TopCoder Statistics - Problem Statement

Problem Statement

You are given a directed graph with n vertices, labeled 0 to n-1. The edges of the graph contain values, and each time you traverse an edge, the value of that edge gets added to your total score. If the same edge is traversed multiple times, its value gets added every time. Values can be any number between -499 and 499, inclusive. There are no edges that connect a vertex to itself.

There's an ant at vertex 0 and it wants to get to vertex 1. It must do this in an integer number of seconds between 1 and timeLimit, inclusive. The ant must make exactly stepsPerSecond steps each second, where each step consists of moving from its current vertex V to an adjacent vertex W (W is adjacent to V if there's a directed edge from V to W in the graph). The ant's goal is to get the highest score possible.

The graph is given as three String[]s p0, p1 and p2. Concatenate the j-th characters of the i-th elements of p0, p1 and p2 (in that order) to get a 3-digit String S. If S is "000", then there is no edge from vertex i to vertex j. Otherwise, there is an edge from vertex i to vertex j, and its value is A - 500, where A is the integer value of S. For example, if S is "100", then the value is -400, and if S is "999", the value is 499. Return the decimal representation of the highest possible score as a String with no extra leading zeroes. If it is impossible to reach vertex 1 under the given constraints, return "IMPOSSIBLE" (quotes for clarity) instead.

Definition

Class:: AntOnGraph
Method:: maximumBonus
Parameters:: String[], String[], String[], int, int
Returns:: String
Method signature:: String maximumBonus(String[] p0, String[] p1, String[] p2, int stepsPerSecond, int timeLimit)
(be sure your method is public)

Constraints

p0 will contain between 2 and 50 elements, inclusive.
p1 and p2 will each contain the same number of elements as p0.
Each element in p0, p1 and p2 will contain exactly n characters, where n is the number of elements in p0.
Each character in p0, p1 and p2 will be a digit ('0'-'9').
The i-th character of the i-th element of p0, p1 and p2 will be '0'.
stepsPerSecond will be between 1 and 100, inclusive.
timeLimit will be between 1 and 1000000000 (10^9), inclusive.

Examples

{"05","50"}

{"00","00"}

{"01","10"}

3

2

Returns: "3"

Here, there are two vertices. There's an edge from vertex 0 to vertex 1 and an edge from vertex 1 to vertex 0. Both edges have a value of 1. The ant must make exactly 3 steps per second, so during the first second, it will make the following moves: 0->1, 1->0, 0->1. The time limit is 2, so there's time for 3 more moves. However, that would place the ant back at vertex 0, so the ant should stop after the first second.
{"05","50"}

{"00","00"}

{"01","10"}

2

3

Returns: "IMPOSSIBLE"

This is the same graph as the previous example, but this time, the ant must make exactly 2 steps per second. The ant can therefore never reach vertex 1 because it will always return to vertex 0 after each second.
{"0550","0000","0005","5000"}

{"0000","0000","0000","0000"}

{"0110","0000","0001","1000"}

7

9

Returns: "49"

In this case the ant can traverse cycle 0->2->3->0 and earn 3 points. The ant will keep moving along this cycle and finally go to vertex 1 and earn another point. Thus the number of points modulo 3 is 1. Among all multiple of 7 less than or equal to 63, 49 is the biggest one that satisfies the constraints.
{"0540","0000","0004","4000"}

{"0090","0000","0009","9000"}

{"0190","0000","0009","9000"}

7

9

Returns: "-5"

This is the same as the previous example, but this time, the score for the cycle is -3.
{"079269665406","506042219642","720809987956", "315099331918","952306192584","406390344278", "999241035142","370785209189","728363760165", "019367419000","279718007804","610188263490"}

{"038604914953","804585763146","350629473403", "028096403898","575205051686","427800322647", "655168017864","582553303278","980402170192", "620737714031","686142310509","092421645460"}

{"063231394554","109852259379","740182746422", "853015982521","476805512496","898530717993", "430534005863","440162807186","132879980431", "685312177072","780267345400","959947501200"}

37

1221

Returns: "20992235"
{"00","00"}

{"00","00"}

{"01","20"}

99

10000

Returns: "-49352"
{"000","000","000"}

{"000","000","000"}

{"000","000","000"}

100

1000000000

Returns: "IMPOSSIBLE"
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100

1000000000

Returns: "49900000000000"
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100

1000000000

Returns: "-38900"
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65

290729814

Returns: "4072397855708"
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86

330528635

Returns: "IMPOSSIBLE"
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90

346187105

Returns: "1373497338767"
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98

227226514

Returns: "4282916812439"
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57

712693765

Returns: "-2734"
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Returns: "1783004040378"
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63

678205406

Returns: "7733576232669"
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86

326931094

Returns: "6551045255653"
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75

655974267

Returns: "4132637881422"
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100

307098561

Returns: "250797157313"
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63

952260737

Returns: "18912612431273"
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77

779150783

Returns: "29137382397870"
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15

950614000

Returns: "6792137029970"
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{"09","80"}

{"01","80"}

68

892634439

Returns: "IMPOSSIBLE"
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{"073","108","740"}

{"008","601","590"}

48

25044412

Returns: "7813856518"
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31

244749674

Returns: "3563157535071"
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78

767534570

Returns: "28856229693699"
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{"001179429512131754615","008632405005039023231","650219163780088304354","527081725156730823773","593508852127846663034","514030226911616194837","225781053108912946426","544606707614950643377","378619080326180918785","046544107099267806882","263382471204160936053","967835815850968241632","096915477909057904939","799393920370203140519","648337586995080012044","316768183570963025904","001202344907076805860","342428697959173390883","882078948553177554074","325698907737877786206","470767543208664664850"}

54

123081193

Returns: "3217957790920"
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93

322467240

Returns: "14664842673346"
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58

974826362

Returns: "27572638706940"
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70

9118543

Returns: "311914960718"
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2

837015982

Returns: "817764614288"
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9

91156580

Returns: "396667857784"
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13

225396689

Returns: "1369848377275"
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69

134996197

Returns: "4568878789292"
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11

287037387

Returns: "1500471993918"
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78

720140434

Returns: "26891844156620"
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34

271390303

Returns: "4299907960629"
{"097701248037723668660262543908177160284219181","606744648484013027918632675786703599176034648","960086162590460547595696458714396094831202260","214028695771260524586656188100025187048715851","816406424986769999363253632080520687449160756","877800312861301206425411812411292990923231561","603467010931077319438358882317125259021136435","186359308618451743917637140424078043556620485","862373040677201643444079545942010853593172822","289525925010161701809457508459691586968219427","718990058702887373380360164470857958179658166","013363620630828626196887775378148274910138410","472101901880051842226965266541967680909919725","021243952680305764333242451779149354705341354","042576012259330846240909052667138575555679492","779325515530908073371146614608747631888033353","562991027818290106482011803456104723955323427","320179472774030850024573227773957258164011953","372804474896784081092803743882517537702442529","481493603199497841801458674292508324570701617","517125361350070420280463380596783854039843545","369793759099240038315003892447112902839642554","157532812294660592082209815432205770391445583","308228170074737957436760602257281283576298135","434021398178395233351900074265730080515498391","463799220559977741771922608341477004116331053","720437348586510857579983720894322628911618473","673368159906395029281004165090248174977768724","604196138191952298235624590409487628602103035","759931200645869709473355585000078567081009657","274589424999971979735655965943069014808269258","987677155725586912835417263300301937801578845","604935209584319323436418597572050264738853617","900157611018993615353737514075765000396608807","935208737022163032994943705685590303011613037","787036177537885840865197450853544470930628996","044674226112810677034927081801407084050912032","468151690880600836007872965380548674703571400","600991181820675793309166615875038049160736955","834967970557727687087691466153856444143041810","107179165090653311875248874287217946853607265","098328092691643417797157803551072804825090535","981260351149306836566704066130840166123430038","097374932294055373986567901426327074699038403","518367124714920303575532642949402439363955570"}

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{"014177703176838818281009541582655374064574259","204208039246651770243983539493087609422546323","590354703631145275263250675259696843213778803","622034978476448157235687816727873296705554219","226905263051421699341420586220334726442840182","263110756951935458727182520241264117284802195","633637046564986410251654494616892149615381999","550708906552699057100519864893700527506173543","448350620152910849864131324150586190618053246","232318041018569386347445625179533076458890648","796530277905168174606490979097577652187958685","592165724810192189057609670356123374122362693","821957737896082365608349782329459971460758836","062522679549809294983819618196478325561557977","116506098179910175850006723414185262542645364","471278209093336087651288824380944888563773609","269126264157705709147924652318622233798361038","008112016774927980943470575188690674894171012","284390657815345314049187240080123088184762837","481537767491799724204206143983467295762658565","685027568194685923870236072569335388783486322","491629545262630676306010464229743652179721460","998651915981524490086209516952772650361732557","714914798841658135390530970297994233672572281","792247272761901620265824028152181024798437256","484808556799726134368937909263749708783452362","523186767256374678568547880434051282271065538","476184869450493090238657054052767648488304009","059153750230077265920090040504246750297811331","026687009900515231838079970100540806609698896","968598889778501556638418398489009884764772767","972450045120124124024511190386207673173547050","211483828052167940827146711418640190929439950","721449610009435531942065108013297033221542566","813353875428408752635179325781583802832508882","081808371086245050181584745745164240629649422","884487492361918589342014990933121781054399910","215011551810729072400217946857971482505983090","402157371540109708414452960461432769600677008","297494758490024931470066045745896737133027220","689093995878237905073546898842801920422902976","457727473043241679680904344763300373032560698","304020021294751387510542888479401823128269093","428294319949844530749902106795338179731647604","121428037270440595098896302970604767882710070"}

95

988816391

Returns: "46013746741431"
{"0573553618868564713301141441","2003580855419295263836268573","6209762010215056907623116854","8030397383714738433223908429","0244006967796069752516050443","2053009961577548156021494299","5558950527415793547574298537","0671127014466228919483240869","7144123505826284828820968202","4985620250480064683385199386","2386777359050498514904434063","9047276045709166338189791164","7611735574370885013846856846","9526309692349079878391988563","2600874604583903002182941331","1006286284846410782002313739","8842944592411827066936166610","9850634028497731003390105821","4026101194598568350365714925","4098710323732183039088436107","8125826617659124352905785851","4812656138990677791140653434","1112596961594695872751088864","3297628090696967348826301361","1407826708818899697342450600","8569811614206387169248904014","1061818991174724353381206209","6832038331342450042509057390"}

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{"0551968834639059879991145053","9013260378152517632529431645","3600872190340275429392566711","8970524503945079097751802369","1523051003655071599610308798","9460501206336814433702873925","9947100416748671485048319706","2108024073536330190538064095","9977188908248513146477643649","0785675610340286237563221985","2623692471093429767382341885","9967421792105156598667427873","9515733675760618123794863725","4248491964443091064099598976","2609035075283802841149669710","7074536659268900640024460346","4194823478156292010495609145","3992621033672680203964003775","6012313776999278740976283885","1549440603970782839070569207","7882157093153473761105624682","5225903118848275734200343006","4946660170483597334008073009","6012628296423471922975509856","3882485640681223782004390384","5623902342109387422792092064","1258730030484716644508707002","8483628613646887270037617400"}

8

36929744

Returns: "142007175337"
{"01170654","60180928","72051081","55906439","46150787","63426022","54126803","86463540"}

{"08834659","60592934","55073185","96908554","81880122","89444038","58233106","49138230"}

{"03071380","40244180","53081134","64200636","48970890","19271072","47211304","46010210"}

47

840951317

Returns: "13649200508839"
{"006194","202714","440380","331046","602601","295170"}

{"043375","909782","340893","826008","488606","005530"}

{"041779","208016","340135","627044","782806","808650"}

33

718078271

Returns: "7393333878115"
{"09073004730086805263","20038138700989182286","93071159403057187215","11600252004065558829","23230096960211691855","05123087185378813921","08122200158830542151","23771780227539561902","35230597090214703871","31006972309274917068","78019689070832164753","18437849647043554613","53259665050506101886","96271648011380754612","13839649859666083940","95120996379883804448","54540229715702030304","15203253610764237065","86735966418923149300","20329093560068995970"}

{"01381405576198323244","50927287193276858285","85011614868303243420","82300108801651364998","06630817344752904023","92679093534514397127","47124503696947304319","04477800882158082636","24239171070370938718","71288106506111654763","06353656640941392122","07131418087041376851","61778107341704807149","05979008784040501514","26853464178275044466","35498068221667402288","61776522178824230239","07335001421414180082","40138372617836161306","47053107125477527910"}

{"00729756919494491711","60262851479589420278","38007941871117671443","81203138352245044108","97910889723172417747","21947066117397300389","32449801060653857514","94343070321434880863","84470957082021588085","63826406708309966971","86590948760722234875","54507495013039990904","87371594294906048790","51187296388980525606","32671477378320062781","53933007569491008446","29302528919082110711","79063105049689113085","27737550952221286600","18524517677414143610"}

44

505894488

Returns: "10248208180004"
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{"0975051885862570057834","5058399856265972070888","0505053036481430547164","6830982162087713038999","0343088225883393612030","8033106325220771523203","7431060501701134976511","7000823005909431083354","6891889502222530783275","3184368610430560475829","0743638123044319918253","4294881601909546029375","7068176349090067184395","3691712007906093368078","9058352669128401961142","3026505793810740511112","6977151215817499016975","2747558862481297503801","2083991066362218090646","4605559572970272498024","6569589157837584651905","9178337464212281316090"}

70

421406478

Returns: "14056013073343"
{"091142211","409192150","580370103","385047218","535907633","745050022","060272072","127068901","341126400"}

{"001282402","002705428","790838971","504086188","226606719","989620149","155142040","218028804","053644550"}

{"026248861","301485889","980938908","436007461","085008332","670160007","011813087","668526605","417271630"}

99

310563209

Returns: "12590387774457"
{"0687401704003893319985260976355025","9088278691270501710238235180804594","3403422541723094210065593875446900","2430717889480012010591070514224470","7417041882115518577696850292959955","3404200851305454133010069257442996","1602460506244677091097224980170796","9325022038698597827541159288477060","2217647205595589453570618455271415","7813859570605542011092049786048628","9767624441091314534938908512394482","0504151262808651245057838169708135","2997013411360553088961090972987527","6197541897340052151470669960632594","5811910774949201078255241436805453","5839826532684670282927262852390970","2816461829206709063891278630629967","0436510542312497408968933917803709","0842018459710469540957461153646556","9791738601877722891026433897644263","3907989076061252590003304381727368","3372299195210490515030151255181916","8598427241400473106379072492806491","5987603744913223071155606846607766","5355722343687215522200240887683436","9154388878599262682619516039173796","5313390161399758141292822101790365","6987223354322336467661082790325886","9581148590945781460590861396037445","3569330534304470621628779516005353","9685660092459624806804777594940702","8584503048932335215684334740753052","1902408493956477137583977042317602","7067138423380095045363089531413120"}

{"0285781924747827470022829353504924","4093507093775445649851008359843485","7605687056710297294594630534875553","1310038639750499071434407104861197","2900073141302201376916847325654393","6901207459702059772357201777326808","1228600952369256702452721486366370","5797749022979540985479527176003271","1508622709255443983067094696925252","4397688830428938254954515137753128","0949944562071197714186701698100031","6431889353607030458240529442667823","1531569826080663499561607093976201","6384267865650034100283094303133518","5512410185111203471970321666139984","0212322065408070916249527130248671","7162388848848754091563298413300493","2160965061037458201461212542702225","8476172398035076440995449841263879","5514063068586350345090676725202179","4310618667204458168705567087426589","7958947869236042127600589443191060","8722600533158562242923046678076275","4115268795742196681949801781628172","3241233719148809123025020864871025","6670973887980892304006880075490966","9878156065064206828616904301447037","7104013739381064835527978510877560","6009572530637032706613766533009482","6776049212137338119488131663006776","4361402827552396534360638156820257","0631013970429095641636642356524060","7701218452472948221118343917577506","7600656815229144455209702452100080"}

{"0114895947140707359367583105315248","8027312348518265201171404147981765","5208952705752294501662088798066738","5250996583702174440660669466149114","7155084856084420616772841677888271","7293006024689650449943010711738923","0837080368243489496997280383377695","2852230067618577369287235794556294","0163233006153019930965634102731355","0895191460457541559122555948173893","7476712160093340272657141179658025","7828347532809207564408616781584074","5771424825340483843904572852479927","8333925552155029812461746994108002","3337104321041805543619338960961196","5977329525822370590545551657989558","3317282086213836059105382070956909","1731930683166718103344761786578686","0275253771464290730462730417478070","0545014473812008460022283920750955","3077514028228095217409063238253704","7710412257086707478630198013514903","2075391229891760525836087940550100","8530854953329574189786804660672979","2980397720889417686280140293683632","6565258458429389127434637053016571","3468405267325238073668312604831265","0622149181604624080043227370073579","7924034126889409415957684659034034","3766180989821084570558116160109668","3513513617815274441352988120880833","0613974656305949096485427407333051","4821289039525645385027979622195509","7735840714408936551448422843492180"}

46

744426370

Returns: "16505421475531"
{"01953405418185239271657999139826","00335950490775106399157066395133","37090662252939055555602880305531","02003965140379527192916008305056","38860971211503120444552550975154","43202014425220570916468240338402","93617005423673346272853015373877","91620680403278734909864079443442","55877674070849605704580880445087","55843429304705301107898890235224","97242781020908401738848638983308","30092976217049172121969518693021","52446512921404316639511221934158","67406910952510780331842283130298","88406337499126094926988164304712","81688125834952900136226380804838","65643880816798890127343646770501","37772762598588379056212168030753","03197870670159450201335615648321","35222304997248818050360978746067","51205722819077895149076064800060","69285107938105112273104488401471","28505624772809112497750173786479","65491235110119341939602046222612","26837175485614958017611207360972","44273368065670738747550030465569","12195576743313043902683619036615","83890568202547781815590121608875","80571151363901804719222343040191","90783844100221347088400954115013","71056090112633900189581655873900","22278290503168261542243909794890"}

{"06015054007543481547963273362943","50661617724489060709693988453496","16054262106886878670285373028437","71202604912710681481686271210857","58990493628368169740658820240017","79876092220789140813661403645854","87273201762663923058610145981065","03078280502367381341971219420605","63553930098375668120313752172990","52705965006081960082515368652644","18245320380311273275891371955590","90455778271048334719722095041763","66911801072408782513238543716479","15048850944340238742190845572063","31471243318750024978280145619875","10112555985845000690980047869734","06718295371138430553435683664318","47775963364694059060516311075515","18296359815539781508694207202919","19107576513043024520247476879800","91219987491734770204099165956757","88197207698554246740605121379248","12922129047593039709350378640008","32066305544157316238703041101101","54131536003370889019742105536637","30161829042615426735499840430270","69340181344961687334933779010102","99561862118379978222177176407061","17878642973264133575955041610124","39229881954211364161016058681004","69618691556789353434443613416405","35343954622611986513176989517980"}

{"02616924586067355028335145298906","20690714321580868006564609008004","47044471914606584583347976076273","66902365489108802505854021019402","09140200801109924721596539768371","56400042043265309030848507568831","41561208463658159480250958418359","98652830656427576988339389797268","37489335002129615896125626643823","49748285402681508594841567122155","74525722440127845362325803137583","24841764305087525809324239587082","54096982509308475486720172759951","40366448949240321707640822593656","15173513772127033453003027530286","55728453325564802865160107937345","09420093431905940651911238177612","62802818259376312004325655942676","40472480931200532609804479343111","61736218170390154940299880226367","17565704076388634589069771997575","87052976964442387088709562770257","22994063927572071179080460332589","80077060189973964035032064528320","33022184293169335381625408266596","84936012427896142425262740433241","08056278796504648293577242077440","62121311029734592008785129801541","27260871011867569789465506610203","49721593826695376156743369181033","73294009837622999267000579673902","04401602430074265632652344137350"}

30

709210048

Returns: "10393473253259"
{"0900235","7057519","1708616","4600021","4941004","5046409","3160680"}

{"0207080","6046658","0109420","0820768","6993098","3300300","0259000"}

{"0901175","1095561","3302484","4170433","5550047","2405507","2868530"}

52

590922991

Returns: "11072321056766"
{"06460997522","00792476873","56065260770","73605374358","55670004801","27782014213","40926202277","15472690859","97687013044","60552306509","36683844810"}

{"05983773107","50972625881","84074435073","25302820232","11110303983","28793034044","56908705010","33164760987","20521056021","08710885800","61590188060"}

{"05483803686","70065183143","32058379259","03609641909","78150524050","59407079915","02863403453","55380020427","48680680059","77374837408","29589601230"}

80

283046860

Returns: "9023533896756"
{"07733730928494323735985866","00999828752714654058391349","23060122033052036760335585","10904486968191324608654335","86250776760368337648984583","35768046582288161459906546","72143608854723405885956506","52226190024302458371788786","65237889033542888180551034","93361929308646691334132535","28631026590063901540331787","03056784318053434698591151","60530243499109660626250960","48273546096550295336997735","00797835230778006752969297","49414135924961101308226970","06145906541778800478509827","25514630788684227010790180","80994819356186166907139041","85315305212221897980626225","55582889295512024278006726","54508076758639856561501788","50652307827003073613660914","07507357020539576570755038","81605024821100320071550302","20976767582606439730372350"}

{"06106640667455413876539604","80511187285855614360773541","29009267700889296241156418","19308551772941862763150413","58110292332805777631595488","55817046757971206101099732","44782505867705475448664986","08791150585030819735112770","64752570048353138181100037","36914270904262500056104485","78874512740811827381884050","45603284270070264177995296","29034291995307155147312409","62601533787070916646793830","16287461264717079578687243","13698825124785905196968658","25569874682509830353068257","31796531190984869038813487","64702433342975088106494343","47885542354989333220941759","17673111998552806918026148","08196315988091900652408169","18725753961278377380200296","55481592237902074462761006","45764311915427684508872206","70400047713245182501307110"}

{"05900187329636327753463646","90766871701180410066485330","72045606382483387487199157","76202951396912516992299988","07830551103257865778406508","09797069744415711168923913","32294001580561425853776856","08991540575176776259895650","52637237034109876073961341","13890842609283139440317500","49193408410925304709149589","01654813008062613758165064","12570774358406369121937717","07205940410100677636995018","07598597714854038769358084","17141040758247207103851542","01120549782942810217954377","35989300452214196005188315","58906931032332887009130937","03747295413344378620163082","11506430277682096332062154","41762273990522719493600105","68795459111506496040950957","52964522418867070596295025","53079923987631049938928602","50322878049262379900962810"}

3

313739950

Returns: "440255584776"
{"0188883231913","6005448139359","2907329957737","0500363945699","7246080501533","4383203258587","8916600535093","2533289081734","1591098101077","2429612080742","6309233314073","6549736200306","3692536387320"}

{"0288355712300","7084987715651","1206919438273","7460978168778","5512019531244","1871206610410","2480260093214","1794968026769","4206738100742","5430646930634","4370151574016","9209143606807","3486221650980"}

{"0503447149150","7098756682575","9801680553899","7230651820807","6889035443713","0683609242827","9321140882678","1326051001150","1865682701685","0633521670559","1624874150063","1024709794004","6325175247640"}

35

755911284

Returns: "12752223360932"
{"0900235","7057519","1708616","4600021","4941004","5046409","3160680"}

{"0900235","7057519","1708616","4600021","4941004","5046409","3160680"}

{"0900235","7057519","1708616","4600021","4941004","5046409","3160680"}

99

1

Returns: "43629"
{"04214110401010422141422230443240131044","30314134023114203440134344223444241301","42032023024134223313211100143124140022","42103002341101332134433104414403340302","13140130124423403023414033430202000113","14223003221421001131231403200333223430","40212104212023221431131142310040424211","40411320313440041430220432424132241422","30310432002142130012441343032124434300","34003134400112321311323244343113031212","22223021230404040444200120301031003200","44240442411002102440211442412422331033","43204422421102320020104042120133212421","30301442322040013102403033413334104440","01420112423244024423033334214101330304","42331032442144102302033334132431101132","41310004132324100414341224001230343410","21420242141234424033134021432002431101","02441302223100420300122242320043042001","24043313030342231100403401244412104003","30321333111240022004011043110323123301","30221214203402222320402332430034343000","11434343232002230002330242030303122033","12244044244403000443411044434424013423","11003021024112000114001401120343111141","40314403423030211324044030014222340411","14230440203222324024331004042100422021","44012331320310143140233034200144204344","40211203343110143100321411130404304231","23232042113410433324421111220021410330","22402312321312003130010320423404210011","13101431134024032322412301211320033224","13314334333422331412141113110023030003","31444311302211004332213201313312400130","21440323423420130414422201114134240343","12400003230344234440220321224102310011","01033303004111303134301123203013144402","14330402022102223343214202043211310430"}

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{"02203404112144201323124001432224411403","40143034201341110241140134000203144144","03043304021234024100402132421230211302","42101142334204314411030232141413101212","42000420201312014442213223004213330442","13321041311220033411412342102211004431","12444104402030414221140313110041132230","14030000431412004033140211040340443010","20441231040233043221043333441402233340","11410410401034022311204433311101233132","24311401100441322201012331324423334143","20121100324000213014330410311414311234","40244241022303240223234144232111130024","41140442301030312203132210342341024424","31403203300031013123441004024410421220","23020134210144002422443003201442322133","44224430110401030433334441244044432323","22404003104402441033324410012432334044","02221143231130041400104212241232430313","22133410111210324440202100102420443224","03331013343432113431040312201102100011","10120312442324024141402240340023440110","40133024243314203323400443300120122404","21334113143112111221242012041010433421","13423130423114004224331400240244043221","23041303434300114011220130001423223314","14340110424413303431140144030044304222","03134212111042204301301044203300033020","12123432343144112103403424400430304203","14123412042440041110011031324032203434","22014102113240423100404021010000422040","23133023143313414140322343343440023003","40203222103014303222212100330040021203","44123134014433141411223410143124303132","22203332140003421302442211220044230413","40430433334333232141433442443222210022","00231022224432020432032204421314042204","11402040030110242404442201311214000200"}

77

3

Returns: "-4418"
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15

10

Returns: "-921"
{"03","20"}

{"04","30"}

{"01","30"}

68

9

Returns: "IMPOSSIBLE"
{"044","003","000"}

{"023","103","240"}

{"003","101","040"}

48

2

Returns: "-11562"
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31

4

Returns: "-1949"
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78

10

Returns: "-4587"
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54

3

Returns: "-3142"
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93

10

Returns: "-5523"
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58

2

Returns: "-3314"
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70

3

Returns: "-4014"
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1

978804267

Returns: "978781265"
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1

10000

Returns: "4999"
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1

30000

Returns: "14999"
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100

1000000000

Returns: "49900000000000"
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100

1000000000

Returns: "-49900"
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1

999999964

Returns: "124041661715"
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100

987654321

Returns: "-1247500"
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100

987654321

Returns: "-2445100"
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37

1000000000

Returns: "17192666666629"
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{"06988987789998789897777978879999797789887979779789", "80998778978889977889889797897779797879899877989897", "79079877779979998779777879799789898788879878977998", "99709898797979897997879989987777788798797989987897", "79880999799898798798978778789977779999988778899899", "97887097977989998777979789978999997897777888988877", "89979909787989889878797888888788978989897789899987", "87999970887888798879899977797997878999897998989779", "79899879089989979989897888997877979989998997998898", "99988998709898988987898798878789897987778878797889", "89987998890888898877978799898997888899778988979988", "97777878788078887977787787998977997789887997987889", "99799897897907887799979887887899978789797878799987", "97978989998780999978987788777879999788787877978897", "98797988987787078888778977998798877979789787987789", "77889999997989909977898787789887779999978777789778", "89999799879787880799797878879887799887988997997997", "89987878887987987078988977977878878877978977899787", "98888978999798798708787979978977987789979979899778", "89877878779777777990989887888889897987878798878987", "88979897998977787977078787977878979987878978978788", "77878987889788799988809979879998997789778988899879", "98789779797787878797880988799798889878997997897978", "77988798799778977777999078877877898799989878799898", "77877797887787888889787707777879887788778897978898", "89778898777779878977977790779899989878788989798977", "99778888879787777897787889098998998878788877987999", "77989899789997778779889797907778999989887797977998", "77987877999888999779897989880889899799997898979988", "77977877899779997878998978887077878888778897988779", "98977979797779897987797997899707779877889987779988", "89787887798787989877978987878770898987877897979787", "79888789787798898997799997977877079987979998789888", "88779788888887979978779898779898908899987778799887", "98998778798799888899999799899777780787799999988888", "87879778889989877799897889978878878098989988787898", "88779887799998997887877778998777898807798797777897", "88787898878978777987897877788899779970788979999789", "79998989888888879877999997879788998899089897878789", "87889779999889797999979879778999978979707799789799", "89998877888989999988897898778788779779780777897778", "78789889799778787999787878787777797777898077797879", "98988777788877798787878978779778998998899907897998", "79897797997779998788778978888979787999897890797989", "87888877777789999798989888788788978997879778089998", "87877999778978778797989798788899879777977778907888", "78799799879879888989799978878979978997989877770998", "79799898979897998979878798987987977778788877788087", "97978889897798999887878789787778999888877788999908", "87779979797987898788789779797799998997888799799970" }

{"06988987789998789897777978879999797789887979779789", "80998778978889977889889797897779797879899877989897", "79079877779979998779777879799789898788879878977998", "99709898797979897997879989987777788798797989987897", "79880999799898798798978778789977779999988778899899", "97887097977989998777979789978999997897777888988877", "89979909787989889878797888888788978989897789899987", "87999970887888798879899977797997878999897998989779", "79899879089989979989897888997877979989998997998898", "99988998709898988987898798878789897987778878797889", "89987998890888898877978799898997888899778988979988", "97777878788078887977787787998977997789887997987889", "99799897897907887799979887887899978789797878799987", "97978989998780999978987788777879999788787877978897", "98797988987787078888778977998798877979789787987789", "77889999997989909977898787789887779999978777789778", "89999799879787880799797878879887799887988997997997", "89987878887987987078988977977878878877978977899787", "98888978999798798708787979978977987789979979899778", "89877878779777777990989887888889897987878798878987", "88979897998977787977078787977878979987878978978788", "77878987889788799988809979879998997789778988899879", "98789779797787878797880988799798889878997997897978", "77988798799778977777999078877877898799989878799898", "77877797887787888889787707777879887788778897978898", "89778898777779878977977790779899989878788989798977", "99778888879787777897787889098998998878788877987999", "77989899789997778779889797907778999989887797977998", "77987877999888999779897989880889899799997898979988", "77977877899779997878998978887077878888778897988779", "98977979797779897987797997899707779877889987779988", "89787887798787989877978987878770898987877897979787", "79888789787798898997799997977877079987979998789888", "88779788888887979978779898779898908899987778799887", "98998778798799888899999799899777780787799999988888", "87879778889989877799897889978878878098989988787898", "88779887799998997887877778998777898807798797777897", "88787898878978777987897877788899779970788979999789", "79998989888888879877999997879788998899089897878789", "87889779999889797999979879778999978979707799789799", "89998877888989999988897898778788779779780777897778", "78789889799778787999787878787777797777898077797879", "98988777788877798787878978779778998998899907897998", "79897797997779998788778978888979787999897890797989", "87888877777789999798989888788788978997879778089998", "87877999778978778797989798788899879777977778907888", "78799799879879888989799978878979978997989877770998", "79799898979897998979878798987987977778788877788087", "97978889897798999887878789787778999888877788999908", "87779979797987898788789779797799998997888799799970" }

99

999999999

Returns: "49400999950599"
{"079269665406", "506042219642", "720809987956", "315099331918", "952306192584", "406390344278", "999241035142", "370785209189", "728363760165", "019367419000", "279718007804", "610188263490" }

{"038604914953", "804585763146", "350629473403", "028096403898", "575205051686", "427800322647", "655168017864", "582553303278", "980402170192", "620737714031", "686142310509", "092421645460" }

{"063231394554", "109852259379", "740182746422", "853015982521", "476805512496", "898530717993", "430534005863", "440162807186", "132879980431", "685312177072", "780267345400", "959947501200" }

98

99999987

Returns: "4553732741337"
{"009", "009", "090" }

{"009", "009", "090" }

{"009", "009", "090" }

100

1000000000

Returns: "49900000000000"
{"079269665406", "506042219642", "720809987956", "315099331918", "952306192584", "406390344278", "999241035142", "370785209189", "728363760165", "019367419000", "279718007804", "610188263490" }

{"038604914953", "804585763146", "350629473403", "028096403898", "575205051686", "427800322647", "655168017864", "582553303278", "980402170192", "620737714031", "686142310509", "092421645460" }

{"063231394554", "109852259379", "740182746422", "853015982521", "476805512496", "898530717993", "430534005863", "440162807186", "132879980431", "685312177072", "780267345400", "959947501200" }

100

1000000000

Returns: "46466666666629"
{"01161", "50556", "54044", "54503", "54540" }

{"01161", "50556", "54044", "54503", "54540" }

{"01161", "50556", "54044", "54503", "54540" }

1

20

Returns: "2099"
{"0000", "0000", "0000", "0000" }

{"0000", "0000", "0000", "0000" }

{"0100", "0010", "0001", "1000" }

99

10000

Returns: "-148203"
{"099", "909", "990" }

{"099", "909", "990" }

{"099", "909", "990" }

99

1000000000

Returns: "49401000000000"
{"079269665406", "506042219642", "720809987956", "315099331918", "952306192584", "406390344278", "999241035142", "370785209189", "728363760165", "019367419000", "279718007804", "610188263490" }

{"038604914953", "804585763146", "350629473403", "028096403898", "575205051686", "427800322647", "655168017864", "582553303278", "980402170192", "620737714031", "686142310509", "092421645460" }

{"063231394554", "109852259379", "740182746422", "853015982521", "476805512496", "898530717993", "430534005863", "440162807186", "132879980431", "685312177072", "780267345400", "959947501200" }

97

999999973

Returns: "45072665449667"
{"07409488245517115276142322168576189279543123341138", "70277931986502860248650900613893446066184963788291", "35084076361542097372601657541200146071777733599818", "26603801250947835120164061898414398808778383710734", "96510996834849925533374380880681989722828907815861", "24258026539246182119762952003918195325258677229419", "69825509125083939679976935766582544161633553282536", "18621460915036492934405963428875812574444429307787", "30382520072975343211325351222640703400531067500454", "95648216801484920706070567384926577457983022367155", "40260611170004830129038857708930747837100834501456", "20356667677091627276513995926532444279237315785832", "41159510645308913474636528103155221748236303528072", "25910850790530104859254139582796177190341753324129", "08745680774313030190429314820559328748143552689295", "94505880132227001337095583783793918280184860930087", "63565839483976450615519645425326826639456253566144", "62682551015176002033628234343684739800880514363921", "98234023198989135102538928701481935979801475550928", "24504405115908387260381033848015413735856908936069", "78941566666714061214052341523168827712604946036245", "88121498245299838698602382627578278020892820552767", "87816095890007255214860689835515584054721499030350", "76783644195574734088152024666290493119955560594634", "90539128818602490221544405042127795540341229822785", "83944698566072726471321630328601260546793478816387", "61723785858733108109249157034220127702410373959720", "28670818303620284183758170408136789555663008823065", "09722829448272584739519028310310407908140795382321", "04075905120989173307660289899042087873076421916033", "62214326054960827407601293851506889870791586394538", "23948513281646779641926315970260762534075531888017", "50590935427267220117591817866992065840378311257621", "61157485649843253832706801195363103403179035291261", "70152290518368861667049894987564860780956900135580", "17746707412183571476823027885971347037127534455141", "26633008138169801393936554050655189602505252067280", "06830643705207561818565926523212288870005995309951", "11233972330484392490574766309080151039089625763859", "30251577941785788423841304177213131515001221553892", "84275840944358410334067556098357904874020541664529", "12499376587897716501326057449061190421970033313569", "59883951362881981334392721761730602560720904325608", "81575792372793638106876512956154138509213350904857", "33030321108187289230282558124988271795034015042329", "49249044985323017198832933283402012107668058805732", "22002316877287959291308192024758100716930373040231", "02771307036319561510973081517179498001850892808014", "73616808657102835561493832337301487898979195896903", "14145763463834278901407349456898997084569362006510" }

{"09735006518272452258698355058150734156417040610552", "50327852729763159895495252230872837541829689816375", "41012285467734491838797114352915567902319878444358", "02909835043525777440411540286814764987386280980496", "82840940748182214669381364522010387331456121918047", "74119010325032263361582193972132092745032978011474", "39967600962303519679275682463091876840379622730730", "73646740124463450201693791524413468870344671812123", "11108910077451678393139637520717067175481752175310", "00500786401480899799960638036942044369189118635091", "08226897780305639774358333610474271572270360989640", "29032247745013343521698841457302777020086450157327", "91140331583001025104064895622217478600213924154066", "81331058938980399697725232833857881351208655395354", "85035084358126022165017738351321942301486613879443", "54427756690709807320153565468158533287696463210587", "00373462011653490343770915400712377333915888024433", "67661481659687191076371279471824881620485944499453", "21743190738426987708783219374443513280903494439853", "81238985106181877280366965138076160310431589545744", "67752688919805029602092673605217115326681586946628", "81687897905826971751604996155607507956853707523049", "85800977447592322319730437808812749193620720053577", "44338644592442425323402072077617567908574256588285", "27673356944596929561783706910045636467639147500558", "86981560604786403410043610568676789451028670774622", "96564069629126470824100361098029897477539129611498", "69748258256193713206899391104824914394952167251807", "57429184481284673158542664610046675811511907634457", "26562965321634905650653326606000520561049402664072", "66851002138435087053563029937909302511833746719461", "28257784206505607244405066263170554899812779218297", "99006425351978491987969564744865049887345775133796", "53402498042615610504870817280119103232281875626474", "37054373805682681266243020510580130284572389162213", "85668935769577002593037615259535536085210268962588", "66167125249270049081001735695066236702566678645580", "04422865099938715199852310738859693110124680895046", "86733173134277336553609563329963551471099652237097", "69569935818961845346415217548385231320008528871086", "32227084743444605537219088809167865980540764018849", "46409291243997766793945469868267586824356026492429", "66225652957443492133733054512856018927384207630293", "99222949484634283378375914917625228615596260906406", "63541884473243251249506854191923222917509989001806", "84550860546293256357285489286888599429987831306634", "08376605207368794808572429201501400574775283590896", "09019160143479690755494209733770531264246035271049", "65987840290582629698395701207656328558801945677103", "63383596119439192607093873086830685398605638960590" }

{"07548841170256880534375606109879537117316914270864", "90013119995935614395455037224305803065408848177809", "00020454216846662885276921607600558443963684115542", "92405760447559184465104995875486026273159598974084", "72080602391379331256206177056122610553312572171228", "09493041430487328239850835158371609053142015904260", "52423800532973749888097307612428639835109625485317", "08046960522217859929695062523161022103550080164490", "92514021016308256424521150517237309844950512406019", "93705608509102690959911475139843440174175095812709", "67884851350472464814866609799341407622862389373764", "13032023437020760868943933007072373159181838884721", "26708341922103511081244505530890728059891153790744", "72146271125850468585972197235279652835735979103828", "61569189298842061731497598155226737947249374219679", "94627731297126607422564153232929795942902531904759", "08828544147591490607311860316841526043069563528506", "56422556136030143009252284285827220391015445992690", "35688956914207878103351725158240815335857992441692", "68520128297688785450100618717107793603449659803864", "31431207484939715732059793750198462139072809209420", "66461364589744167540203223989397552958970410382732", "35607296642759607615020784192529302260925165474921", "97164317555290839924425036284126691434684384746466", "38061169058111583490819307470763926989517007126943", "02223331023099265663488880513737406194624301358374", "71239082860781651405790539084388074332086469777925", "56764506253668634915444396707634219596118360690946", "93613630752795331695838711430701786516991129530463", "28950081857047434254024946388019320608803124955298", "29006742634361141292609895207409253582468317872508", "53061951740390830814342646548200821406242066627119", "72513089841667102833126315453447043214078970313610", "83313214962492219009525171316530302436259376391058", "19054884838750250152462455494929690306233905709901", "79341553497548136371511025010734311079059212034700", "18311883359283459062459851876759431004608117445429", "07947056492551214332194935506173162040829681963987", "53005413573784280416583721971211213560053085322679", "29612100800598124302004196539748940877500380949354", "78614739705446584787521776949311495502390988136009", "54874998385215316730522150262836745377884035893170", "93357364940097865223537910509365596199175907503203", "88594037795906876909179859040525807493401140106438", "01045359427082301257518531608487575502480495012479", "02247701717851574372922525040884433522050432608156", "23891156818719920412800460039854544809897098490080", "73025070279006415129706363676633248171906713381091", "30183034673254827936546419876013556868246533948900", "15594750901413298639951107692246932341801689576380" }

47

1000000000

Returns: "22982999999917"
{"0550", "0000", "0005", "5000" }

{"0000", "0000", "0000", "0000" }

{"0110", "0000", "0001", "1000" }

7

999999996

Returns: "6999999958"
{"04251332132564603122305225561550353210221450636221", "30011244132645355430532332402003504402115450014640", "40001506306142660661533434351543551011450344343333", "32404565404120630652433100313024062251020412355341", "66420202420465460061063166421045465106421265115614", "01120013203455220212204153313251443245553602524323", "54324605100412055211046642665223433610405320523154", "33622240102234344456412511022543243265255406024460", "12140130034104334020554454626301513306242630162562", "52016535502525532524021332035654253626500542305335", "04165216500325655141056250224552042661326636314620", "50322622646056203066044435514562624664062640345042", "45660343261105113563460643201626223031355345136213", "54251403411500522133466646041655311531613061223434", "05454642131013036425336051263321146331555054345261", "53441034545060403030365131521316632545023600621024", "56335542035132450611620404622241664440423214430512", "40445562514021604001314266664011543102434634634322", "24446143011010226201501145201501226633322421244040", "10001252045165354510011233401603651050064551366645", "44054106115624243523060061050423001411221063510640", "22500420003233235320306202151661642462562624220562", "40431430044451606504330553556253324440232001156010", "24150666261502134310640036320202016555254443436260", "26404065140105144424351504156556414663456354161333", "14600541310002142564230000613022321305345123316365", "11611615034050263134315522013344336425101515512623", "43201525642415050146134060200252612563250401015522", "51320332512136233665360360440443406410441662465043", "30233636161315252356144566424050663334051112030053", "06024416056555266616406336516304056210113546255144", "99999999999999999999999999999990999999999999999999", "99999999999999999999999999999999099999999999999999", "99999999999999999999999999999999909999999999999999", "99999999999999999999999999999999990999999999999999", "99999999999999999999999999999999999099999999999999", "99999999999999999999999999999999999909999999999999", "99999999999999999999999999999999999990999999999999", "99999999999999999999999999999999999999099999999999", "99999999999999999999999999999999999999909999999999", "99999999999999999999999999999999999999990999999999", "99999999999999999999999999999999999999999099999999", "99999999999999999999999999999999999999999909999999", "99999999999999999999999999999999999999999990999999", "99999999999999999999999999999999999999999999099999", "99999999999999999999999999999999999999999999909999", "99999999999999999999999999999999999999999999990999", "99999999999999999999999999999999999999999999999099", "99999999999999999999999999999999999999999999999909", "99999999999999999999999999999999999999999999999990" }

{"04251332132564603122305225561550353210221450636221", "30011244132645355430532332402003504402115450014640", "40001506306142660661533434351543551011450344343333", "32404565404120630652433100313024062251020412355341", "66420202420465460061063166421045465106421265115614", "01120013203455220212204153313251443245553602524323", "54324605100412055211046642665223433610405320523154", "33622240102234344456412511022543243265255406024460", "12140130034104334020554454626301513306242630162562", "52016535502525532524021332035654253626500542305335", "04165216500325655141056250224552042661326636314620", "50322622646056203066044435514562624664062640345042", "45660343261105113563460643201626223031355345136213", "54251403411500522133466646041655311531613061223434", "05454642131013036425336051263321146331555054345261", "53441034545060403030365131521316632545023600621024", "56335542035132450611620404622241664440423214430512", "40445562514021604001314266664011543102434634634322", "24446143011010226201501145201501226633322421244040", "10001252045165354510011233401603651050064551366645", "44054106115624243523060061050423001411221063510640", "22500420003233235320306202151661642462562624220562", "40431430044451606504330553556253324440232001156010", "24150666261502134310640036320202016555254443436260", "26404065140105144424351504156556414663456354161333", "14600541310002142564230000613022321305345123316365", "11611615034050263134315522013344336425101515512623", "43201525642415050146134060200252612563250401015522", "51320332512136233665360360440443406410441662465043", "30233636161315252356144566424050663334051112030053", "06024416056555266616406336516304056210113546255144", "99999999999999999999999999999990999999999999999999", "99999999999999999999999999999999099999999999999999", "99999999999999999999999999999999909999999999999999", "99999999999999999999999999999999990999999999999999", "99999999999999999999999999999999999099999999999999", "99999999999999999999999999999999999909999999999999", "99999999999999999999999999999999999990999999999999", "99999999999999999999999999999999999999099999999999", "99999999999999999999999999999999999999909999999999", "99999999999999999999999999999999999999990999999999", "99999999999999999999999999999999999999999099999999", "99999999999999999999999999999999999999999909999999", "99999999999999999999999999999999999999999990999999", "99999999999999999999999999999999999999999999099999", "99999999999999999999999999999999999999999999909999", "99999999999999999999999999999999999999999999990999", "99999999999999999999999999999999999999999999999099", "99999999999999999999999999999999999999999999999909", "99999999999999999999999999999999999999999999999990" }

{"04251332132564603122305225561550353210221450636221", "30011244132645355430532332402003504402115450014640", "40001506306142660661533434351543551011450344343333", "32404565404120630652433100313024062251020412355341", "66420202420465460061063166421045465106421265115614", "01120013203455220212204153313251443245553602524323", "54324605100412055211046642665223433610405320523154", "33622240102234344456412511022543243265255406024460", "12140130034104334020554454626301513306242630162562", "52016535502525532524021332035654253626500542305335", "04165216500325655141056250224552042661326636314620", "50322622646056203066044435514562624664062640345042", "45660343261105113563460643201626223031355345136213", "54251403411500522133466646041655311531613061223434", "05454642131013036425336051263321146331555054345261", "53441034545060403030365131521316632545023600621024", "56335542035132450611620404622241664440423214430512", "40445562514021604001314266664011543102434634634322", "24446143011010226201501145201501226633322421244040", "10001252045165354510011233401603651050064551366645", "44054106115624243523060061050423001411221063510640", "22500420003233235320306202151661642462562624220562", "40431430044451606504330553556253324440232001156010", "24150666261502134310640036320202016555254443436260", "26404065140105144424351504156556414663456354161333", "14600541310002142564230000613022321305345123316365", "11611615034050263134315522013344336425101515512623", "43201525642415050146134060200252612563250401015522", "51320332512136233665360360440443406410441662465043", "30233636161315252356144566424050663334051112030053", "06024416056555266616406336516304056210113546255144", "66552645511346031121036231011440103245026063645135", "23163414406651613361331001432064003332550445336445", "65206013112031552100663146222651506256340524512000", "65426262216002604241524060161250500406421431406223", "10656360150435431525510115605026562006512335066620", "20130266146315212215230300264446560306201210532043", "44440421263651362135155353451615340210316665602113", "43624351106132542463663320326354436163003416063041", "41552053026363642501635503524036614162404202306456", "32061034054323262666316433200063342253630301400654", "31633245344055500126460214361644035232564052031021", "44040111600335415024544305463606353103243006446246", "62343300014506420251666663136323655005105540415333", "22316050123350641600555021102224433111123250022202", "23653144646611252341361642262212501163341030103151", "22536241161024613526036225456246223225134324510246", "65040224604360400456612156221665462203463200021004", "46550442436314044052462562555532210232255260402605", "15411116065105001211061043043502144243043333131230" }

3

1000000000

Returns: "1487999999670"
{"00", "00" }

{"00", "00" }

{"01", "10" }

5

8

Returns: "-2495"
{"09", "90" }

{"00", "00" }

{"01", "10" }

1

1000000000

Returns: "400999999599"
{"05000", "00505", "00050", "05000", "05000" }

{"00000", "00000", "00000", "00000", "00000" }

{"01000", "00101", "00010", "01000", "01000" }

1

999999998

Returns: "999999998"
{"0540", "0000", "0004", "4000" }

{"0090", "0000", "0009", "9000" }

{"0190", "0000", "0009", "9000" }

7

9

Returns: "-5"
{"05555555555555555555555555555555555555555555555555", "50555555555555555555555555555555555555555555555555", "55055555555555555555555555555555555555555555555555", "55505555555555555555555555555555555555555555555555", "55550555555555555555555555555555555555555555555555", "55555055555555555555555555555555555555555555555555", "55555505555555555555555555555555555555555555555555", "55555550555555555555555555555555555555555555555555", "55555555055555555555555555555555555555555555555555", "55555555505555555555555555555555555555555555555555", "55555555550555555555555555555555555555555555555555", "55555555555055555555555555555555555555555555555555", "55555555555505555555555555555555555555555555555555", "55555555555550555555555555555555555555555555555555", "55555555555555055555555555555555555555555555555555", "55555555555555505555555555555555555555555555555555", "55555555555555550555555555555555555555555555555555", "55555555555555555055555555555555555555555555555555", "55555555555555555505555555555555555555555555555555", "55555555555555555550555555555555555555555555555555", "55555555555555555555055555555555555555555555555555", "55555555555555555555505555555555555555555555555555", "55555555555555555555550555555555555555555555555555", "55555555555555555555555055555555555555555555555555", "55555555555555555555555505555555555555555555555555", "55555555555555555555555550555555555555555555555555", "55555555555555555555555555055555555555555555555555", "55555555555555555555555555505555555555555555555555", "55555555555555555555555555550555555555555555555555", "55555555555555555555555555555055555555555555555555", "55555555555555555555555555555505555555555555555555", "55555555555555555555555555555550555555555555555555", "55555555555555555555555555555555055555555555555555", "55555555555555555555555555555555505555555555555555", "55555555555555555555555555555555550555555555555555", "55555555555555555555555555555555555055555555555555", "55555555555555555555555555555555555505555555555555", "55555555555555555555555555555555555550555555555555", "55555555555555555555555555555555555555055555555555", "55555555555555555555555555555555555555505555555555", "55555555555555555555555555555555555555550555555555", "55555555555555555555555555555555555555555055555555", "55555555555555555555555555555555555555555505555555", "55555555555555555555555555555555555555555550555555", "55555555555555555555555555555555555555555555055555", "55555555555555555555555555555555555555555555505555", "55555555555555555555555555555555555555555555550555", "55555555555555555555555555555555555555555555555055", "55555555555555555555555555555555555555555555555505", "55555555555555555555555555555555555555555555555550" }

{"05555555555555555555555555555555555555555555555555", "50555555555555555555555555555555555555555555555555", "55055555555555555555555555555555555555555555555555", "55505555555555555555555555555555555555555555555555", "55550555555555555555555555555555555555555555555555", "55555055555555555555555555555555555555555555555555", "55555505555555555555555555555555555555555555555555", "55555550555555555555555555555555555555555555555555", "55555555055555555555555555555555555555555555555555", "55555555505555555555555555555555555555555555555555", "55555555550555555555555555555555555555555555555555", "55555555555055555555555555555555555555555555555555", "55555555555505555555555555555555555555555555555555", "55555555555550555555555555555555555555555555555555", "55555555555555055555555555555555555555555555555555", "55555555555555505555555555555555555555555555555555", "55555555555555550555555555555555555555555555555555", "55555555555555555055555555555555555555555555555555", "55555555555555555505555555555555555555555555555555", "55555555555555555550555555555555555555555555555555", "55555555555555555555055555555555555555555555555555", "55555555555555555555505555555555555555555555555555", "55555555555555555555550555555555555555555555555555", "55555555555555555555555055555555555555555555555555", "55555555555555555555555505555555555555555555555555", "55555555555555555555555550555555555555555555555555", "55555555555555555555555555055555555555555555555555", "55555555555555555555555555505555555555555555555555", "55555555555555555555555555550555555555555555555555", "55555555555555555555555555555055555555555555555555", "55555555555555555555555555555505555555555555555555", "55555555555555555555555555555550555555555555555555", "55555555555555555555555555555555055555555555555555", "55555555555555555555555555555555505555555555555555", "55555555555555555555555555555555550555555555555555", "55555555555555555555555555555555555055555555555555", "55555555555555555555555555555555555505555555555555", "55555555555555555555555555555555555550555555555555", "55555555555555555555555555555555555555055555555555", "55555555555555555555555555555555555555505555555555", "55555555555555555555555555555555555555550555555555", "55555555555555555555555555555555555555555055555555", "55555555555555555555555555555555555555555505555555", "55555555555555555555555555555555555555555550555555", "55555555555555555555555555555555555555555555055555", "55555555555555555555555555555555555555555555505555", "55555555555555555555555555555555555555555555550555", "55555555555555555555555555555555555555555555555055", "55555555555555555555555555555555555555555555555505", "55555555555555555555555555555555555555555555555550" }

{"05555555555555555555555555555555555555555555555555", "50555555555555555555555555555555555555555555555555", "55055555555555555555555555555555555555555555555555", "55505555555555555555555555555555555555555555555555", "55550555555555555555555555555555555555555555555555", "55555055555555555555555555555555555555555555555555", "55555505555555555555555555555555555555555555555555", "55555550555555555555555555555555555555555555555555", "55555555055555555555555555555555555555555555555555", "55555555505555555555555555555555555555555555555555", "55555555550555555555555555555555555555555555555555", "55555555555055555555555555555555555555555555555555", "55555555555505555555555555555555555555555555555555", "55555555555550555555555555555555555555555555555555", "55555555555555055555555555555555555555555555555555", "55555555555555505555555555555555555555555555555555", "55555555555555550555555555555555555555555555555555", "55555555555555555055555555555555555555555555555555", "55555555555555555505555555555555555555555555555555", "55555555555555555550555555555555555555555555555555", "55555555555555555555055555555555555555555555555555", "55555555555555555555505555555555555555555555555555", "55555555555555555555550555555555555555555555555555", "55555555555555555555555055555555555555555555555555", "55555555555555555555555505555555555555555555555555", "55555555555555555555555550555555555555555555555555", "55555555555555555555555555055555555555555555555555", "55555555555555555555555555505555555555555555555555", "55555555555555555555555555550555555555555555555555", "55555555555555555555555555555055555555555555555555", "55555555555555555555555555555505555555555555555555", "55555555555555555555555555555550555555555555555555", "55555555555555555555555555555555055555555555555555", "55555555555555555555555555555555505555555555555555", "55555555555555555555555555555555550555555555555555", "55555555555555555555555555555555555055555555555555", "55555555555555555555555555555555555505555555555555", "55555555555555555555555555555555555550555555555555", "55555555555555555555555555555555555555055555555555", "55555555555555555555555555555555555555505555555555", "55555555555555555555555555555555555555550555555555", "55555555555555555555555555555555555555555055555555", "55555555555555555555555555555555555555555505555555", "55555555555555555555555555555555555555555550555555", "55555555555555555555555555555555555555555555055555", "55555555555555555555555555555555555555555555505555", "55555555555555555555555555555555555555555555550555", "55555555555555555555555555555555555555555555555055", "55555555555555555555555555555555555555555555555505", "55555555555555555555555555555555555555555555555550" }

100

1000000000

Returns: "5500000000000"
{"0000", "0000", "0000", "0000" }

{"0000", "0000", "0000", "0000" }

{"0100", "0010", "0001", "1000" }

97

1000000000

Returns: "-48403"
{"0050", "0000", "0005", "5000" }

{"0000", "0000", "0000", "0000" }

{"0010", "0000", "0001", "1000" }

7

99999999

Returns: "IMPOSSIBLE"
{"09999999999999999999999999999999999999999999999999", "90999999999999999999999999999999999999999999999999", "99099999999999999999999999999999999999999999999999", "99909999999999999999999999999999999999999999999999", "99990999999999999999999999999999999999999999999999", "99999099999999999999999999999999999999999999999999", "99999909999999999999999999999999999999999999999999", "99999990999999999999999999999999999999999999999999", "99999999099999999999999999999999999999999999999999", "99999999909999999999999999999999999999999999999999", "99999999990999999999999999999999999999999999999999", "99999999999099999999999999999999999999999999999999", "99999999999909999999999999999999999999999999999999", "99999999999990999999999999999999999999999999999999", "99999999999999099999999999999999999999999999999999", "99999999999999909999999999999999999999999999999999", "99999999999999990999999999999999999999999999999999", "99999999999999999099999999999999999999999999999999", "99999999999999999909999999999999999999999999999999", "99999999999999999990999999999999999999999999999999", "99999999999999999999099999999999999999999999999999", "99999999999999999999909999999999999999999999999999", "99999999999999999999990999999999999999999999999999", "99999999999999999999999099999999999999999999999999", "99999999999999999999999909999999999999999999999999", "99999999999999999999999990999999999999999999999999", "99999999999999999999999999099999999999999999999999", "99999999999999999999999999909999999999999999999999", "99999999999999999999999999990999999999999999999999", "99999999999999999999999999999099999999999999999999", "99999999999999999999999999999909999999999999999999", "99999999999999999999999999999990999999999999999999", "99999999999999999999999999999999099999999999999999", "99999999999999999999999999999999909999999999999999", "99999999999999999999999999999999990999999999999999", "99999999999999999999999999999999999099999999999999", "99999999999999999999999999999999999909999999999999", "99999999999999999999999999999999999990999999999999", "99999999999999999999999999999999999999099999999999", "99999999999999999999999999999999999999909999999999", "99999999999999999999999999999999999999990999999999", "99999999999999999999999999999999999999999099999999", "99999999999999999999999999999999999999999909999999", "99999999999999999999999999999999999999999990999999", "99999999999999999999999999999999999999999999099999", "99999999999999999999999999999999999999999999909999", "99999999999999999999999999999999999999999999990999", "99999999999999999999999999999999999999999999999099", "99999999999999999999999999999999999999999999999909", "99999999999999999999999999999999999999999999999990" }

{"09999999999999999999999999999999999999999999999999", "90999999999999999999999999999999999999999999999999", "99099999999999999999999999999999999999999999999999", "99909999999999999999999999999999999999999999999999", "99990999999999999999999999999999999999999999999999", "99999099999999999999999999999999999999999999999999", "99999909999999999999999999999999999999999999999999", "99999990999999999999999999999999999999999999999999", "99999999099999999999999999999999999999999999999999", "99999999909999999999999999999999999999999999999999", "99999999990999999999999999999999999999999999999999", "99999999999099999999999999999999999999999999999999", "99999999999909999999999999999999999999999999999999", "99999999999990999999999999999999999999999999999999", "99999999999999099999999999999999999999999999999999", "99999999999999909999999999999999999999999999999999", "99999999999999990999999999999999999999999999999999", "99999999999999999099999999999999999999999999999999", "99999999999999999909999999999999999999999999999999", "99999999999999999990999999999999999999999999999999", "99999999999999999999099999999999999999999999999999", "99999999999999999999909999999999999999999999999999", "99999999999999999999990999999999999999999999999999", "99999999999999999999999099999999999999999999999999", "99999999999999999999999909999999999999999999999999", "99999999999999999999999990999999999999999999999999", "99999999999999999999999999099999999999999999999999", "99999999999999999999999999909999999999999999999999", "99999999999999999999999999990999999999999999999999", "99999999999999999999999999999099999999999999999999", "99999999999999999999999999999909999999999999999999", "99999999999999999999999999999990999999999999999999", "99999999999999999999999999999999099999999999999999", "99999999999999999999999999999999909999999999999999", "99999999999999999999999999999999990999999999999999", "99999999999999999999999999999999999099999999999999", "99999999999999999999999999999999999909999999999999", "99999999999999999999999999999999999990999999999999", "99999999999999999999999999999999999999099999999999", "99999999999999999999999999999999999999909999999999", "99999999999999999999999999999999999999990999999999", "99999999999999999999999999999999999999999099999999", "99999999999999999999999999999999999999999909999999", "99999999999999999999999999999999999999999990999999", "99999999999999999999999999999999999999999999099999", "99999999999999999999999999999999999999999999909999", "99999999999999999999999999999999999999999999990999", "99999999999999999999999999999999999999999999999099", "99999999999999999999999999999999999999999999999909", "99999999999999999999999999999999999999999999999990" }

{"09999999999999999999999999999999999999999999999999", "90999999999999999999999999999999999999999999999999", "99099999999999999999999999999999999999999999999999", "99909999999999999999999999999999999999999999999999", "99990999999999999999999999999999999999999999999999", "99999099999999999999999999999999999999999999999999", "99999909999999999999999999999999999999999999999999", "99999990999999999999999999999999999999999999999999", "99999999099999999999999999999999999999999999999999", "99999999909999999999999999999999999999999999999999", "99999999990999999999999999999999999999999999999999", "99999999999099999999999999999999999999999999999999", "99999999999909999999999999999999999999999999999999", "99999999999990999999999999999999999999999999999999", "99999999999999099999999999999999999999999999999999", "99999999999999909999999999999999999999999999999999", "99999999999999990999999999999999999999999999999999", "99999999999999999099999999999999999999999999999999", "99999999999999999909999999999999999999999999999999", "99999999999999999990999999999999999999999999999999", "99999999999999999999099999999999999999999999999999", "99999999999999999999909999999999999999999999999999", "99999999999999999999990999999999999999999999999999", "99999999999999999999999099999999999999999999999999", "99999999999999999999999909999999999999999999999999", "99999999999999999999999990999999999999999999999999", "99999999999999999999999999099999999999999999999999", "99999999999999999999999999909999999999999999999999", "99999999999999999999999999990999999999999999999999", "99999999999999999999999999999099999999999999999999", "99999999999999999999999999999909999999999999999999", "99999999999999999999999999999990999999999999999999", "99999999999999999999999999999999099999999999999999", "99999999999999999999999999999999909999999999999999", "99999999999999999999999999999999990999999999999999", "99999999999999999999999999999999999099999999999999", "99999999999999999999999999999999999909999999999999", "99999999999999999999999999999999999990999999999999", "99999999999999999999999999999999999999099999999999", "99999999999999999999999999999999999999909999999999", "99999999999999999999999999999999999999990999999999", "99999999999999999999999999999999999999999099999999", "99999999999999999999999999999999999999999909999999", "99999999999999999999999999999999999999999990999999", "99999999999999999999999999999999999999999999099999", "99999999999999999999999999999999999999999999909999", "99999999999999999999999999999999999999999999990999", "99999999999999999999999999999999999999999999999099", "99999999999999999999999999999999999999999999999909", "99999999999999999999999999999999999999999999999990" }

100

1000000000

Returns: "49900000000000"
{"045", "505", "550" }

{"090", "000", "000" }

{"090", "001", "000" }

2

1

Returns: "0"
{"044", "404", "440" }

{"099", "909", "990" }

{"055", "505", "550" }

100

1

Returns: "-500"
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97

1000000000

Returns: "47384499999937"
{"05", "50" }

{"00", "00" }

{"00", "00" }

3

2

Returns: "0"
{"05", "50" }

{"00", "00" }

{"01", "10" }

99

500000000

Returns: "49499999901"
{"00", "00" }

{"00", "00" }

{"01", "10" }

1

1000000000

Returns: "-499"
{"0540", "0000", "0004", "4000" }

{"0090", "0000", "0009", "9000" }

{"0190", "0000", "0009", "9000" }

7

999999996

Returns: "-5"
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{"04970536848291275950167376016457653338633413602401", "60165530143142111862455001098227097160301375277027", "59071385922355502397718206987504157994373525514408", "87603768297349838514474040583563510038580000562867", "07420023827282886545889985779819560583237487763766", "15161035876215177454731454541090163803974845700557", "30297400681489056252270716629433900030213021041847", "66545100199055070931422629861932901536490593908810", "60012913010434546391075902754502464339126573734052", "22891572706733682412269105165426330646391311360243", "72784709590401905160750958877286421847866930182427", "23484027473022583705464581469031882041861342670180", "76921589630309109145948539681249530558188217979352", "54752530322130305939245692643679817726455160577091", "05349417143679014471231198580767841969636630202669", "55883826267440908327867577322465720127262571721027", "06323443970086570004196697800099774090803017641394", "86104840704122372095650763118567431236796867631173", "76053778358919868002140440597596011871551798463227", "02037758486646474830413307214034588578647235329300", "92595013059661290312094834119605815793121412135132", "01568657663108508915106362038537982441464092682292", "90054575709963184221460239867016114664108095432410", "95785476339853831591082081882876395590853092587517", "65083038062280166441895301336117483919975630431582", "85296223499535558259614330863583747194238887161574", "48976537188167913643484028031783402171649243967491", "10095392699679337065378552400163644042266713363839", "91424616115799165789905559570848184245055598744473", "55473672026886996254157075140018013646837325798284", "36843623350213037583359184640101212240266438959846", "94371853992647337887570182641530222809468597879723", "83937030329919060569215826137102087108434874463514", "39371672077512277750591203460913004861354647689224", "36101375156945690211282164211255420891811724473182", "70894434475312398875006712861200797086139529595568", "32996108171539664319596550472264996201375356776701", "52182928939688684117422792752058945780446400488278", "72230216595083102716085446013178624429012891934023", "58562643228358116088865811721949728419306432364043", "71674646094602254258848776611558443303280873793310", "34302772124274792800905934874982278908838047786622", "88616122311822427742844654215501613268292403278981", "03513233848134324572658479839729003459663980545981", "89479979271964666640940182489315774613982156058947", "95950896823684353855126149850411306510540432401556", "54551977430951738998458999305758487835373665740569", "86691897837115142211687148572563967074302499759053", "17560607654645161032469247887036673776904716218300", "56329967353059539271579316109724508475686666388030" }

97

499999997

Returns: "23667999857850"

Statistics

Problem Statement for "AntOnGraph"

Problem Statement

Definition

Constraints

Examples