754340194128182,186314588093986678,960723407828568151,961915736218701358,573833103354824256,107735184749990072,874200148911253778,100722683135452619,148586054899232124,26421270712246315,128835866213699312,938566960320175615,710051956815910182,149298979702014900,601027706677296243 }

{298076866396839122,483155487336850950,307277419506865295,276203164903065833,886140753098947863,708500976903046989,724425854284358471,379644764800144097,158325552067456897,15564808592153324,258353353085517368,215107480792036531,80157777399661648,807429695601432797,583403571731215804,400924942100393390,509117461098793696,859173974594731900,993265204284698799,427249647737451763,346079040451099639,124825552908093696,254434807841399603,723732887680051985,662053063409146419,886193282500509455,965192969542638069,934554640233670825,500259537539357472,513017091421026074,954851753811189846,682701855772448365,803000665666075559,2915233071962654,86977203731933296,752095554119896581,143951458574345962,699577835055796161,516830469619752099,509644443224911618,137188202506466770,923038819652787483,259814031465613234,371323849976427895,67628032172986920,874541027880091811,282902812989466312,979661584855090971,511012832282724571,580087480182842896 }

{893297325369848508,624774857671029202,185829934009667315,507340127021599799,888219841152312823,154115017405612401,872845141556918226,64496441701291990,41782628221581349,142317505798892917,300431731896202940,373891870277664423,751260498894094693,931212253378687647,870693056511602786,388089653519936809,39482470856097795,778899464311808093,328019518426715742,983095766902303971,726725384014639048,996653551522133698,378749873745867320,143841175394774000,481794764678522635,956903819083558805,350580859821971643,870194996015394323,363818697032629962,174657578862944022,657621953942837615,133413902447585357,242598477701902457,124286569955955973,369067344894951050,4899576149126201,966233980930990623,140862092529590992,410794525123311005,704960745720897764,989403998799660694,871545834058421863,261309825526221977,366359318633104823,185680364982893449,963699431145799160,941555132921671122,456259214769387740,36790200937912079,18077488954075558 }

Returns: 1125899906842592
50

{312732008203779025,1448645967048944,431807339639668606,60381498840392723,413767432571650609,735371735926119245,15286017523701144,955235550377778104,556959894063795712,104187230608142640,351478967986554593,280015240807782513,552924470744179227,860676835187967775,13501521501600922,513898486971114377,592011940669598649,162131386174595471,717572958532638825,163277766853279190,147247894656817999,802359405475496225,78404594076183782,142593452085172952,117644756007647261,469053651222112830,477078965663145613,570007396198128209,410191708365678227,79226457384644378,597657756386033353,659905751584998627,258274506955667769,623417732166029750,865972602959672975,980804742040294835,269298538126436271,719055431627151913,235045317329399813,109964067677260137,90204311565895905,362368538841424043,604448580423726718,573403245602877538,185062555822715605,353434719546932303,709053400218451798,16396574630853944,814744535283649924,702757104718462703 }

{695218614335197469,693936080739207609,279287207929131218,182599830079102819,59380211615330905,774974436883652780,885964083800264716,407860965728493416,625438707391029043,603590267561516247,67794653845896552,185889614154904178,250037771880579298,540606996528997074,664813104730139702,514267306012417446,170058160070458460,808283510673073440,444755147703112117,893857710055343758,757571763805975871,288011650090138855,477595960926066218,579305225568506726,652446756829016456,918499110115532911,459743940835820456,786708829941421514,729194167069305610,613187192211401235,584539070130642167,837482917046843472,861577745582158395,892129555205256884,249125226310363757,768759058173834294,266707838101865417,618720089766486617,910373048276170982,872244080268756228,682815662632606319,14998159234000039,986502956916773705,919260910894103254,861922218175938169,176013050909981887,259034611139818272,936285955248673778,129849709935111853,342853955439498973 }

{619975801161012103,180003702829172974,551186846092090733,753238837512721488,579072950957522942,363581788016320008,425427106921495176,704725655397461974,534836999156537044,274350084761228618,155233134784455362,156064229240992720,460070296495268116,449222816935325950,823855137523214600,273142429200000947,316498832929860336,225813310720876867,997501646154955904,388986463003100263,747906623416065589,455024733729729392,186811963725075331,800885274800133032,373304999211313968,504860324847584240,378443011134711674,798367715722107779,185841215976292583,156979190126352108,793514602837775156,812860529923062137,705897073954053766,606263351432760372,338888834570481103,518779539787722852,693539894103909227,696295766341221082,772664008693789401,270368405017202720,917139245252182494,62868884561215288,921178461071991778,26282378373693928,20380336231847512,702003277034018980,735782969689816569,388103574887408344,40795745505150894,99975688538779529 }

{765905973214153285,347355576523055421,292321937492656043,368690112287457360,931578866544097229,382658663583348114,339308950352114970,717335948030065572,591776484366516338,341964303510070236,559405500292696710,761785013777154005,778443804398788947,108002215950755259,411191266935648337,66016661763882422,774498694015583737,528250450188683458,849199905148851094,952380963668006796,157053428612996307,327537078222296090,932485173849100469,79298860815063956,722814530813702080,98504910537253901,635183699207182830,879580647293191217,965150230924754989,381264517060629743,677854921095693968,438093542221407083,666113068783745987,994920111110914876,495455409616189859,228384973423272334,379623966103563410,96743260425004443,219662666102485091,394452001657973867,758037748106572366,12480324826212286,547994693793534691,794500875615194794,307200897122962498,557516769429625048,672595041179573992,195900796395392218,890662214632719614,665711387242461130 }

Returns: 1125899906842608
50

{544353742177935688,580234261820645520,645859522482324120,346529413184336094,629876414468307174,840044365062147210,126198725100563334,310114736144029605,644258992005849820,946889619150438858,544375570251554932,207752217285763673,979748458076572485,673568078620261856,189283315233506793,814591042899139591,714200194187884191,515600358466517320,12537485225437579,22814037777363515,109961122218979044,171121145803166383,469362590259396771,587666669480354889,27816155925691594,989035204801248163,394626299142993774,368141762200058408,750014466108874916,662614005401656118,973355494053256126,256863594054167931,527149382699120323,802525457946031772,18555201043341321,844159076556776849,283974421444717403,972563915153941298,239204300773778940,36731269031286285,256611637244536316,405056260554580718,895330272696429997,699400370493396750,789254896345590549,289676472614828047,609049807633286821,34661502447609127,835168484710817728,611146178517572936 }

{54959391760945917,809670791327795047,678887623135289298,222092808069099032,953421093240255906,90908986925827092,670764555399344214,735330495438125116,207570109751405193,358748630530491893,350842906293154841,527017415591313239,949303077127406217,439862642965603209,91259023167149360,667522136455234354,373547939876441183,593912059879202156,983010558464095864,206077604565192701,939455107872201336,758139545855344524,961205868439274163,809538548199556408,384345906953444140,13176865252272850,903522480670126510,308659902233540602,871472944160922192,193866068660347661,936277581062818568,343770770318727133,889373746322385673,683057781110348352,763847269592605936,559722734348071231,487492727901278081,767138363366690578,178032050398919494,958589172252637712,871897875743085525,632634225606622044,854564197481915870,409666975083893416,879575950777228955,462989694019469613,152682518370758030,550683839146527014,188376605958623178,475840504663479216 }

{20443902347116629,152002518284516152,125282249517741031,441694959980918865,183864905204529355,656800572577745074,457744589211796362,982005056219478379,240645425316372306,987982677654413736,191202187131330749,196796578697497968,616243036521603127,451871097389694228,360617933203736541,431921367214213225,353479546812997195,531838496693037354,345524426457457371,976818875695217595,568679487672479097,139677705781997967,538654651759977678,886717933056181172,501904541388562659,889911255889727723,726072506727999542,419977515578104588,96890733074435649,849032632033679733,736497732960716151,128732581620320717,394914556711744578,623390558521288302,689958924672855550,9659740316415870,569936666181157701,758978151129308165,964974018574150299,231097053018179568,29654496452330469,236650974890363234,695498416561613745,957848522324391508,828509469622117913,171643870056934547,632055710457074363,459878545488250022,704054027641439681,472988003384700783 }

{1019676780915837,864322867163124988,709326402733763312,659480669737887261,136826526643698361,69322626833874931,373250075560007733,976245453488123306,675415422477303885,128509037747284216,324710668225125394,74417035466725390,834230439036944186,423116958003277167,340015316161679774,334498809202827295,717081118568484714,140401965998613194,212039306963395894,907066598226718713,403791504620046866,141759056685262202,69050774727090484,101145577946011007,431724242561297426,440366661422921472,937921370672309539,481514150596706188,627159035899330006,688586158976678842,55378812490199931,192379309134338049,245558452348223937,101713025438029246,855207245237764524,68776220348772614,780201887138682631,557034467059626427,375912549931126706,280778374908339023,261578402678998187,962172918840632016,324366645881810440,221386547321140067,985185231303984312,133478806334284878,271300347467094904,591586027381788839,744872602341370219,390696398410477440 }

Returns: 1125899906842616
50

{513413833433824585,606114817239181346,69700207035558146,437679190932172859,183286156613182751,637198011887285130,919726812476387282,37338514157764365,864286685897341657,665454698588871121,133165368050094419,554396776906071468,667842886091422479,791278493396962970,752568465173769641,283976927462191565,804069674463943570,157279138097388011,654053231201335267,655713409878551509,534059135122442124,413647743508539242,657016601442055941,263977741219188926,954178637922049198,568759608067483770,771591441355637279,979871376896933511,531602121944283180,250253363857346976,276555868678191387,495633814693109205,797617797361529094,752939474111710437,189072892864459878,722298534748542596,298374898992589141,949967599393473823,425792474656976096,168063870519567913,50750206951129483,769989233913635438,12000470301746814,490400509846460447,871601197444417130,757000599360268450,611358958318379523,688808130590242168,822821170744853596,520693363139098104 }

{963946798834528441,797360726214639593,935205920280013293,485267436212290805,777292061491567390,965722973781211950,232200563696640366,560761055967358204,247252164498870969,866330892942748202,413646998750876508,657585594444931438,201675454243247653,768071751889992714,989921631505103302,834105661198335223,91052959435580054,786146310220256278,433641959953562145,379627481037617372,800058285327856556,538547591011746943,255762032728726371,558772757150838361,976684407714589021,577392716009619081,901149480805055055,780423403960668166,702730648537845598,423076884091123216,332100121390727347,675307758261181246,711723856752119410,238118697174731147,289210821071324730,609091792304566206,417457003743898822,116385555464155917,488153161910026014,929672005828371356,243523851445459404,448213803771425299,127607204919110939,96189606236115463,447956233829328062,752537963287848155,435516257441264343,347104433728164933,918075948559213210,855274824658992028 }

{488581472930760007,576838197138609915,234337174024151362,479540058673643924,135079805217606666,846723740307185961,737606700907428607,741440581542785818,365584025934620141,31588324211489310,19833498690555547,474676790242963435,504400772410023511,546099821263282841,821403766619380131,575794760713631696,322760853432342350,498331553884361107,64468726656827213,203313215082773068,468593922495774769,270356293781801559,332702515479791960,800608995773013199,343751011973266656,847315429887501096,391233886244990019,172990474140038366,169663970818805129,587905536397833743,65295991383012461,470987845117512271,10363296942717798,623102338190195381,677525253814349670,990755358862308149,573446234843553387,810204594602621767,109691222970530330,171277721863798613,25534545633623191,825062766986081115,302967243487604762,29365162558557956,821135566949029848,856604443824540074,331864650540817379,840218326428081721,528039223285972038,671185183852011240 }

{285719500639900162,703190042337731620,883403549415672832,829634968656230665,900094111411742064,629886469373828365,332815693684561304,350672016155982374,556281070101835906,190359912625063020,590525140528326686,29599664052657343,673279189377921013,658890353486592790,887953453070926355,956397099904395531,158841777198699076,331531584877155664,10684569749506644,453449323952013531,489595501123238546,616861931497954125,402077898011054282,399685879185986960,862075407223620306,679886017756001743,809745720855038666,440526966986502592,167436724257353618,161781411123095641,728496569548322075,377468019216384391,427726266292116,288716112529893575,286230853167941604,259252208567576224,392072121487381310,65087372598906676,865776756475243483,816660957956779429,714718392447244224,190983776066187768,250151286621850238,364941774937519626,94735362008279447,900180029807881113,629519628726100827,361940702285180835,802407738518768002,810534141308129307 }

Returns: 1125899906842620
50

{928684668382171923,539782641828769807,642526415338951734,980860487703278549,532802623657757926,351978443068504147,60685258709301015,36002678793176034,839489071664077493,392147429411298899,511063513178877781,51655205034261492,700458633223117048,622690402220440354,364353118036122695,473098924820996351,669043242620748591,397336745447111738,124794063369014906,906484262488561278,688984798239299302,326179123484450964,54588609132529586,110234552450992808,330753561547465450,805664397115415419,111261657529412014,50805097118436486,60399516640700744,658373999096042821,331371869058198148,769675726631817443,886233571977421871,274219620884584792,226414660674598429,46491762776664466,100703998682715674,233282877058699830,962984651675145068,250030590831568531,663581774271462624,841371386000259954,295794388230975703,366535359962328528,990735605750651917,392807936936966518,57997816951706821,391682518602188754,106917918321461868,530334347018638357 }

{104422616665219477,842810910006463552,400529731413291020,393348280823711820,716858170692735494,108243242560324400,183322703144788512,957098915206261092,986525838019784125,144825526345591644,649281294861761868,128101325257119200,489138085234698437,268083337234734062,451118854465745350,971247811976125865,632515143515083693,968972216365628261,498426581792156043,402905566045271018,18775097011550921,444349548758319229,554930568107617906,864411508878709344,376813266686341010,579160331257883940,539539174910565881,236975671768620874,86384436076573670,250367670559966702,720734434011963707,39276339440717976,680909905042208996,684892635695617315,35988079327825800,525645392345710741,134280266599568146,766765175120135433,386578745422564879,814267554398001106,745883696583444004,904578200012395376,656983926458525117,659786813588372604,988396505322899102,187751850244144463,485356881176062185,208615353628800224,495129869199018977,370905799404819808 }

{192682530358140205,366658964082212483,866878208513749313,850385147398435762,135844406217220497,7540364795350412,379665762240810787,10096172143925698,551057484355803648,70947672560880802,843703380022456695,273111226874439407,546826041136941644,731110993689342222,73168772400545140,748234963846081505,552514180693578907,387003387142473008,833420946175283704,864703784256877300,410521052030780635,169000654343999135,142124336268177490,223100261644704292,397564988496077355,949212506167703256,280551497317959653,5029491910574337,138647044175256036,858152036597719485,882306137912403497,549322044947297702,650080387152050278,72808587433241099,839734968079393496,617213209286713931,32799547357510963,830727253347782217,460606550743766544,74376225089988281,161620001512782591,4691186833075853,679610938084365960,404013372308360754,492472229199452307,179268109494094254,927710676969722508,113308632591382312,873471690463612209,447326481429015049 }

{166549977406625543,878208077747612923,944702044926642235,494984493455352856,731508966396040190,731000200918029628,630161692296702313,601588461748031866,6540059553441029,692063013589236678,192331839830188364,993566077708212364,387501750547449299,776114216656376417,805318238605107841,317074080012015053,350552445293872650,985479663198693314,516287940206923440,135213325108471811,702985206352277723,279812508040947880,38927963349651227,302486925292299084,363909812756859821,434618487989053188,152039378879491392,663617335770757969,595124458313485685,315210774532789307,819897163946048370,224622089358965673,234492853986324048,980999161918466684,868463583929440270,34209632426219528,903370564578464619,814590979806353199,524316550101778487,59516210762773093,19248487513445186,26064049058867254,37676642086883738,369055134449836762,263818114445613964,152831644797222626,137046178553920324,791143721821517781,308264699070190525,979727101081233854 }

Returns: 1125899906842622
50

{557207112857180569,793228500851722552,257273758781620748,462441353051668530,464693935351226915,480534797494633291,36794060287923126,911983818925408048,109710120358914163,227123330548884687,915622626656440674,69497308399556632,463743141947193903,364410946816886122,265290359360183980,384055827199130995,991296490846874688,195310582976630600,355698700551353396,947097512689382220,228514393047597969,184708244077021083,789959978350521515,269521077219734926,35384340889111140,181073174748453070,345898621294988436,651354194114330024,563028019393147504,696129026793184593,22800918733172191,998479476683080018,915720235049333730,615841795515484497,142006818231879964,615454664855612463,576477929401776453,446420283614057409,486371847381568303,375683915278883286,643168017522917133,615503718470742704,33058549978676384,586281984474101975,838543701626524737,58111002345197643,380369460887967849,878589582593881340,176102435903070296,725643405424907380 }

{926337414647301779,368408550122927290,417271984527906585,603971235208913136,224108452549938988,349186119546555469,932193129545446857,109458396645917814,791977258918758055,119174291208605849,976432297358657477,241655224548683341,469409169058708213,28477074220891905,207549033787438294,973543519144422365,900769434652518509,94667644615597736,994901884768566605,227951419052885677,588870492158796614,999855623208577998,54419134919321588,161766639890411100,387113691970428641,943356721971224267,948319858769648241,60897081218646562,234369196114714226,352677098490075201,453435243322228961,401530102813886524,947083010299637743,611803022093578428,167674065524811164,223523874831336480,590105207089934109,156787013492996016,278919493396455034,623424508152037335,532843309202429925,601464562826157100,549953627842220097,292997167397043438,136913169593769599,726628283327233938,310910163180713941,103729926790304913,396904965278080978,859550357996358865 }

{471353575843948131,616368072548364788,258631735332492426,258186712186874499,936271501276413721,703413063429777591,65732557471589459,181161489593431919,923636633723146432,316730298845032499,970748462642080409,566155144822411811,481338579743231218,350342464025778446,509766286667331683,152773896360356459,509491649910820949,135357342522058132,739796232902068691,427721645482872965,352176926014768779,796250653116197278,297690188717774868,822769358636028144,961536062795741304,78662600168142686,71941038134918418,30784163209748730,697855725895424918,591908637952689643,706138161714434928,552017917424286140,617615854884803329,698179278601568294,448325209553067789,139552883889938804,742799986455010232,346215220353958854,953200174617433640,915622479374724429,571311615933375206,313133931730978778,606407153644461448,901406542871378600,49375821067987765,712227898331299645,946691601233544403,907616924672757506,916516901168654838,36074465697603744 }

{36739445069860811,950423887696466031,283876197444959044,899223624785976124,644898133131853850,428756630008823002,856482311316299282,690184682722643535,784683103779028781,374304431059781649,159459147278571015,603137562376449846,789778677924997857,777420288343358574,105270303305533358,475137684664364778,537229554159303721,846007080664108998,799472830971578497,314919312530757791,907732719373601167,635092352927002587,500264738121542560,971631585732823537,332758876686532724,129967849437145525,247049503442362667,854685853438509941,576415543377789784,918268600654793150,40820008013937584,797088104791866228,32839708364535889,881181984033885416,775898341592117175,916263556900404650,364370584592655723,476666868833050005,923888958283005376,974916867108160890,124335327771244091,764072423240215434,24313989752229087,175224201383918874,835249433601162588,230717178304795604,202789603914426838,71482346285502323,449375451908590228,321292187949331672 }

Returns: 1125899906842623
20

{25271205,377873713,973398760,1,225520915,2,38901792,645889860,3,264750398,978580985,0,828622563,827066747,484545899,899362775,834771908,113045222,1,487437458 }

{9493161,594322541,424486024,1,872927691,0,2681827,54102699,0,266277890,885573038,0,84024466,510221836,617201947,328821458,572591567,122757905,0,56861515 }

{7907797,269585255,631433983,0,218600402,0,8229572,591874804,0,235618419,172542115,0,386528223,811041893,817232407,793160706,715428300,590644547,0,120338421 }

{729387,564415135,872978767,0,501439400,0,486076,145853638,0,419689285,324490136,0,256665602,714836884,265009988,800873956,753435923,864409770,0,917689838 }

Returns: 917504
20

{954589013,597264866,826635033,733463469,906722284,702272197,783313815,285372926,150653449,336913515,929974901,422625585,363876297,155328690,490749247,138706754,264008567,721425990,849331624,212422873 }

{264629361,377586271,666161025,47627264,740343563,244508378,646230479,707185524,23390976,415274422,295095075,84911619,617031355,19982997,41451934,685256885,492596587,276361624,240452823,493209479 }

{17386697,23994130,116506802,24167233,865678744,437398929,21144468,657607921,559311608,402325402,363360247,64924881,17953626,40705141,20831155,373896,751269430,130478107,465510004,149267874 }

{3015927,30912934,295831033,23817410,636850235,719042344,772252752,134063450,697017638,746151099,542335424,131202918,12623265,169769808,13267440,17003993,145831317,82846030,96261573,444691980 }

Returns: 1032192
20

{136198276,178624166,626674210,397434793,846527911,458057800,332560212,889436683,185804228,226622131,213175770,422727683,706877693,82559361,73102487,677803523,729481907,399948452,569467900,654347750 }

{105448202,779715120,254029650,262930634,536624667,438195113,554612708,526019111,943081224,711992109,336655967,793218643,899477370,80914664,1183930,984474266,145864221,315922624,399294562,220117769 }

{64552661,322485606,19108328,378006837,413679692,615017331,369074529,759612120,739376700,70103138,415214410,377425200,110767074,595228711,544315,122567356,55207389,43118471,14199485,965184968 }

{560478266,590547591,190404058,144935316,524414242,350461601,44841256,831623736,802131238,125320399,590890095,291272491,4056417,608021239,154144,481054282,19078935,267435497,949993518,845570536 }

Returns: 1046528
20

{146931325,846357283,161092902,507985012,836767651,551841963,618550206,900789192,112524749,469195655,36868686,906612260,558712573,537230645,511616027,840134445,543510307,404733433,975462594,232744815 }

{718157153,723948620,404039665,502781410,808653588,444381791,875142869,604862069,3768761,56610094,50101555,233165028,484851523,151932464,494100351,402298724,324835309,866005645,913606150,3122150 }

{653480456,997247865,890858995,94681417,150572221,645453445,839708361,10263578,364431809,627957618,7590107,401673825,542431500,22022996,858957468,812767953,303632668,178544265,924664352,8239993 }

{48839069,595881253,850154688,98390186,428495886,798629309,283158634,449281671,238571136,512060358,4827738,497885755,13676150,111640513,836677202,123078397,303645094,620991417,117106943,5351112 }

Returns: 1048320
20

{707785888,366526635,970157334,265126866,523889600,185258841,817757873,327786772,199081945,357466792,503414394,77968413,519269478,277675764,950388496,345853306,596417023,873555359,100916174,705851861 }

{597671279,775212851,768558665,918279001,198776404,882950281,945367928,523304984,23453429,754113460,4849135,918915474,929456193,648355314,212161749,387070321,580121280,808123341,464038419,321283209 }

{224971435,628192218,505060373,158539637,841675568,923674147,402648500,553698486,613233686,644251703,678671727,402454638,867589182,971818246,402511077,318887006,708492991,202816075,469088156,831956256 }

{466913566,147507776,7872828,34996849,674459833,699493345,997944689,533042479,727047557,162521950,612940043,152966152,536055890,614932163,2876644,883748004,548055687,214629685,515099411,628862958 }

Returns: 1048544
20

{982927015,742221464,634145333,80850867,222650660,398521518,883845931,749566546,846286033,934284054,944888006,984546052,142637038,174089293,599485394,383331106,361163147,448965163,436593268,913174944 }

{946285753,470724716,898168065,812250281,598230386,288836381,595428538,420138848,832271771,815783580,867041961,608584720,676477018,77750441,482622500,449540251,613449320,349263922,297695680,893929278 }

{444498655,57457929,349332585,733591221,588746675,101562479,115610175,285015780,493654148,248772731,549461163,921520390,214574328,733351050,708319924,132981014,931787587,829022558,569581276,811311458 }

{162771275,51091487,138013366,683985123,83619039,849573652,79496460,640374176,924275,57837788,292026347,378817541,367097962,448156357,447582498,230114898,397421558,485245118,499081145,153509403 }

Returns: 1048572
35

{395454338521645436,684801276553108795,257040882807755638,585590309921755254,541184048818130649,9522529564729571,887458655029784390,16942814348933824,132664392876319606,261432323928804770,523039860818242379,578147571534579816,489206973671734837,964084643104258276,239928777646844983,957166658468084342,442150613452361989,496294754996670958,250754494298549658,938671087589761060,108258866635900808,888274584939914708,79421245776595762,55194199172506041,423598229445117848,784668991235159509,343531576496369492,374498422854778889,190980460405635551,565597526411030345,618648240435426452,394558175691265727,435866953711245122,263624918172786886,551921617392022900 }

{534209520178940638,868421968933328010,120922337878168653,355973698309418820,391364694757473685,536120799750206288,508190938526110450,541247807535822269,194306107084362521,853196194500285243,926836834634781281,552093506788670445,692527459794928576,496908888059145985,302799259883306308,299343913358948156,684292601374683578,428053123167751832,82271747611033694,254318377049789176,743797025809336359,483978886051812881,484602733988061013,677507636168289828,993051876570340917,726219997132747726,982992350655318362,16393508982715246,492745613081748081,408419081179447320,311274431124129416,318169931306485261,793739384083055868,958799770228669300,584583389417622009 }

{512009226290266162,726489264143133005,47932476074497522,92347413681503378,527345770475671055,966681179711792074,606477511270052815,661654614126178910,151785017042627957,344474189468791105,335590069051603901,77532017980703629,26101058016155158,981342514490578541,236385262226466534,821283598779039431,751660208925183875,445471645446689363,18099665936741634,877461217039676069,461902831208949631,790514887528550478,956162282003471453,200791471614354584,23690897451318525,54420488739626749,42085043784062423,620214275344088067,651031462124188192,720414414136080590,255050612729297478,87317595068908644,369793101107766206,60204166784361508,74307391416686617 }

{707127210345990332,432771834154344793,343023277367716918,412044273634354166,23406221214533114,370454896808781745,526689672983430849,434792011991209217,647704349395573299,436266506833090501,831917146054405068,815607224061384847,102447836697327131,608634036095407525,373584057778675814,520524969284088692,301418423078326200,108120975837036674,7772176734541273,293820380999701901,950479313984101876,945640230683510974,529758367107526820,208115312282233327,17471109656261216,355507261241356111,837452148217328138,564191050667698425,539510783035503255,918384407774970604,731690153443458,470878737250865173,4182856323723522,329609258571168505,323572038955683234 }

Returns: 34351349760
37

{363196888049645689,958157076484310653,175716239105227891,231203044927878489,96924678403367706,339786763982928988,518848122957999761,489926799426634641,722642472585023318,365477124043414873,933122950970075239,564848519932040706,995209822054422962,154142248311859922,98106591909741206,601960853238262695,731576798087322517,55984263650241178,411305139890330987,731584849795207939,287683231842359883,769188523679164189,912694412038193017,243050473823715943,431494276181610662,194059581561989390,500996509675530272,675856636898540242,622148749550025026,936589226033362317,488255878052438315,541184447188938078,324083697346219522,513960190482000497,660158184898379481,241798930072539142,662985678935900550 }

{119575217414331734,705847278004303018,90033024617238091,353126353139661897,128191275809649443,527412988148130817,98902554498196100,442567113388435236,297305937090285082,360541191813362218,609676322574548712,930584051980561795,483638058280647859,59616850208098180,874052730868446962,33960393802027118,923108265439083168,959733274117855958,75649912989550481,377307423645261530,706412049339868603,466179406116813081,760262101165902521,388078563963328534,197946152971299071,397111969690421675,113789515573180962,328896476467987709,169817325778980723,636058937799087911,480977960109471695,290291137312361404,332916729939498598,202645439013237,796047730607314654,622019846475989211,829432297855904513 }

{650899047712195025,114497846535913875,26344660978181303,839503070482278309,395975982393744,98312323772892705,298528395232817144,414639802884902861,208913419796024532,532361106818237368,249599766309295788,187141692037268776,862364875046673,925072341461860236,740899485538171295,53135140335119610,728897975329928323,460992357379726724,654556366645505027,949946592728456437,352568226903897284,876249701101928605,92959085040486476,480003920625500402,533909395680037706,16584692379028791,614969237187426290,676675606461489771,172163670129377511,126192114992455621,165339935966945047,157823785954877832,408145923455993867,15949277265095323,2721314740166059,45074855479259396,579286963085129257 }

{246842927007961070,42587431595827590,99153301584818796,176568177684211050,16776217262384302,393550291598773649,12836428488049966,788773588075090586,478046432104251749,431531536108284338,870279241885263373,78391237342111669,289767904524389049,566684018093584620,898506375349915076,7251999283269825,777611469872823034,992991862528190084,908546090826648993,536180892725823697,325412959163112290,778651605527670308,251830047184169473,619646868050284096,212859678145041055,555207103166667482,254999048221899740,697431945643979272,23802794958624946,51935472777801341,1719221848137066,540281635745629879,691117416492430148,777415642860378016,959686069168618829,4717342289247273,599236953322755191 }

Returns: 137438691328
44

{59670260728123115,824796613717808101,139885170777350564,145743868201361535,198461422817130700,68731569475764393,795508483397320934,273235551001479180,838707801338009879,158305521285821792,253630558171630548,488548996739023509,835786162504077159,921295422237980908,766294305059564734,243594703293951353,1380496736217744,240642992037462397,496192935598290389,393266537704935406,844540422870284731,854404361867576883,717030514606971999,706661008611557884,847868460546950904,290494977603861763,880792922840173387,871480622429791513,26175995665948674,583610553833488255,717315270667104336,361323932887834076,926589732313191361,597211940342717502,261012398835154446,520890096782549651,544885491830477017,941378331215789167,977373067215839722,509830610906011189,586058370214965204,82893078573236687,324909245823874911,161157707278266271 }

{758333275012293542,491396546442676864,950425491475996710,481055111021267806,23889994990708208,393155255275870106,151238042696382640,225099256068602123,470868565076120382,433625578964293119,268817911590729471,88680905809043429,8262012129749258,329692339564211916,363420851972010978,657117727416916279,503220581133810680,582416177470629938,418270257712241197,417817290476532633,84593305392562485,407649182985812288,358818055376191159,971246674878722007,23923651325603178,279634011273495347,769980677486363772,389825046740227941,28756622394122837,335268225055449442,295516964082565944,568564231647599067,420617314188022217,535452258284759777,257059402602859360,276840473715121188,34567383891940066,949314146124786638,45333568814192403,695708614920822788,928743919644307179,81916455358034409,480927687196814649,790757193309206631 }

{679881237275310252,360102569294176766,885195431847440330,834178018180019235,513945625418502,412940447897613421,573977409937544262,172988735456053759,648859835720232046,840431571445339201,724393959548885850,758318133469599315,459448631182589847,75142270914991314,463656037568097122,465314406079849737,454642191787822312,970727384422140704,560253216308094707,627455406392997132,400107997613888249,480608928474405036,726137476569160705,471358947116684814,600895561529086,541535984932263664,568431232303665116,150554857910791769,10011724476143653,702642923224911683,619017172812979124,326526372032717099,46996482129332335,411648339431661200,478352902863649619,452917901970762289,787281738963603776,716754523569602081,252555620039840958,981157534960674438,708580408693683301,486473133507838815,931289054216235765,159455168615607906 }

{41994771967912555,448517767409528022,431057479051744256,613305227532695166,649904222241420,339497423924635047,880758860509508900,519220450615438424,181776887659269889,757885078319803055,92487550348750384,132555203207660843,287216935311905545,79614100775845584,514206346164532077,990334178616403566,719205596104355030,116131052695451472,666944458114897038,108456354332086750,147238884246077547,316300065525256422,414866932247172898,582384829036374742,5907554926830520,919852151708340403,683094868622080473,320619739655478131,3098932190498741,918307634430451218,350917482684716762,464572918596757888,42405055208278140,386614823452329533,422189068837971604,934856987510578466,416719385179333930,813895932674360679,772958097896259138,463665862095449637,592632913782371498,836668814078507716,634800217200310403,8996044056673213 }

Returns: 17592186043904
44

{218437938952464746,524122359250418053,193806677462340426,241183522154170803,732908355368080825,304979934540779850,113446063113939571,920202817190209420,428932880749799296,483625014936153345,142297455570408602,237240835658869028,850259944079369986,817449411863101993,282922816548650174,136012387569437173,711517363746263868,753835784900560401,108014566327061878,477392265846907355,543607722019833531,646320870571929945,10979097014467202,284776337897762886,579066845007298502,111539286268923540,809551922082209456,447777983782461443,213825042752302356,918268356156490028,436034312213355832,33309794841579621,987375786206989995,998572447051681478,79519195046697352,935031769981634202,738003748768218555,209138208304229847,567425236705650213,732295929626607890,396117315234770027,932784798015183965,80307813726485780,49356224062854813 }

{585726922368963125,212195333800415829,768977695101693784,816235182602485550,198610235331833217,916232983643756395,957170057587047349,430005977578107499,295775962500494255,125266521798669294,194709828692352856,581313644635315024,777680315338086984,126481191271654908,609620792403150762,168788478744477975,389630926255663401,95727455729354578,297050491616490903,831373881598170584,722220559516849556,712712922667579098,570626804757624596,718335632560751561,399793403338933633,245965262277653680,586580919793277669,434760798239725944,879219796928318159,716352750585007727,20740966840819083,190557746558373502,300225763053711440,514133229111715842,715909015495489482,605157101755796539,799119539842148227,748433672880836098,969888398184494787,51937017837880895,931317819983343032,311771070990872662,200600529471297885,293318504554254296 }

{562545957234088396,779518010574187124,831684455362610914,114447769081814890,363844141788939814,879686797532622788,31720500448417882,786789679442360154,493373843918459766,414580646369744942,525591102698400571,38646986814039024,900425408120053544,806563653620817688,46013081493219706,92430694819290163,12720278023143476,278496776474863296,755309719719283548,186908097505852364,964547151437064151,729174815475717249,228754774358492533,681835621413509337,862542884204811023,778737200530113457,511059802229161487,712843936620367068,219258769609914949,860467004298515205,578791060435855540,501157921601638536,503354093149393127,598317526337430303,55427506311167959,50450394124794750,617677671084043524,329253297088825356,967821794024603534,682409213533590096,449172078748046467,346566075695895350,163712244983631383,376877068573706898 }

{305175990510764508,590421416693778356,344349991141595277,30553752552182130,383074683037655293,555108670253569439,498229566781005933,64041505291184060,389468395377024688,28732948798464961,484322777574892492,332989727461145253,595185683927943056,736824909052453875,686579090267008701,899816376362737074,528192751931855849,59288197546920315,550606412064720727,836643045778621172,356405575636843681,213081646530092765,444965651685362084,537591542805796857,233002601711602839,948378422370625817,236367436811015180,298885874571121103,620192696414569194,716835114264543224,636201921658325168,69478729808525020,398806594112584127,836391957222987220,211640799154612602,173581787980900515,898980735808015979,236199528470847488,925663565931070020,760062443928645830,613080452041257204,178592514146579150,665106553585382977,687432700472230933 }

Returns: 17592186044415
45

{419870169388480015,748474329596097763,137645511515139466,123881286663268388,918739487982278785,837922549921483360,310520912585745589,98280829769598540,836653597427680380,723798005107846606,312216035860263284,526943581205702209,415573370264280098,553482930967952986,945089148748372524,116634117244050378,52312688533532648,438315360921789154,671738068186509338,846075171606104828,668384313285439241,41745331527481660,68113829142241643,30933399737664808,213294695750540954,401301806827339143,988290607443494015,96869004803665704,654073659307930127,356973433466465389,88255182650584137,643244523650958327,511169009372772048,911244072916692711,992062426985185027,838410212659268044,655332458296634953,439792846083619960,757775530548920303,339394519609900986,300024701610968200,352518459043498229,772520346356078907,801756194356080425,484090407533040748 }

{202730977121903377,70331913956564355,662214382944197909,174186561935407720,756248293802081601,917990091978682212,19054128973425064,92163000114233830,228852685639927362,649938543117493847,391637351234308097,13582951446626407,969359350612056831,777798779257869789,108455352247660939,990502300015260850,599503803562446557,103139091346608842,444042394117221259,171880723219053442,221638148247362942,538142645766533913,473292410769624025,552829099217179577,460534980571536489,627676029939190522,259001849265823861,173680435461200164,630864266225118498,93050761721672745,993557060544428208,888811525531626680,829965520843926091,736566695471500433,566635380468381135,570145109665738012,362515516350521548,368569776607804290,311248583730061508,449097095437970606,947520486011001397,720868806794559886,514713591422562586,157091761750800537,571753901698833075 }

{535468569281474309,383331036495630009,648177697638020144,786749916067841573,301789993754584521,98185037756401340,897593708996907367,394426050682610880,212189354504900037,564803246495980226,167386163310597365,195146687782096949,938594062551628252,504716691089716243,662417256990589710,138398497675269726,563444227443755028,782044875380897825,124398715619141041,688998462721513470,349015214022442993,159250476544221949,445530020708206926,593240858573201462,834635688275497936,375554427452363736,195972542350987119,162781926959382831,147967434131760912,122304921830965583,766794950960581666,948148080557237825,324434543753935020,861236070611802496,148135329797577887,119233176638183584,7469056754239706,779619410632106864,233713223846259819,824768194809671165,183255613699699161,673722706709905720,392928824256624280,413345733460096481,353712463126718218 }

{412509277345213624,778329727046632598,6255772601201370,776222854723974419,279489646200754685,83295258395064691,142607654672147033,469107544345648855,103596226394492097,968451791453109500,943459852688228463,365097220982785180,264646657482242049,820706992192504505,735374225194543862,426868596804697574,281030301798496952,15774239964832825,129594986327401903,625201051445336626,306685963654799235,813497668830798723,905541536382093996,80790477902069949,824524443995832190,705155162286304089,268614173789254922,855482267733653068,131433470588014540,658866720966879254,324861420678981441,80672395641441972,939175150222626665,513129111400337993,969805799856964601,344596136529109006,987675399403739889,769634526586923947,963922648699225580,44977270175723210,455217246079486925,381311731476471913,381306154140159834,397962864351665487,5975671388614638 }

Returns: 35184372088828
31

{484604490964965150,134441223557864367,248511917130596588,622033499716614073,861008295301885391,460547479838221973,71118050051094851,987348447745813292,386273816666773353,404099244418769951,545060918331156887,347105566607048748,179207916738189691,775106175483582327,106696905559780499,499148221212495151,643178294480684550,622307132958916185,476356851115304331,926568823134028811,744393979027064785,978377075179769673,684192755591018324,641027683599007416,276589772033942078,994883266720340565,620064202540764727,641155024546043167,168952800739413241,859392262398363590,584520805791491888 }

{370088977619022240,553780090002095020,89156980025941588,361352814357619231,534226012983136757,889202125312657230,988136027211173501,214533632655211341,515136547317132790,650891291964065,294576887653942172,162723280422689672,140545104367160952,951556492277031195,890548613762023092,151448779136662022,247756279113016376,819711798856560744,608300830387257669,983286998632627813,301379985587111247,235915986825248142,101448533677290593,945146843338384667,365699508722028925,690491210310245453,7008902679791325,286577541979281357,813385185988825835,964271687096093074,67813390154821924 }

{836581475098223481,258336527850248527,28967337342946461,914682754136635128,330389564233743657,892913652817181433,366356713448187319,493785986132920453,962649843611987174,189765431249168,271988707684292055,459853249903783951,814934043543176131,388484886508892485,312880664590188834,550327918700922530,212821181971571688,172301172264309466,385081970585525708,21860503509997756,488092776229703819,590940044866845234,602268934758897105,46526033068919735,642204657585202936,613125279452106462,1011257572681785,72047367945117687,987751953881005707,89602179852543077,575224541635385155 }

{223379866266596132,958258271091190,47969226918916213,651665313144428893,120743362030478183,658958496146868848,282725557632804044,350789635513979773,887517120459110652,420049785139489,48145065481717835,596993368842304832,595802983236823038,579600347806462760,943826144190122438,344877587984471018,405674929031386479,543001978558660498,950166972631455032,122293348059846966,980514222360559004,321382969039794691,842365753564926336,178383282053526999,71204494363421044,124940689535580478,8386096019152427,553907274257566749,357000990176350876,827103497595852445,161471254537832990 }

Returns: 2146435072
50

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

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

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

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

Returns: 0
50

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

Returns: 562949953421312
50

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

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

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

Returns: 562949953421312
50

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

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

{1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000,1000000000000000000}

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

Returns: 562949953421312
1

{0}

{0}

{0}

{0}

Returns: 0
1

{1000000000000000000}

{1000000000000000000}

{1000000000000000000}

{1000000000000000000}

Returns: 1
1

{123235458}

{387492387}

{237483423334}

{23847883883242}

Returns: 1
50

{4747561509943, 598218898554587034, 537972915281858960, 147283093722583632, 928114056102298407, 918635207712852600, 132485557087904664, 130596668736631461, 23826888842453383, 118189949359130080, 322253275542386207, 527228668476153313, 56210991591079480, 277335663966801522, 345204997046578360, 199794141009933122, 57448712149455704, 114216857619541730, 206850614515606871, 669726781229313359, 119385911993711824, 510696081160735048, 218391938427621325, 577064275560527748, 548853999927633258, 688702126104276153, 301446629906928352, 275872006965105320, 14040360989520304, 253945152587905590, 104857415168450852, 759609912643267176, 247635227422130253, 111363277934237616, 322341804243848724, 887024134541876338, 167688961288452255, 134654455114311110, 217339652298039768, 704854138331500325, 478599053346366810, 50378994464424129, 520744194500448815, 462945146606212420, 95594538084690398, 329425101288557124, 830873154039393410, 306171316451933632, 599195985808753292, 515922894764253072 }

{4747561509943, 598218898554587034, 537972915281858960, 147283093722583632, 928114056102298407, 918635207712852600, 132485557087904664, 130596668736631461, 23826888842453383, 118189949359130080, 322253275542386207, 527228668476153313, 56210991591079480, 277335663966801522, 345204997046578360, 199794141009933122, 57448712149455704, 114216857619541730, 206850614515606871, 669726781229313359, 119385911993711824, 510696081160735048, 218391938427621325, 577064275560527748, 548853999927633258, 688702126104276153, 301446629906928352, 275872006965105320, 14040360989520304, 253945152587905590, 104857415168450852, 759609912643267176, 247635227422130253, 111363277934237616, 322341804243848724, 887024134541876338, 167688961288452255, 134654455114311110, 217339652298039768, 704854138331500325, 478599053346366810, 50378994464424129, 520744194500448815, 462945146606212420, 95594538084690398, 329425101288557124, 830873154039393410, 306171316451933632, 599195985808753292, 515922894764253072 }

{4747561509943, 598218898554587034, 537972915281858960, 147283093722583632, 928114056102298407, 918635207712852600, 132485557087904664, 130596668736631461, 23826888842453383, 118189949359130080, 322253275542386207, 527228668476153313, 56210991591079480, 277335663966801522, 345204997046578360, 199794141009933122, 57448712149455704, 114216857619541730, 206850614515606871, 669726781229313359, 119385911993711824, 510696081160735048, 218391938427621325, 577064275560527748, 548853999927633258, 688702126104276153, 301446629906928352, 275872006965105320, 14040360989520304, 253945152587905590, 104857415168450852, 759609912643267176, 247635227422130253, 111363277934237616, 322341804243848724, 887024134541876338, 167688961288452255, 134654455114311110, 217339652298039768, 704854138331500325, 478599053346366810, 50378994464424129, 520744194500448815, 462945146606212420, 95594538084690398, 329425101288557124, 830873154039393410, 306171316451933632, 599195985808753292, 515922894764253072 }

{4747561509943, 598218898554587034, 537972915281858960, 147283093722583632, 928114056102298407, 918635207712852600, 132485557087904664, 130596668736631461, 23826888842453383, 118189949359130080, 322253275542386207, 527228668476153313, 56210991591079480, 277335663966801522, 345204997046578360, 199794141009933122, 57448712149455704, 114216857619541730, 206850614515606871, 669726781229313359, 119385911993711824, 510696081160735048, 218391938427621325, 577064275560527748, 548853999927633258, 688702126104276153, 301446629906928352, 275872006965105320, 14040360989520304, 253945152587905590, 104857415168450852, 759609912643267176, 247635227422130253, 111363277934237616, 322341804243848724, 887024134541876338, 167688961288452255, 134654455114311110, 217339652298039768, 704854138331500325, 478599053346366810, 50378994464424129, 520744194500448815, 462945146606212420, 95594538084690398, 329425101288557124, 830873154039393410, 306171316451933632, 599195985808753292, 515922894764253072 }

Returns: 1125899906842623

Statistics

Problem Statement for "BagsOfNumbers"

Problem Statement

Definition

Constraints

Examples