Statistics

Problem Statement for "SumCards"

Problem Statement

You are given n cards. For each i, card i has the number a[i] written on one side and the number b[i] written on the other. These numbers will be positive integers without leading zeros.

You are going to place all n cards onto a table. For each card, you can choose which side is facing up. Then, you will arrange all cards into a row, forming one large number as the concatenation of the numbers written on the individual cards. Out of all possible orders of cards, you will always choose one that produces the smallest final number.

There are 2^n ways to flip the cards when placing them onto the table, hence there are 2^n (not necessarily distinct) numbers you can make. Find the sum of these 2^n numbers, modulo 10^9 + 7.

Definition

Class:
SumCards
Method:
findsum
Parameters:
String[], String[]
Returns:
int
Method signature:
int findsum(String[] a, String[] b)
(be sure your method is public)

Constraints

  • n will be between 1 and 100.
  • a, b will have exactly n elements.
  • Each element of a and b will contain between 1 and 30 characters, inclusive.
  • Each character of each element of a and b will be between '0' and '9'.
  • Each side of each card will represent a positive integer without leading zeros.

Examples

  1. {"1", "2"}

    {"2", "1"}

    Returns: 57

    Here we have two cards. Card 0 has "1" on one side and "2" on the other. Card 1 has "2" on one side and "1" on the other. We can place these cards onto the table in four ways. (The first item is always the number seen on card 0, the second one is the number on card 1.) "1", "2" -> Minimum number is "12" "1", "1" -> Minimum number is "11" "2", "1" -> Minimum number is "12" "2", "2" -> Minimum number is "22" The sum of the four minimum numbers is 57.

  2. {"123","32","2"}

    {"4","321","53"}

    Returns: 15300403

    The numbers can have different numbers of digits. Here, there are 2^3 different scenarios. In one of those scenarios we get "4" from card 0, "321" from card 1, and "2" from card 2. Then, we arrange these into the number "23214".

  3. {"999999999999999999999999999999"}

    {"999999999999999999999999999999"}

    Returns: 999314005

    These numbers can be very long. Don't forget about the modulo.

  4. {"20"}

    {"18"}

    Returns: 38

  5. {"587442411746014", "7391939024138512", "50980017755152835", "488662892723915792", "7026824218386174856", "52371452738503046620", "7317861954444022766", "923007240569260396", "40394883764710929", "2944922081700832"}

    {"337900896168224", "1680756932473764", "60195764231473580", "492449859170499416", "3439143338368292504", "63371534035998249791", "2992684350669004880", "254375621668899054", "64240381324840589", "6750847231270874"}

    Returns: 198073141

  6. {"2","22","222","2222","2","22","222","2222","2","22","222","2222"}

    {"2","22","222","2222","2","22","222","2222","2","22","222","2222"}

    Returns: 243348427

  7. {"38","380","385","3801","42","422","4222","429"}

    {"38","380","385","3801","42","422","4222","429"}

    Returns: 995836693

  8. {"10000000070000000001000000007"}

    {"1000000007000000000"}

    Returns: 0

  9. {"62781617619181","1301414442311","811500941155219","12456703076711859662856599","2438831","239868694546084","7607178524907898817","855","342033340340221322004102","384168112235101959635686028","3180152241748934729698457","408049392375402","3140242040232233341002111","7248568588284010129837","36117114499104828","1012020","10101410342103022402132443","2123","5603","24420311321131013020140","759919230348799129","111023320","896715441896709341680950","8936351161838736667217201201","21041100440100311342","10011","3031312233230442","4674809","47184425731945678434","200431133431012","312814316","463","186119","2301114043320411112302432","6941912627","263","67539284","411123","2434100321013","2033230343200322340001","558825951533","18750940239708730","21012","539481358229418","601138248590571752","444422422","213443234202330223","4430402000314043021014","2210102303133430","7136","344","431431231333414011404032012341","20411034423122","7556946543137349543","95142208084889062514938322","30133104330220230","759083167","3043233222242244","241003343420332432401410","53328746372654523700320","45298857325719108279151","48436124978396950359790","27161581620189740668944035","4234230301402413304423142433","44132997219510549198276","2220131142","712241939147369260249770","140816857183","1041232230231001132223","6682469798406187","9680039940334494189402","57329043271977624288938","44401314102331340032434324","2333030142222233130030442","7391398","204","5729952139508567020","44793152667616258575109","789036425313120653000479","2102204241213303030302111","22412000420","414323131411233","1204142204401","6123437422241101","60055045790127","52087860041235098356992","88728911470370650357247","8806071853160","112403120021243201014322432223","3030411321033423142010","920148325","5220134177","1240","8016252432037957324650","82494231295149759687695503","68733852130114917394","951040754734505981122698","441340330123400340212014203144","516743","8106"}

    {"334214243031","984734485504515182604909","42332024","130","23300110223423104","312231344313211200032","1412300","22001010221022","261081158376833055991","420021120444213140340344032430","22102431402","4242120","730425284129","42342213214440324340024040","3313404413303400440114","66382377556028688277791496","217757452519691102147","1980002045768906872419184","331202224142231122","11407215","12444210414211344","460569705670426","43230333024212214031133242314","33013","31897162849383","4815286791093609","4061209","410121023012344214201130310444","4242222102400232100433","6073434372986423664","3300041123000120012424342","401134024402104233321003210","40301102114144","731820737347450464568354","2414010","1000032441200344330421031141","200","9626520289744162396","427182919290657263183445","207046642","42031444","2241003301","430088515079588185","12330043112122214303104","400330120","460577288904237876046537162028","43050191071724472922326","3482483905625478","92980950078907907744607","43343304110420300210010443012","311030003343223","467738785","776","102404340124042","203103324031140410134","39928610936947026488750640274","3301024310","82150581208838486276884148468","5746967986668736","3304212332040240131331430","24124312214411433412140101","3323114401431041113321111123","133213423031411142232340","27506367571591662809184778","232340","490","1110204022412003334222","20002","76826288975","414131221234041333202","3213041401141","1022104","8050272","2588801480328402","30004004","4446812714","232244413","32143033231422420040","1422412112232321004230000400","919684890183649837028880117","98022286264","40694359275975153471084238","80453356591562","12322","312113011310022211423330244003","3343211323201422130","13414443","4014210140140114412","907","531498459","103122243","31013220332414301240","52755451654012502881112049","21321","131310","21310000100112044311","14310204220443","126542534101420297","40300130010","4124241"}

    Returns: 850009687

  10. {"1001010010111000001000","111011001100011010100","1111000111101100","10011101000010101011110111010","11000100000010001011110","1100011111101101000","1000110100110011100000010","11111000010101001010110","1000100010011010","1010010010100111111","10111001001100001101111111010","1001100101010000","101101110110111111","11111110000110001100011","101100001010010","11001011110001111","11001101110110101100","100010110000100011","11001010100100110","1101001001111111","1000000110000100000000011001","101111010000110","100111011111011111","111000011100010011011","11001001010000101001011111000","10001100011010000100101","1111011110111100011101001010","1111011101110101100110100011","1100111111010001100110100","101110001111011010100","1111100000101111","1110111010011100","111001100011010101010010","101010001100101100","10111010110011110","110011100100000","10011111101110101001100000","1011000111110000100000111","1110010100100011001011","111111010101010000010000","100101011111101100","10010100001101010","101111001011101110110110000","1100111011110011101101111100","1011101011010111","101000011111111010011110","100001000011101111101000010","1001111101011100","110101101111001110000","1000111101011010100110010","1100110100011001100100101","11110011011000101001","11100010101000100101110","101010001011100011010000111110","10001000100101101010000","11100111011111111","111100000101010000100010111","11100001000011011110011","10000010010101110001","111011101111010100000","1001010000110101","111101100111111100110100","100111001100000","1010110100101011111110100011","1000111100010100","10110000000011101111","1001100001100100011011011000","100001000110001010","110001100101001001","110101101001011101111011","1011001001101000","10100111001111100","1000000010101110010010","1111101101110111110","1010111110001010011101011110","11111010111000101100100001","1010111001010101010","11110110011001000010001","1111111110101110000110001110","11010011101110110100","10110010110100010001","10110001110111111110001","101000111001111011","1011000110110101101110011111","101010110111001","11001110001011001101101","11110001110101001","11111101010000111100110110101","1101111101101010","1101011111111111111","1110011111111011111000010111","1101101110111000100111110","100000011010000101010110","10100101100100111010","1011011111000000100101100011","1100000100011001001011110","11010000011010000011111","10001110111000001100011","1101111001111010101","10000101111010001111101010110"}

    {"101100010100001010100011","101010101010111100101","11101000000001110111","110100010010001000000101110","111011001100101110101","101001010100011110101111010","10010000000101110000100","110011000101101011101","10110001100110100101","1111010011101010111011001","111110011010100101010","1111111010000111001111101011","1011101100101011000000","111111110101000110111","110010110111011010101","11011000011111100011100110","100100111010001000101111110","1101110111011111101111010100","11101100010110111011110","1101011000110110","10010001101100111","11000010100011100100110111","110110011000101101111011","1011000111010110000","10100100110010111101000","110111000100000101","1000111001010101","101101001111110","10010011001110100011","111111111101111101","1111000001001110101100","1001101011111110","11010000110101111010110","10101010111011001001","1010110010100011000100001","1001001010100101000010001010","1000100011011110000000000000","1000110010011101","11010100000101000001011011","1101001011100011","1101110100110100011000","111000000110100001001","1000000001000010110001000110","1100101100100010","101001110011000110","1100111101101111101011110011","1011101101000001001101010","1101111100000000001110000","1001100010111010000010011","101110100101010111011010","111100111100111111111","100010001100101001","10010110000111101","110010001010111001101101","1111011001101010001100","10011001011010101010101100100","100100011011001001010110100","1000110011011011001110010100","101101001110010","110010111001010010100011100","11101101001000100101","110110101100000000101000010","11101001011011100111111110110","1111111100100011111101111","110001110100010001011100","10110001111100001101","1000100001111000010100000101","1111111010100011101111111","101010011010001100011110100","1111000000000011000","111000000111001010110000010001","1011111001000001010110","111111000100110001001101100","100011101110001001000001","110011111001010110","110010111101000010011","11110101100111100001","111101100010011001101001010111","100010010101010001","1001001100011110","1110010011111111","101000110101110110000","101001110001000100101000111","1101011101111011111110","1110010010001111010010","101011100011001000111011100","111010000110110101101000001010","11111100000000111001110","10010111001010010000","100100011100101111000010000000","101101000011110111011001","11010000110100010","10001001100011000101110101","111111000110010","10010111011000001","1101110010101000111000111","11011101101110100111101101000","10001000010110100010001100","100101000110001001001000","100001101010110010"}

    Returns: 540493430

  11. {"11011011000010010100000","1010111001001111","1000001001011001011101110","10001010101000001011000001","10110111100011111010100001","1011100001000001","111100110011001100010","111011110010101","1011100110000011001101","100000011111001011","1010000101000011100001001110","1011000011001110110100010100","11010000100100011011111011","1001011001010000","101110101000000000111000010111","11110100010110000101000","10000010111101110001001011","111110011010010010001111","1111000010101011001010","100110111101000101110110010000","110111001011001010","1011011100000010000","1000110110010101100100010","110101001011111110","111010110010011010100111","110011001000111001000100011","100011100111100","11110101011111110","11011011101100010","10100010101101011010100110","1001001011001001","110111111111011011101","10011010110001000","101010000010111011","100010000011110001101011001","10010110100001100011110110","11000100101111110010","10010100100101000101010","10001000101110010011001000000","1000101011110000","111101010100100010100011010110","11110100011110101011000011","1100110011010110011010000010","1010101101001011111","110100001011001000110100","1010110111111110001000001","10001101110110011100011","1000101001101100","1100110001000010","111001100110000110000100100","1111011101011001","11011110111001111","110101001000010010","101010101101011010001001000","110101100010110010011","11011001110110100001101001","1110010110000111001010101001","101010111010111101101110010100","1001011000111110001","11000101000110001001001001111","110101001011101111111001100111","111011111000111010100","1111110111101000010","111111001111100110","1011111011001110101","11001001111110001111000100","101111110101110101001100011001","1110111110110001100","1001010101101001011101011111","1111111111010001001","110001111010100","11000010101001110100001101","110000110110010001101101000111","110110100101010011010011010010","111010110010000000110","11100101010111111100","1001110111001101100","1101101010000110011001","10001111011101010110110011100","100000011001010111000101","1111000001011111010","11111010010001000","1011001101100000010","100100110000111","1101011110101111110","10001011000111010001001101100","1110000010001000011010010","1000010010101001011101","1001001011010000","110010101101111010101010110010","1011101000100010","10111001000001011","10101011000101101000100010","10011011000101011","11011011000110111000011111","11100111011010011110111011000","1111000001011111","101111010101101","111101011101010010010001000011","1101111110111000101111"}

    {"101011100111110","101100100011001","1001101001111001011110000","110110000001011010001100110","110110101100111","111101111101111","1101101110111101111110","1111011110101110101001","10000010111111001","10010000000100101110","110011111011010101100010000011","1000001100010111001110","1011001110111001100110110","111111010000011001","1000000010011011000","1010010111111101100010101","1110000000111011011","11110010110000000","111100110111000001010101","11100111011111000001010000101","1001001010011011","11011110111011000111101010101","1000111001000110000","1011100101001111111110011001","100010010001101011100011001010","100111110100111110010111","100100100010010111011","1010100100011110000111111101","1110111101001111111010011","11111011010111011001100111000","101001010100111","10111110101000000100111111000","1010000100011001000","10110100110011000","1000110000100110110","100000011101110011010000100","101001000010000110110","1100100110001000101100010","1011110101100000111111111011","111000011101010011","110111001001101011100111010","11101011100010011011","101110110110111110","100010110011101010110111110011","10101011101100000001000101011","1111100101110100","10111100110100101011111010000","1110110110001100011001110010","10000010010111110110","1000111000101100000011110","100011100111111000010","1010010101101100100101111100","10001011011000110110101","110010110000011110101111","110101101010001101101001101001","11110101010000001101110100010","111001110011001000100100110010","1001100001101010001100110000","10010000001101111","110000000000001100111010100","1000001111011110011","1111111111101001001100000010","1000010110000010000001100110","101010001011010111001010","1001101001101110111","11110000001100001011011000101","110110100111111001110","111111011111011","10011100110000101010001001010","1010001010000000100011","101001110110111011011111","1000010001111010100001011","11010110000110101","110110011000100010010100001","110011011101010110101100011","100110000110111000","11000101000010000011010","110111001001011","10101101001010110","11101001100111100110","110011011110000001110011110101","1001111111101100011111100","110010101000001","110000001110111001011011011","1110001010011011001100101","11001010101011000100101101111","1010100111100100110101","1111010100001010100100","101111101010010000101010111","1010101000101011101100101","1010000111001101011111111111","11111101100100101011010001011","1110101100100011110000","11111100111011101111001","1011100111001001110","1010100110010110110000","111010000011011","110101000011111000011100101010","111111000111100","110000011011100010001001000"}

    Returns: 273519239

  12. {"936157465041100493627654672891","743014238016856098084517799622","805282247603763654967524154980","443824682002689248085099899770","582773543423787273844797824101","890558739433101710107218002470","432771322627113405772933349095","797620602538196888276004369326","855281278291422551718043249214","757735464861380675199549418524","789503901364795549630505608316","121824241841308215889902008691","104687796827746904110137535191","183398762017329888441360381792","413937830014880806967585526351","324478972046437293893007959850","917886027065652110049518813439","472892362261673471145451206544","793100266983975660322608516395","701090093973252487550069506270","520442439905503547080869483710","940260756044791968636666555279","851807416640037076592906093616","684397580411351672651952636927","475324000782978155101464528791","756982304125041009142688272488","880000035344001562289351234452","869547882629390775440056590794","438951504876780143014218891226","874947862503468328857696666790","613153606438961153573372167671","227652193195775759658232828297","395218717311377511698144170673","221347605326167085896975553316","641263557447569113230685241285","660706602331010263849595357078","940684061395240445751732316598","544898334931133803722116585504","927527179283411839317384925145","807605485573667403001299305400","493444131156539772059201831977","540009438428728071121158431482","651839743918266363900676304450","207686083715922938224300488629","927166062646390575656497908013","756574381878545132396882257425","306253550980979725475871056047","573386787880100535825926898066","980594152667205899736934995021","955504540225132321513364238158","657378455816256562857617090095","242541584686894422277279498514","642861753631305283582839662479","358957746552830836974298753778","570515450699169997313081742334","379147306781384415404736392814","105239149077322706163694536897","345672628679900880100060257560","221259120273785886974831754565","263290966947590810797347821478","420717060603516554918469579542","581993781634069128848476907693","123047096326421592885767629877","221220732414850997008988417649","113576760997586907994669298192","975015532771495382554359456029","534280401564307551425199218119","745535283355606450472203581947","742208120329528892533020727935","121342182234249992478787002406","262861008633750764429067564196","993728278240331995803400707607","822265994442622475018319398354","393031576193570299143370415857","968414022823783408111680752678","858151383761496887508510639805","473910875587657706858816745600","341735648994043104833492150718","826578692272156901238174387867","602440797984668539708783860074","444736513726925097478893374304","324968766244697350164912117453","540554383049791652867437210927","568224914825249659256045061389","420188435006848461129298716114","421667015900447985130929726665","327557501115842408445010616727","144171052486098539287561406486","527702916495471488165305240352","223082636933868981121806759938","428598729602464821258989979835","101480450478408290134081970498","848124936569065795070851583913","733457320496436327171323458345","412268911991527712317984858039","114713918031166321403450458555","937976100020232430556581795573","719808274933594816810575245317","290184741965973077223711523942","188543852299187357127766212787"}

    {"986099441678555884409166922721","638736524891166786767846448543","380422970444865884533182425450","272523758959321168837006393081","394221651334731406504067734310","225670824545272584277855091655","248432048509310800140421450372","948538485655756812121645271636","756840936074761887164711656110","773966512262479855541507849748","608398691284202041034773915841","509444676087855384043686358714","133903152189566794877012238399","636580384533152876633720312123","257001833222450400676679779151","223287083074419011285545777315","798785551680281487865859374322","747258168872978445597711681836","610539460725839918848295631851","484863525444660136917485303741","182322606562760885146704676533","488064434535413024537708389960","399593880640011793599800408888","129476153941907970470263215097","627906525112844720277260045032","686031858636350225259619381518","362376641686954049513659642479","484170369657751992615107377839","697172305340424493722463463189","750632786046564488610880401729","102273505717304050188057887948","834958485230621455466706089077","826986393640809884967712346538","791836027969819801406623262303","893435963646000508087710577240","556086924289562939077378274733","298045537276866469289225531858","813167407823786801707352935060","272002108989443402870196426846","890255829657142187879528472317","425386571875791715257426651922","310256585983272156625344766534","780891900808905555072538185679","101417237081368433385555030889","694158748689529297323177098738","728179385772356666121833074448","639793619467223377000790170089","347423115384828681408725742282","929980064931770582417440811156","696221983099472846500511335501","564715369877186083553677638388","823865798707830620727022503286","853194840219106204374456943237","317408571927960816025329062289","461681201293224004660862729620","434874108539639728716050457134","430931575488821846866845269751","597878036715341124116770207355","656606220228187471622642707246","855089772025282219518367153808","364916276937153274061135699751","245210203167210856832330798363","342370772597492358756505510665","416728748635072444789896293637","593538435965262723584187398145","112422969766011374718234602721","335862641762602523546079871875","269981379534039991448267428256","377377316831010785946011313143","466624806881355392310154186626","724234262389242701149445219782","873495774663425124261796672164","544966789227899325197741106150","995810755381587798667491854935","543874684387086652900359651999","303571473048070869996332982779","800391292341728373703916128995","858164717681244070894296113070","513055285330631442543271765621","151414997935695786030418594995","566485317241229918209029425001","606353625550410547127805716860","955385305247679333058775888114","487663631276775483358507767046","234547954592585550182889341043","901738146813784860949143430779","929936020389724051229251397471","956802496254205527757948344695","986898407625660136114466270501","159830940268923998120305744669","131932620632133836067158365837","274516125852439359782715439790","163649734590373336983833624611","282280000228062315112369632629","435607019623154142586117191054","742082591589449780117894502198","972447459976328227420177141742","891585147044238555361355791481","975067470759847621275338500861","451654237186596675041288690175"}

    Returns: 316186946

  13. {"42569104623458771322","623686210531504844134605545335","2125974248202312899","439760263891149242","136981652333266085","695827102","5581120421749134","5347667711227905932591","27044927830737195388143071328","1109123833498095782282666341","35724254746659120562516039","889869640452924","64949446388381952624048","15989090065154871454","87733774828946353662","119768357","3744848447649249483","4101881997121801","526692304807965671856432981","1955125999180470901422","5888","1731048978262054","3136188739366","8583152464765618196","282087154874463","654334640","2900225762423","546278190078129890672","6158038329693108436","7623990180412631507390273138","9606752272932227730600991","6840248299642534163061175981","4121684722740975516573203","21720926822030234","2906426995","812303774","19250775528030155","781713083070752575469798","45647334223422489","662844158615101567496266926","64937544045306419252466233","2510525124484937814708461","9523023173870749052692","325454800868004692240023","247488114622","3199768","4408035899444723470","53424045379652","73","9020619077991336709114004","728570363973629743227499676078","1902307426762505","805871924939992521429797234","448755934850924743213037201","45285283905349635589032","121765609667979528781082738322","9667825692133545141897","6627","6777162131020156133462599","9727408085174821414377577463","925050606810024442022251196","681757084547688809727830002","28435","72649254317244996339005146400","66508952224843202486957","970254399101272432345119046","149241462006623553637","9114308767567769107417","670916262100697088003560822","54397481792720044251220","63829579699991099","3413220","978380824972928672529","31260449385449961047","763681058483715337170734419748","50057427","22939640524223444987290","44169612970195647889","24519219853638182","2397370238165330454443485110","902381495746364737","6084044","3110","41922113662209912779521","412162536711031485345","177717654614744548","436729998493069579888801","79596608331062431215229964","698116770025690057628667478","61987762","1513748","4166419292868942314","2658","57212111465347374333792017","61519395522922913177259953678","7441453739488873007669413","87968778151591809011812060495","656593871145793956686683","6863033836287207703910277","451850404713814011408846"}

    {"34747574796923582582496131","957997324921015","8352","222","770765119426403","760124748182519399965827467311","22803849477606389156","5886361765449668222590404535","2542591096844027838499","10099815156915862","45082119712655823","9543830197515451831","1062467411637164616193644","5677269704091218212979071810","6850500811","796278933828781187740326395","60","834670743905424729039","59187268483246585587","91268969936863480446123652350","5122558466176820255002455","5696083490727492256174088","37443651605328844360994862","1241574395625010","97057306280462617208876057945","790731803818220073264670323439","369407061412512","88989729148094571530","6645220393297212090827693","1045143668608384","479434127173","521740482203653","157396145752","13070775","17602869286007135047962","14017914982849754312","515599327936060","3027088378359709537727763","136581312907397","5832444409327498","7532852812913536333","15707051580460083232727077","9850525086691661656776","729072874744729","480714652709439454483","1324998364095211813391913","1323098489402228","940165289878336046826803443308","6152166387374259673001665","4155","25662558309472335147592676","8475066410141868374697","213135416547147207013452","40104538045844421","8693337276710665","78474725278440605811171294","547592802106909367","8521060984156075198569210684","372831126900876105","2193360673791","267107731221","49745911382457147601","5015086637023734202932133337","5562659758908699253478386","4911333","7025731","3986356979490554","76781015994982070019431558","24298428872","416482679760619336","208115618881","5657319060229448085663630","8","460707643837135805548815","3329137943265142","37675358238065404","47073896415","9802667517773689","84510097521240994659463280","77793810504174225","184041855","87756781401035837655","40128266813581946325","254586873456864894271432234","27283934828888280","3130732468503039721016","6352062195985947472849161255","46238484885","13970110844398398","485005911085835720794","9167259705186758","36155388532185217163","221878178793059893","52799859857840221","4832649760981116236182014364","8204612021092808494","4064954085","1","928436805052837288296","199354599430284598286061693"}

    Returns: 610178149

  14. {"62234","27","170608281159064870779257","304154","98197947917148357","74224290","306239252028","28372108761773601","6935026488","7631001947228126787989950833","3347","860","144454669420050664006390972","1584622614494","901089978","3078014261986682960","304824649440922742043","47271265480879269138","584543686064285919301","3076914281016553677","36","7867","7","386124","3720125983086","5","287","431603200595551121018541237","239836214215522","19339","8338644945991451819187382","26708926767826131643","246","22261","30494722012751512","5621162905957","5149","1916","423440","150712012645","3305966714608272556179733","442","8868179614737133037111535275","4000449856","3678373772106097138205593275","671145181163077695718230415","1388878411","1806164305062","733689851","822499219","9615946","9936819877297026732","9231832851698040549197588444","386482219020383203622270904","7620375784821067","98033343529765247147288","95278736411367845819184","1908358161322220839905848","779261","374409998848558919013021866980","3418944642971280129958627202","44933256769346","9","85113561","8979","7875880385868","83755976669466159802440405","3704635757729277","9779085185198","9897472017032199965553568376","8703780","2","8828284255","512337363","396223123731383674","79896352896290753002531108","90184060014704728768310849899","8008879148027556095268","4122732029160","7","83717","830813","1574835","67336135522792210","268002269635","27","649722106476","609441885352464","480975747","986633200578","279920698666336661","35698878094511671689916582289","17919283870743123","69310371650939308","835687385333454900302282","3979911670710","85","897787944513855403392511619528","331399961019428717818","88485124159728"}

    {"466807033610","898350772179694360379","91710457","573","9","21147493986511660514394837","300801754635013350841540119","5334218490305105043275465846","77353389","252671391909240244740865055","66081717","416514713063879131281","80286","9363386152800157","3728081","690624853630374359324134","904394589391815","72","32","758842360856420596953705156049","34446123575778","2156745528304759","7842437257424261051457","29","41403540237574969463667312374","9727831518242178920826","6879614","749173282","18570951673","126238912280943788","8252598885683773197661525895","92665532317075695545","3167504750995395081439088786","357721573180070834995018","43646090252589476738746004","12166012422","126181717","14367746334391375279975160","2139740988391","9363005639735096157467","20110","648321435635380601","245537","8254869091","157384993095538029487037","265405559104692589736173750344","4328","29770396181804075350990887093","4659925623777570024","101807451381554","245771109868812569","16514075413238591","4","91721653875507840","9305877745818","23572949805123","9512005279134964429","20862313301073170105592","388896731803642023892396904701","3794818732327660153894","80939","4450047151972273723967","73414017362488379380","31450071","9845","975924280745197963397851","742750477254760040","4","3684350522","376595917949","18413937271","715161","755639847223425399547918","287007","7","3002702054034","18765900650111548596923","1309124755702767619","5422171609334094","2957","3533816813026560215049","664162848821","9200206390337597661","1677057786","45856","707850386015148","4876734243941520999652179579","4","555526864530286826862175073972","129260660755236393","819469811095540","1709747756603664601","9041493086","8476196292041421242966","13286","61","412644702428763715669667","6770393648550","834","79758269842345429611"}

    Returns: 926667571

  15. {"20765552966817979709376572644","271269218734","6912334364116511551077866148","48803372443","4332703654","51088796673944678900383808","6151689348881352640493207286","362557891481856176109691858034","753811177672597547756625","42827070386463903511466722","718114743580","904544416723519799287863831025","357833065302008","3794484511390672398283690","641621277592325","4752924244873526639712780702","29432957322566","22882321351205361321793941713","49590975455010","3459989879210827875805253182","39624906303630199661902768","2749821697295258120","13908395620","72139003082111109089962834282","5705323018465452862797","97900206741026205469777993","412174996345118","59281344569189750","30005250694128145458576797","8096854665324951184","403244093911996685","5267143452011049968074577330","1585895265044","48609107975328644","91055307781654345657248515901","8711464683858","21118045619139","3740959634","879456665348","877730009640172659371313","1756539482120980650","160008804475031917683349874155","6510483031303107874177459420","2302168193887106","44733644697813286648","343555025409","29737247567","237399334705859366111","8055610451221559908","17069135174928293767086678","5957530912","9345843835502","91378366331606991845770048","47530038666506","29174197427662919239","67468146570698321131114","817430702439515309","8519528904284281872549","526508695426536","96854280054094115456196278","535628366306715877","426577524534901963853226","6606196123242918145","63671550068341152321","8760517575297509","80124818200402800673518935777","392834150948442","29747236000352796411047732","913958788335703466107","126533322134061232534114654594","100626155606644935644792973","79705837458233","8639679584631734179179585987","56082226889","6687049228739222985163","151075556400984563204","192001603254","338415469248155651468","66579694421994517007","3147494945435936787839017","756066007320660625802639","1144275821359789424365","3309279301168296","7463964385998270561484135","3550589151768738999227122","99615869539329455444","379814874263","7327125890","6870872527332618773829942","915587210344886","2260186015","7997893150936682616498576346","4249377418838275600","71794034085","80689484210","999993435047507619","8401564681596","7880087133","763738871354","6784541204950037283800282325"}

    {"14359158173880752","539730459188546","66665628648896329","89049914304186134330753191305","24708504097380217","1517663981277","57026831396140931362","50927992308865149651992929","7299918535146385968","894722904901","7406866611","627941628256","8388502430119254","10025766090411","347540133044116766018752170","3314482199240368534","680826110722907895732400983","1901257466960680","6942646640983303627500609","31800267850249749075","42144968078034073829","606301673229","807121790926471306028","448266143560246140","33710765770315260","40361005898034318918","5774038703650","779343361536249404562328701572","96972182000","12070398965453984873677","77158533378534982655740413200","27525796434763209473585","4948059006951048018021741280","820121627710","3708763632331","202823118316767624109984","527777601864","3783357595012322125360464248","36737441101100805","231797445058490423061931282","8977577373","43348530449709394","602694540772676","465027519064818122011395","5273651100","110149055033209","184208046821462719","84817963368533609259782143079","96101701537889183","481501424592011419367755","627081069986201457388","554923933488835223873616","70613086355783130432286466","222101569759543863927280","5371739579362732614634086208","451333246715408","2583149659819042581417643091","1287574019269981956","36682121084","85195636864838583037","88585931256275590","846492476734333063020","16902396065194042136306","96293326619168273594201813","3365879749080899096","977531973467241780573120","50893612616","79914684525874088790213741874","478322326017000","36174519039821754952723870211","632289744262027433890","547099909422766432925386628923","65242905382","52342978766987","46485207270111543695013342","15597471784","4708193135824998327453727","55816258134230853690","37671653363","483003979724953159122111828","91049146083117244451822055","55595351548535935729","5529433766497437447196","4176138130323","756633122408026582603366618299","1112229097813311595175","79982657927400397893619921150","270356420314488335702634","14127809542643597937569365235","7232032262229033674137280","94353932356415222861969527","115761180411","3674099503136596751115","71341711909","6024306432265903703994","5804202372360643649529609","83011781930601669","882763184885783203427803","857314112331225743379659517","774281832489231843955629866"}

    Returns: 904956021

  16. {"3989945324744479343","99745994820580723190292","814333638283780034910844","731787210980411359274780","908310325041337","636095781956476322629528037328","87352494755369927311","483","892852987227549756","835325450666","7185040","859101040951899543278657334","699981725994253455","47716278500185160758152204419","67877822971864219","521589032101028","8667301870638533169414096995","846130516958651","180880697859207198742018800","507850","8083944539496875974","385756834969498684886","702381706232644814892561627695","9334587019717874020907","719253506259","92","6","97999645","9544688916763364849598315","8998869327310659775044","2703494584549838915","7687880511343397145971433113","324907090119753973","701311589890597","2126716","695861153019179041152899503","9182280530303248","131510342208419312750110","9231580416226908070552211615","694877089916118961348690393206","80460032957","5600744937","4753327327106319519286451634","4489399303489937244439362970","40259727173873351738752","570477104994448280","22871770293","55661925921799687772023","579512","1019675935919","62768099617368010","9776033281","15945974691087072867","1218405769334","5435363040807","175855924282","2","972033","852040","2818707","5786446","5634700686","955519726895895147717692","668862247731698821156900739","6924082","457642118844869604663854","25990277079","720080","918","1713","957715537165840774","9663","37006632","33346","825252","25535334289494","14397","9566379702","82635821447755376723","171174308833086284179845","254304535408568","495778826156419104959503","61473739382806098","822714381554356204011957756714","9836727150","833012884781257215646030276","35336259549220462226659147","348","2874591390","48","797703780479401004153476","30165171112423726603477","741300903174809","88217927305","780612311318","3799","889","3123","923316059793867937","3146634594642014"}

    {"42918748106938882447","40909050022682","8053626588034592945562131132","7866411165671978580161431","62311190089427908","74007005","6545","41232249569","36800304287593582","58881487647796085529876","195699","8269961892700","264803458048","23268","33359799358843","9959215095029","186626207504933125775388462905","175636679340092468178","4906626388933","50544678339152178851948","887722798192799048996","540469","5","14916017476802243335982254617","583261445254616","697182693577671959472430249741","6631133","897199","30455661734945","79125419402","811165500","730079523781273654","864323236044560277283602535","917729315578928","5452181","9087373163564887313839","6507346","220910982483","5","87707183108086980088121","626150835378","1358665373","92273782600470718645304197969","1438547868040139104235438","409478116718","70963180715621825055223","763065933495881617410487","16220213372678241","827278044513445358022259","309459763833988385934882","572736286429650173854903099558","491621698488171","48493887629942437708","7997812828805856","4848","344680300776673306688162810111","701605947129440","785157","775","84718174902806569","2525972544","52191778707578","103420581641623","79436701606741383630987225","5691330383879330294699879568","5","80398542177068026278682","38877959627946","845","212502587166173","43633415175657577887","97397232696632179688","3896","7445426351318536106548","11900312828","7417","5459995486012905877495","4173648529747280779813","34335","282414334406831168301335","1366605489456298580349","61322884431543950042","74378095050038181997","30756338","9060323565","989204","28348039432","4989300737","26918118753688834730947","8055900280924455866","286424178781","409230","87","839663555376838","4333340858903","378653","8185943119","37777943286403427740","99118114234044435264416399","1671448"}

    Returns: 445353376

  17. {"30","63","13","54","458","896","6","502","8","631","24","3","5","36","56","63","720","73","7","51","616","2","88","96","35","32","39","865","49","927","8","5","5","7","9","2","3","87","1","51","552","136","363","24","7","28","150","81","27","368","567","259","58","9","746","88","570","16","875","95","681","81","64","674","512","2","82","42","563","1","57","556","22","22","511","112","62","239","64","3","142","7","80","790","3","93","4","55","9","647","9","251","69","1","746","433","608","9","936","82"}

    {"145","74","208","703","46","712","154","13","4","2","56","4","754","4","554","8","4","354","767","88","299","727","525","20","462","879","47","7","243","54","385","65","79","9","2","50","226","9","71","6","85","37","65","5","3","5","8","6","32","98","898","272","320","318","769","4","5","952","244","5","253","31","765","551","14","6","217","504","5","6","59","699","84","10","403","56","85","864","11","7","15","715","872","23","7","9","1","711","85","357","9","580","92","72","36","9","7","8","23","6"}

    Returns: 127283489

  18. {"10", "1010", "101010", "10101010", "1010101010", "101010101010" }

    {"101010101010", "1010101010", "10101010", "101010", "1010", "10" }

    Returns: 348141541

  19. {"936216398164817152014247627258", "93043394206193760798237700099", "931638377905445423737202342", "98249023287322431816243174136", "953156819267407413196939828", "92134326738587558195003982", "9072396601474999308106572217", "9763931661243365535327013055", "9734212520825343311477917416", "91509315585879878339072833", "94313241179968967831497024138", "974721952579171041698031021413", "96430120899752163602765029578", "96943177779334486516562394631", "9245594681373174092170896512", "9038319526224418081894645673", "992787923996021557973440111", "98677588824169417673000879036", "9806405659074802133234003963", "90545471413389175832628372319", "98034016816730169519412579733", "942022529719082302847009450297", "932007287080996004858272256809", "944227041261451654967814825232", "90972349815725342032327227272", "9851689687825210751194476304", "918619970203461143292463794025", "980526562361902309518227118", "93131158884745335216873424", "9742542794516193860266909997", "97434587746564124617705328548", "95309988335085363841275296", "910630485873192968638561053552", "95492127737633104924718632", "9775332923177463542204328949", "92849373184078805275194181", "99422573673121674694763780294", "9787879224456046408797301742", "9258812671110688233708802362", "93503814356294900160103496594", "9563514852009664360511802261", "944292706504699502599249348531", "97566601511353093973375410210", "95660356028096222221751413", "93985691013082723592936183", "94510581165213718424418951390", "985210994249292276433992421", "91039572095033668493357431", "90153912366555643823949904", "9158818279920488565390957453", "985625851363702647233960796602", "9182634819217925619699396427", "976276067329116173036739893", "93096204539374316635153902967", "9423883334291616482763896050", "91815227993748341430198339", "904551324400399356587197297837", "9595545698881975533705405148", "94750910860334840359143239", "91445612568463224325005774097", "90726505635381792511321120048", "9339233408097778480209068391", "9863592573994254460375298844", "9051228174069049182842604571", "984346179105531882748208085940", "974411019695109391873174363", "93417796959626728487346439782", "9292983122157716728598002507", "9584677898551643284310067547", "917823149591412382304101581", "965099312133845258335240846863", "968524567374468899097643614", "920404753490451044954177887357", "97442199880659260059757521621", "909118587215387991670095557154", "943932962308932830528317833064", "940353742806926457194923783116", "92689011137990140952549423", "982076477434871608253782144", "96067008653919898290065856989", "9668572061927179568363105674", "96767630565632005455060220986", "906532722260569920940212725", "992483394485477744215446993", "924559293325847034552371069523", "909794253501503555646581590562", "93161956164993652626916593", "993737576393250117251325390982", "943522594845267610527415102", "910483408601874249207074199994", "995532647148511260807701510420", "9860457384621296358311241543", "9850676586938596190306038765", "987056992807486902557528232", "943976087446852687420556208552", "9210958840956399100917255078", "985094484656137478273175143", "96344068170671020520228772", "93484203437808647960098569", "92000281560161188954977792" }

    {"936216398164817152014247627258", "93043394206193760798237700099", "931638377905445423737202342", "98249023287322431816243174136", "953156819267407413196939828", "92134326738587558195003982", "9072396601474999308106572217", "9763931661243365535327013055", "9734212520825343311477917416", "91509315585879878339072833", "94313241179968967831497024138", "974721952579171041698031021413", "96430120899752163602765029578", "96943177779334486516562394631", "9245594681373174092170896512", "9038319526224418081894645673", "992787923996021557973440111", "98677588824169417673000879036", "9806405659074802133234003963", "90545471413389175832628372319", "98034016816730169519412579733", "942022529719082302847009450297", "932007287080996004858272256809", "944227041261451654967814825232", "90972349815725342032327227272", "9851689687825210751194476304", "918619970203461143292463794025", "980526562361902309518227118", "93131158884745335216873424", "9742542794516193860266909997", "97434587746564124617705328548", "95309988335085363841275296", "910630485873192968638561053552", "95492127737633104924718632", "9775332923177463542204328949", "92849373184078805275194181", "99422573673121674694763780294", "9787879224456046408797301742", "9258812671110688233708802362", "93503814356294900160103496594", "9563514852009664360511802261", "944292706504699502599249348531", "97566601511353093973375410210", "95660356028096222221751413", "93985691013082723592936183", "94510581165213718424418951390", "985210994249292276433992421", "91039572095033668493357431", "90153912366555643823949904", "9158818279920488565390957453", "985625851363702647233960796602", "9182634819217925619699396427", "976276067329116173036739893", "93096204539374316635153902967", "9423883334291616482763896050", "91815227993748341430198339", "904551324400399356587197297837", "9595545698881975533705405148", "94750910860334840359143239", "91445612568463224325005774097", "90726505635381792511321120048", "9339233408097778480209068391", "9863592573994254460375298844", "9051228174069049182842604571", "984346179105531882748208085940", "974411019695109391873174363", "93417796959626728487346439782", "9292983122157716728598002507", "9584677898551643284310067547", "917823149591412382304101581", "965099312133845258335240846863", "968524567374468899097643614", "920404753490451044954177887357", "97442199880659260059757521621", "909118587215387991670095557154", "943932962308932830528317833064", "940353742806926457194923783116", "92689011137990140952549423", "982076477434871608253782144", "96067008653919898290065856989", "9668572061927179568363105674", "96767630565632005455060220986", "906532722260569920940212725", "992483394485477744215446993", "924559293325847034552371069523", "909794253501503555646581590562", "93161956164993652626916593", "993737576393250117251325390982", "943522594845267610527415102", "910483408601874249207074199994", "995532647148511260807701510420", "9860457384621296358311241543", "9850676586938596190306038765", "987056992807486902557528232", "943976087446852687420556208552", "9210958840956399100917255078", "985094484656137478273175143", "96344068170671020520228772", "93484203437808647960098569", "92000281560161188954977792" }

    Returns: 282221991

This problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved.
This problem was used for: