Statistics

Problem Statement for "MaxKTrace"

Problem Statement

The digit in element i character j of mat will correspond to the value in row i column j of an N x N matrix. Choosing k rows and k columns determines a k x k submatrix of mat. To compute the trace of such a submatrix S, first extract S from mat and reindex the rows and columns maintaining the original order. Add together all values along the main diagonal of the reindexed matrix (values with the same reindexed row and column). Return the largest trace considering all possible k x k submatrices.

Definition

Class:
MaxKTrace
Method:
getLargest
Parameters:
String[], int
Returns:
int
Method signature:
int getLargest(String[] mat, int k)
(be sure your method is public)

Constraints

  • mat will contain between 1 and 50 elements, inclusive.
  • Each element of mat will contain exactly N digits ('0'-'9'), where N is the number of elements in mat.
  • k will be between 1 and N, inclusive, where N is the number of elements in mat.

Examples

  1. { "19", "90" }

    2

    Returns: 1

  2. { "1119", "1111", "1111", "1111" }

    1

    Returns: 9

  3. { "1119", "1111", "1111", "1111" }

    4

    Returns: 4

  4. { "1119", "1111", "1111", "1111" }

    2

    Returns: 2

  5. { "1334", "2245", "3456", "5678" }

    3

    Returns: 16

  6. { "1234", "2345", "3456", "5678" }

    3

    Returns: 16

  7. {"4073", "8166", "2937", "6308"}

    4

    Returns: 16

  8. {"090", "000", "000"}

    3

    Returns: 0

  9. { "253547", "687599", "959258", "183097", "601022", "562282"}

    6

    Returns: 23

  10. {"768162369", "862916457", "392931394", "626092038", "407847935", "215898827", "637594361", "246236273", "216318141"}

    9

    Returns: 38

  11. {"8247249687", "3039155233", "3760813913", "1035947678", "3465062620", "6521841979", "6307385454", "1776535834", "0926041040", "3556535511"}

    10

    Returns: 41

  12. { "494599520389852", "303896953907791", "287493604901139", "149554299340006", "893640109028429", "564962730433253", "075854577852319", "453201529585621", "950489162577436", "630040569640126", "415141646262027", "837673828874883", "785041862021729", "850806584119109", "217671590991247"}

    15

    Returns: 61

  13. { "123", "456", "789" }

    3

    Returns: 15

    There is only 1 possible 3 x 3 submatrix, so we simply return 1+5+9.

  14. { "12", "93" }

    1

    Returns: 9

    Any entry can be used as the 1x1 submatrix, so we choose the 9.

  15. { "12689", "55555", "55555", "55555", "55555" }

    3

    Returns: 16

    The best we can do here is 6+5+5 = 16.

  16. { "494599520389852", "303896953907791", "287493604901139", "149554299340006", "893640109028429", "564962730433253", "075854577852319", "453201529585621", "950489162577436", "630040569640126", "415141646262027", "837673828874883", "785041862021729", "850806584119109", "217671590991247"}

    5

    Returns: 45

  17. { "0000000", "0000000", "0000000", "0000000", "0000000", "0000000", "0000000" }

    4

    Returns: 0

  18. { "000000000000000", "000000000000000", "000000090000000", "000000000000000", "000000000000000", "000000000000000", "000000000000000", "000000000000000", "000000000000000", "000000000000900", "000000000000000", "000000000000000", "000000000000000", "000000000000090", "000000000000009" }

    4

    Returns: 36

  19. {"7774896788988447173910","1840510756718244694810","1336721644038733170605","9586473719283313245773","7957058558851063478056","9319886320889200347277","2242288600389360985737","8371525832712570725886","9407629824123148487454","9645316264578751862975","6535664189202376085458","3481498271633744132831","9960246218276671029050","0944422841971586733976","2433145760947394527994","5617622824053442615946","9881006356430112888433","6894550967248398498944","5720783360955253367339","3133479357366571682019","0755817126464870298170","1794059053760481098417"}

    9

    Returns: 81

  20. {"81943639167880630344511765281","24107097308145778373095943863","93564352364011051466939806683","72925230359382200549833397125","95851297429853956701619299142","22300983259829397402407465741","32113309814834003609763114749","33318094016802181999285386903","65913333044028096891053409670","94349760415963060174715602019","16267997741602391217031768689","22809908197610361369421418432","97947631713562492246896398087","55736612194932580231054295713","33651191471290182427035411007","98061612040318613027941328884","65786248365063237947130395391","85714698638271771393332191100","49402627455825123523374389938","61556353624436324715347663561","66677528214735059486306504734","05036706799943135759307556656","74502457527306308347542509115","34281396183639033155107062169","57277758349153940871732575874","68072100545148376500432630528","12050243543479465205451859309","32205770042276971043364963148","48433906866802223873777212751"}

    29

    Returns: 88

  21. {"328743117130160382","712131430068909014","502310742242250111","818708643392583842","193687434337364772","203452675140648204","719366594482041825","405553406479541473","337923067472237180","679725183459466922","536538934104007679","901766646162557797","494035975224290956","929009471392242180","217399807825128469","829351375949588801","329004666335984460","101697568306282693"}

    12

    Returns: 96

  22. {"6493720811446790306703371235640047892","3250210925140240629013661596794262902","2649198314814532621778001471504826437","8693520494185161362659098460410224495","2111505584391751009946980904456109222","5030059649434485989474674497426308877","3027581038771594441742433538818257284","8384270671705267916067506955662426212","7906233189496611667408524500324185408","3299327921969134967839587242823861675","3289069130843007634305847525503698328","0198840179552930649285057939687424930","7570138790157474110417138985951222906","2832551435267517465434302216554032349","4079599688784321702843825861497472242","0238471123440348008317458393117757788","5561381052601614206021114288324292675","6391863860016727978969606785100673235","9825079466437298761348592990949108949","9666218734723257274503584185853293465","6949817424778671078956309636862866277","2159606420951637535361920185318231526","8364689431235636393448865650283122756","3034976999320625591567268817149979529","1023716763115275682889574574980464398","8216719866293528646895224132912184884","6809902998655671974863073620369220648","7069300256149048532103705426206044951","5845094191611710095783055647950794953","5268401486108660527251700582364633022","6884283511862779560758239649099649638","7473841175856142104338992934630937652","7667881538652908374648500245184461032","5604311863337587219874643931254191748","6802951073516879034383819346624890472","0107968383037774219846800008763534338","9403072492459933361751197760506701167"}

    1

    Returns: 9

  23. {"0084645306704896433","0104171757585075942","7494528669218443982","4849148350698005761","5244042309351613802","5249769062780844928","6976839560192688677","4631587316406057619","8390712696151709703","5922051764512248385","9611339646849630266","1061678243021892284","3694264557418559830","2879031920605991173","9660119454449653956","7337673218718298297","0138571954093425059","9553453948696487461","2855446606305075132"}

    16

    Returns: 106

  24. {"444702","038399","345802","582161","085294","864154"}

    2

    Returns: 17

  25. {"7438215868679288788","0004857265089455973","3960716217266911621","7143166730852083339","0422562010797462746","7918353374515833902","9799909962408504498","9172470149267999338","7930070982216398415","8876356745540887657","2169916666104571004","3774937546210376703","3765872099614411067","4370592729557204533","7456882486738229771","0308049661726596611","5232204605776535405","8960218977429289237","5811854511724229255"}

    12

    Returns: 99

  26. {"1532154422322253579544813526486617118000942556","7912966483374776059881196874351243207464355353","1129198235015451169397186016110941685486443855","7620120470607278770665120959090637271925410219","1936247517316114854813417377134485970518353170","8861942742366402556608493751344288952024354893","6454566485990328641597603499102634637866951169","1224217827762370860352384868603811105984746671","8819537454090875441343470854944255302639736653","3037496278572895744517798263719162692127535878","6687707915699128719405541196642330269334528800","7933282434849883240230956812780429860879056992","1686581356745123169274712873353025128156281569","3430524877524918005501307147029108674845504039","7483554524705598370378787828924661829911523787","6370412553288712803355966900389412230854777892","2088150962021756267660173676150563022316136938","7287357536720825632566923781470771224532617981","6843316280684265189844733466545603595800956906","5622127038245220993656982044588425952677272945","3782590444438906422193506039702463115293484465","5188679164402286105286310301649371952764573383","1573974662459580322455208062819507817342836401","5015330277886641787053357489890338221585143823","4910146570975199446022679504260491176995275759","5350637682329178042633115552295970474566716592","1402108127873678996678772411408901542498395733","9379166225559381226958751580764775431210626389","1358203247097552898228172739141098637163848470","2382344483818691794348043365549144757303826688","4555447227000633462702125621407077029564178954","3408324792585405190777498471903677778091864793","7319899050989592238390145598985875268474034809","1031612472972405105715709856659748239233148386","1933927554162094436336571773773844346208019543","1065288201225508756876226774010272805489456322","4715857793552073834744926662838194508876856511","0123484029340730067694127765920974963787932410","9478064487435226572198572279632501279225984974","4094744245325549431822299073560736797997646394","4724885179737849713570877256461423828926273718","8241805570507669371742303455509014027223484188","1312853941450840895061959457798896117273412010","9172297570515435041176637721594444422358253098","9803933910344082355358277168504028355537539046","6991254214534114515088607292132504274016436566"}

    12

    Returns: 108

  27. {"152","824","753"}

    2

    Returns: 13

  28. {"932103359564163817571753800012563051","464901300749222300779233525874452542","146866889663560156047965991917012491","378968069212578928146938561599833675","387801713044473939695672976869907158","023523698835676425381554393809106338","093035204881606799337684285724969946","828513456504590007579435788055449067","571075166252896172629572436073775346","377371197611586814783245932249085579","984846949316920057045736190684748251","734836842579338088972735649480629095","218798232213103565813927425984809305","705061000942561661924180254591779447","470155783192589928073184465754574781","003185656718786642981973385558949580","512457170742748453420589371298563201","413118351789697938922964306955312479","068430720374596903907062017564596154","707354918700745961133734612532573701","166867471237259707131330185518082626","514803719731688512010127450946612749","405274688021388456220354073122479803","798605216299404559334659948576562287","624449707164455399158488593845325001","030967368906875141844035558761767871","660587306501480657523509842366353258","179067886439477261261672665185524314","980036157164200532440990742611937254","038371470653161367447808618681388144","518331666910542135387207894390045259","841228046630686080001215880220140120","962177192089303500868179716357802229","125845933117547189025932564893932874","851996267183555176055999362493946024","209070526130216781275648631449047074"}

    17

    Returns: 151

  29. {"3166934525016531936484","5301669608971056235336","4983931397238726175808","5147840825208756697878","9341005397070129288009","4804265505463637020911","1389931369973110734533","9278208061044223118987","9284251177074447306699","0753591697094706303269","7551588986412673967076","7890859426822717245564","1575361145108247571831","2757542492579073149252","7443686430184597088723","2785512468090446809235","5970664325341171142119","9867127637394509146451","0196470901917181208641","1733358066234624543285","3816829387903573449493","4416036699974214968805"}

    6

    Returns: 54

  30. {"340469","050165","711516","260510","166557","385673"}

    2

    Returns: 15

  31. {"8310784772929141809508929648","6982450554461547768236191460","3764784423284222974008010397","7878047299167184318498728232","7638841795622238634454987142","6273442290902105999279868457","3539355743535767167645590928","4216683507239398657522791753","0172413973048991189478957715","6627160522309046185757652993","8374842131165919378756466048","7693654330906875815444903776","3343294344053371993277686168","0904593300330255617577524546","8965109128650824984270586400","2305351392198216748551304058","9769256669643267451437182062","5501362199020976704466724708","1072881578515614375420946998","6828997032790501933819986954","2957082129389411920143386451","7103663528685825898648286177","4141460788876450549297243149","3455327337128908687603556636","9527055922719119891983748369","7469953118097078471175598661","9796811015951369552727425249","2221296353333940586667674976"}

    23

    Returns: 166

  32. {"40695773427668812414334545976616264899006193067","70746870411365828919858143307997422617876334940","41417977211852284230938890457363625971741420388","02833299454744438698484365992683914560728357649","62828597577751655827942653044785450699713789823","42611294425502335330074107688648572713366827267","41830632336552499933448521694808194071550120522","78978002875893712740460425054754508216755923791","28991364260507605764030669958577416028302089132","13696302891947495626350300799370850064625898178","65434045903274635169916808946969180599842347033","83045682779132317133061774046485733067413304864","00509453399158380099992175490800680806140251456","99342813749123243805253159247209074633383435423","71399065985272740711432258928780325142585374769","14733727632357694666780291487635757955720471681","04794167452870711672492981538831951910838614514","03776466473578737616270001942457626108912517281","81609945200313181489887654706979308472226819470","36480637902732316831136840578367342571664067883","07439471021232017821471602743790478059730684032","17456656663969719681547852387086023405398484173","07059078740552858982248141343365596019795019936","05742802376060497894068980894262403671231168986","33311006334831064034584691303538688061665275518","83660688997156191101091937922442727294570411878","55276647521340549973325365685557390166731506106","83338827893264354222115467196407883919074357915","12191756253452848856582065407994549211654727744","92691725537823692960408225299254828270970310585","47350523480931761310510347750729098086802667376","98404413537399386689169576551411034100751474180","51390841857633053206524215795973993626054082436","53946651376949647886816665845690627352241810077","76305095171237398904252727678855664185166298292","65483777435546090197878972343219059751453564911","80137434000294394311340412626104375162451791250","05519002123674655976347391862534498594932223795","44040034055796114088245461454478546880849001029","43459418627142276579863308105532626122783059258","97120230237216764367869736807041773900288626189","43793299580424483296646588163946387623792495817","24403017628411893535644772202685207316915246861","38442356337010786833051596718292964718404053553","77507363404776301447976514185860813044789460363","24998241526010040391496931882256917568980751020","29212601570186303336760026806028290904070362887"}

    43

    Returns: 271

  33. {"15467997068","82473222427","02157272505","37650518185","21485590254","84365763830","89597840372","98597361996","26649059438","75068398214","29732112963"}

    1

    Returns: 9

  34. {"1433463459661315932035198892111631646","6958534166262525867377318656615197056","5162899977172237118802034559222056196","7152175946442636212986835784946397898","6299167913193994344600347499013059309","2867894661926207549021381142484145777","5398951440553558848562796270969503644","8237296578163932310595245192580979532","6062278127425756624683088858882833962","5369227456905825026504765395913033089","0969380319386052760741317883813065993","3116982132885863984448042992622746396","9151351536673026924366420872497617842","8354572256558725856145224564874110068","4701908942215512790524596319623140123","8179675700247913623117006572510207113","2225745236730466154379586276562672796","2902680860275498641673720271212061004","6921935611378294430501564322986314971","1286388801961152171790541792339734818","4992731141919304635672709061848714638","2336875824370128045431482255591473065","5491509124385209239638691603867852960","1618816518885289229243357367589920980","0024368413671553615248843216955799835","3651968112400393552904292313446504342","8638709315290755914935587403043914291","1568224411582006191250083559035251092","1830269777709723230558262678910376581","3651611102215301506425091331742961435","7909980759821671450784783979671892960","4336500662126096536880221950300542094","9762533258537722807608244918707597901","2994015249431990362369043945817151218","1522653681252429821328922012587927364","2882480994987422147335155074567587133","0004117662815083786427949436758883083"}

    16

    Returns: 143

  35. {"3694","7163","3115","6256"}

    3

    Returns: 18

  36. {"8419630643840","9344465497607","2452681768719","5688079102876","5933467650485","9909074906084","8785738114433","1003367596796","6884666651125","8258066701915","6217978378701","1519446177689","0664972846940"}

    1

    Returns: 9

  37. {"826408015709894870850271536027300","522097947455348392167906374700721","521845629953468011815544213184428","883963891197495606949485775745436","900450884771560634927585410345650","401346805551820923510274095855844","836426356803701369594388587389103","527066085957114690733922078761135","588654961036846957576697339786365","766161329537288731991636416381586","173177716919164679637684225490000","280358749475807294893999321658530","121677821722206359870500650006697","864512007704953745135454393531446","150257829131825181669751212953590","751731594214305803043106313597325","712605430721471709301974540791429","243238700673911195502579834363940","290463552870734516203008821922669","197147294130922075331445187780758","642340225955908440694245631792574","588194324815013947144392523035538","890474866912148052220733775738560","187316980570169794053589889621676","417880003940173986428580062123550","577263027226004119549853322077319","995514452752023788567019706471352","033303093522719554381415017688300","328494419472411839150769685715009","936503728819277403138022243280317","184715188352603687309089550818251","521806615716523148786587389367290","767114286667911195661683229625790"}

    12

    Returns: 108

  38. {"854919342812050848776","624908891947607495460","340682880644019026182","004315125595442897550","112914203660553594823","351807910999313403336","604058906246429943234","236950088375905483692","807902706470080291045","792045887134596869274","900971389808653148979","384152760971128067241","859226364060200109337","354490023610364764642","536606919034511372132","122157411392725084109","696302634287148043976","918377508505499418410","227468013306280101053","668142733133826019479","038962793111440250688"}

    5

    Returns: 45

  39. {"6650463013004","0376275818784","4424581687039","3200643971240","9180536058339","9461785386628","7451120296198","1279882801331","3172858500516","7306839427462","6484180848199","3126302488445","1662104773276"}

    2

    Returns: 18

  40. {"1266364584907680133594780","8871835522319477331042632","9348583846524467582337985","9667093352335988131901529","5658729208463862186737480","9481534011619881513926811","7337348538042900367239776","9132812906464906667727945","6629375145389520223560828","1087703743876023817112525","4781614886685497821930600","7742036724150764788977656","8392515328268779498558133","2679783617009040536494953","5814764011348322061185357","4106490150778069886303125","7024306310817594429037655","1425494888994726160331815","3921753447243513366470928","7793008336601547881111379","4834884625241904161944140","9697757652133049694495319","7748359892914074522756014","9127211428272406300048854","7998673436438414304088339"}

    23

    Returns: 145

  41. {"671142154905976974","892554338236850773","568367861494481073","229227523558654427","595295879603628564","548668339816120996","073291270735663850","107807539769589490","012921167964484217","491260302565933938","452587092818479937","703728730427173104","794656024838132246","844013062373176288","417261280263081296","216086971666898600","756477900258110518","591672234700082080"}

    1

    Returns: 9

  42. {"416023591583","287827552127","383664543412","893709125662","574286481307","021035186091","037749254724","378038793767","649128427019","095932945820","166197777478","256537696793"}

    12

    Returns: 71

  43. {"94642021427492415363224782005125660737","51289029805597983154035423366378380370","46438547601096589197609952708845238709","80791427126133981087325209202803077021","90143839085955042665034545543580104343","94297535466001181793823244495122456248","37042657735185623528659947984463860609","96788924840248392409608168189606530510","48493582513862319925574562510225587140","69421068421324417953218239180254503074","73784866235496030547982571024300432137","93556949180269388870599082252268398309","18678918072268932464808092492403866568","14904923970258452991913286707818858543","87823150357417468237124199066047146626","30581626476388450954250206341217250344","72158460649197871619779623242018863795","74719643171271707398847142362867685841","62489224756135919816118203248813576534","57223779721608938651016610295362163660","66607038375670055125649690993743802237","02048128999401300538912868200725283823","99257177793755697914998915318605630482","30423893718600464514014344160959796304","51528870316690586691138943861028303233","59624440141080211364672542031614555788","76392312511261052763798472565074498713","98680251142064435207123638427790646101","96433262847311734781683667384244097044","65572174178884267203015348930594874831","02479802383650959713028496471790922747","81608892156017362947621584637848792491","15078707510128676209778230391038596421","48615927463107836620191346792934351563","07473781266429072640711448921435952882","97220025841701607963080855821464123699","49207380205993472593762378735988686812","52878418255005990502767473516206810240"}

    25

    Returns: 209

  44. {"3375935909004634626763182075927303125586371778","4719103151279810420638273700738839335746299193","8104372833678213098683471873545415531641898130","2227653416593716383498867538107173962283389076","2452571652036293734911971192819744291316131309","2319874356341673198031813823488785052681926934","2701809742674396141235543545642722867264877999","8353623961842888227786949198756664445749527084","5708139853721282734967365235903570881315267613","3645656939452916846240080140545590582204462935","4209803649816205174087606120414284596392147156","2313037032586911017976350259292417090947961384","9017363441301378103148523734248655991356386586","8615919619696589095723086962488430858090733969","8470344074751548014325300589670459034446475992","9840167188532489558198723104018584005202715395","4986301947755563889251383650310276827717869595","7723338421459263353920465497617702601645800073","2282276967424581310208169917396812518782720691","7479561133754595710660280314083335764866223106","7286040521956860722707373635426287371535264404","7635708714843067752090876882872672691524654544","0522712624800543931174850174712795789095774243","4723665897148338842024909104679146518332595118","2763711927859333718779391022927372656149347528","6378877596110799631276832453279343023221324854","9283463363560233237033212012222211127057517804","7670011010796566286995750846571361911971981125","4788182554852697723037158714600070176782787902","9223351858599925071894432133035099798660579479","3548645446034959002470230741473245881872532374","8448215057071972657226597743839701626918355432","7487450131509974138586643142816049370336048059","8737508711262402915241838842496877037465905349","9708064690897071860900450790595430082753638819","9710105771076447827370999510721474310014478066","4674437165434319100521935569989221351310294556","0127374140615802744402048827193413977254239826","0736844983446632419044045739459893484405993445","3205135412642787524959099355442049144967288308","4096615146590717278317822876478229225107346546","5532935220128650058499600514467092730630886869","4015675336117344480128622212521117700043232954","5340074857199091270194990820562277183690562854","5635540369760804449126194111139821807367684667","3314527955888665334987314611241328552508966790"}

    34

    Returns: 261

  45. {"487479587365307555171442268950","347844633541442422833147111834","376979426793229616471176637146","793309877018667207531036199463","051856386160538768044093575026","811430199269942415744739809983","382862588817011396914388427174","675440111331476340543335309202","912539730282863471738392251817","126869589693809996826377219695","432888691292159188944197310023","763948320849346649067626829324","802694199077005310059414352064","892819482667514428281901698029","733642237066170182614161417488","016197262432527854294884479496","307194668135695953343604969312","396838931746159548218133554903","460495282785224211620169572185","814250230321698019209777532118","552337341617938551549906739147","030395942968796756949589697612","773775282081472801625057100616","764871307157975745838900307153","354831670936972016577348542625","287931312390284508718645721402","449813482748310062222415457484","790609870634544278103312293610","581947239313934881103289076000","990847142936324795314780782946"}

    9

    Returns: 81

  46. {"00265196244000216673839487334557235595825259732830","16976128111133197284807119488870979319783892053616","41172181873535949285496725729094215461144625548151","40264996973702062326664317922704136217486545770156","06797452173607034241725944040631789866243654592557","39443472016125754934810584187820257200692091537541","33556660206879468158192543906068298374519918592525","02517425733493660276895448862494866234083276336162","93222410563339525568399711493028961136012571126596","51944359121021420768158217516182308860046957480275","85016407015275083657267473121777314913936436999902","25198352196106739208812594537360522082928945305812","16826325856189797303280143110201407711681334082623","08029948337001902400356949618054156156690216805551","17824968035155492194512200283425301814398854900664","00109226469612559265714494345530648541509823520480","78717603405785015044319629701828376734630898365092","85255761873755594060190874434385190817567392401992","52815414589034887983095380824308007515338822742915","49434827204070402548431221537520339831319874378660","98875209397767826539089238679967275006418221068175","11739818608444148381201675283101031042368010321644","46967442579759836691197201485651834691877491297377","09967507235418117534039651659847664158626206486943","18097032225612949521552686616834591511807384703288","15599714350403925671964196893251588024642668520476","98473753365296127525901047430567541764591191791970","96969512482399903895068581209914980055197722034476","98936224533806665563635496291443333675514919480283","49900755587316885578464321336615428672897260176277","90667159904395689958696748547816321934590475640139","56006861893954665517880449265525278640336448069537","25069319705741349212878146550672402754516079199473","59520391511212298790417573171678390084971234799564","77536958206016506373787767498564346316905293597283","21061611767217907339467152840554142974615037006505","01879812081416053124513940725229036704771648703095","63224216864296844238632366849922058671063855472292","55319658568158024629861543313239612828034068136221","89985853942112485659410527985978826206569827158006","02036090817379592902234295554328124610992140221962","43525297625328574393446607875305957618750051196749","81015953893412580950633482217464362283233172890655","85005517029822621290218109761589465425190819829587","80891132671407696870171195716218608288068708453822","67850634212187428297393330946475325210993296856160","31719186900128051428593124741663259772073207142057","14093694857564613359055124577391547120968058308029","30708134918562802642424370207067842888066286518001","02517456568226256437876867370606442318023987380466"}

    35

    Returns: 280

  47. {"885383345894","805848668214","796682805229","700301041806","828759393021","297334093171","688844328098","737358646599","967519712706","350806004758","280074638872","017617911329"}

    1

    Returns: 9

  48. {"9363809522510402229981599796232092334115657594","5988560539595494893314319925987620427165249849","2125586955662999188616926827800363658265745222","1398687297768275731224591152374618975518683002","5626529888721684559034245661078732965337705725","7303263443812528936517709410816672083754837353","5428631450512220301394757982542963583812930182","2631764158340163749504433658691104750609696496","1699540652856240199810677559288269322883939941","4029213533551180269388117232811953330225306097","2248033627066492323256947617355521081416428563","3809738677678945987424852366474313755988537914","3297710187743760043345310767805449804824642294","6870438276355159634313061080403726138360439032","5056420550930660536599547849701928283621310716","7803012001432612350611854221451767186169219742","8870909226413840244840541907623537591966998718","9830418975819034502768073567065631206422953459","3424443964372615103091456002570887322899551211","8161413818954915626525161058777055874061993095","6759032155274710005460880868213810770001575043","2128092742377964322436549848436362766643362750","4140160933944258760348232188610100001137824569","6778964021845783165024198539183787753750357128","0845841522962362268295351379733180075734735784","6432314628097030816411678943373413504446384861","8907418196531229023758083711899384717655463491","4128494963863097665362994450539902603311696685","4308592663041569987378078652245364642331243132","4678924707256901261300578865923613568386605958","5224046499496847360933493908348679059803880155","0235752177738012618368641711018215039597879046","4114545579348108886861038176379387465918935139","8267167811254911133551444975275252730105963947","6075809492828322379453246208354358163787568686","7178460055007172323110682920491699457475823173","2222408288028455604343067523151740232117304285","9552295157054289718857183418892631909602136766","9115560529689709567408279139992733405227665636","7644309511784708415676134390905633468901549579","3224722621854388243912256074647105629752633866","8264801432061074558598781290460273835928518892","1739609601990839832953980434479035703807416759","9909900705238975572949805337539295179058069979","1041042716213047706485919942333399237897773362","9339503840099596067606554384826208532017651874"}

    8

    Returns: 72

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