TopCoder Statistics - Problem Statement

Problem Statement

John has a sequence of digits. He and Brus will now play with the sequence.

First, John will repeat the following operation k times: He will choose two different positions in the sequence, and swap the elements at those positions. (John makes each choice uniformly at random. That is, each time John chooses two positions, each pair of different positions has the same probability of being chosen.)

Afterwards, Brus will randomly choose a non-empty contiguous subsequence of John's sequence. He will compute the sum of all elements in the chosen subsequence and he will write it down on a piece of paper. (Brus also makes his choice uniformly at random. That is, each possible contiguous subsequence has the same probability of being chosen.)

You are given a String[] sequence. Concatenate all elements of sequence to get the string s. For each i, the i-th character of s is a digit ('0'-'9') representing the digit at index i in John's original sequence.

Return the expected value of the sum Brus writes down.

Definition

Class:: TheSwapsDivOne
Method:: find
Parameters:: String[], int
Returns:: double
Method signature:: double find(String[] sequence, int k)
(be sure your method is public)

Notes

The returned value must be accurate to within a relative or absolute value of 1E-9.

Constraints

sequence will contain between 2 and 47 elements, inclusive.
Each element of sequence will contain between 1 and 47 characters, inclusive.
Each element of sequence will consist of only decimal digits ('0'-'9').
k will be between 1 and 1,000,000, inclusive.

Examples

{"4", "77"}

1

Returns: 10.0

There are three equally likely swaps John might make. If the first two elements are swapped, John will get the sequence {7,4,7}. Then Brus chooses one of the six possible subsequences. Their sums are 7, 4, 7, 11, 11 and 18. Thus the expected value is (7 + 4 + 7 + 11 + 11 + 18)/6 = 29/3. If the first and the last elements are swapped, the sequence becomes {7,7,4}, and the subsequence sums are 7, 7, 4, 14, 11 and 18. The expected value in this case is (7 + 7 + 4 + 14 + 11 + 18)/6 = 61/6. When the last two elements are swapped, the sequence doesn't change and the expected value is equal to 61/6 as well. Finally, the overall expected value is equal to (29/3 + 61/6 + 61/6)/3 = 10.
{"4", "77"}

47

Returns: 10.0
{"1", "1", "1", "1", "1", "1", "1"}

1000000

Returns: 3.0
{"572685085149095989026478064633266980348504469", "19720257361", "9", "69"}

7

Returns: 98.3238536775161
{"1652032429911007", "547420218806349319256", "0163197091083813015782", "45886495561569867943", "71858041493356764841426836575808", "316625261873581203866991044993470248548647", "315167", "041479578798", "5813855100465408673907745961503719014103", "1339492822022683257344", "917074984523152384501095786", "9996138678622894935145757540553475217415796544", "478868905", "11873099891526193114937789648327683529116", "433347", "206504728324689215908815", "63706", "6", "8209877114319", "14853", "879031633374148493762638533329", "453659180159552453943568", "298893659564697923600054452", "54248943558227734556538762532351241553", "0897169365545393630469914685037394336558351624", "71440977", "99", "17893815059146271523024434632056482965116749", "845109", "659271053948657342659219311121775858685738483", "11114395317835840375202777013255835", "910681218357650846946", "62366447413", "690306575831679853", "71324059566096657933123793076021398685873936979", "570672685794269958", "1239437891746781633967520838878238", "8734595290108757695279433833304893784096290", "13355594072205852861049111757", "2582765453926897625323"}

249874

Returns: 1499.7912317327769
{"91755028432946073020748442944", "714489892860739115499437928", "262735652524169157169", "48164092742010833819377218868785956505", "879555389999858228564460772892882226544970660", "94266729", "592571933425896779052684129736380108775", "349659742584387736922867279549690419935", "217754366245200475942984242847305990042126", "27813154", "5553962", "4585114900685", "99347009044775309553426566381994944447035", "07446250113561971496421744061358530500878958557", "406114865253514131169", "26292931414860188502982", "6263575491798201061269"}

335301

Returns: 741.1404255319151
{"004632377870864721939215510128479948897", "0174906632712337808533420145359", "375761604850969252822324968302162", "95392935920058096694090", "269086527420618377798114610845138263635338", "246505155072267516809445301859529422238266079", "0210454638080985372287378100463", "6784580431464263446", "101198301580904279380056791", "899015277952322299", "0863849969073061840314640475684546", "269208658993840333414480982900144433", "042017066104", "107849609064113008143757495", "374", "9314908637520094278", "74518892441160", "059366634236234", "28741598483134524", "058880055221950661", "904214434070816", "792096566232555367503985135", "388238905956012214254874", "2915666777481088", "26584445499320417503408618804627", "8959024955268926366744786817694362", "389513499051", "39374146632589148870498698810469114423512350066", "69624952", "170287598510849884062314397662795280724", "069461644534543262740591475197", "19542789876713982476452", "5229780539026165", "9183604807", "2596937810157055667046407617", "3810401554796469241002846333383277386715693113", "51346", "514549755228406740322255256", "6809071", "7092487694635", "643494188", "97247610229453778126", "1210912868463244816111547997", "48790315197967348873514311743682818204847587", "78405893154740236338914009056742813877034427", "5333272001092778662423064430313"}

119321

Returns: 1691.9683655535998
{"462123717654081695", "5132046922683794996900674993", "27688925333034400560025639304935", "00696056937014", "144239598435709", "80298248981171630885499914114718154399242612422", "77815473295691194", "4229039150740041862614771600731802162787936", "203420571482553670666622405", "3955658109", "999105127727505", "3406652086799037051615491378519012573141", "6264502750371204357050622587732908481", "791400553", "112070760290959301", "197269532196350537303886137668", "6599529365305132897373031752304456944132311", "825534", "84005221085280434597084353659463"}

3275

Returns: 686.5093501120697
{"29367596099", "79", "2555035291091174328017324490159", "8752570531647", "15366", "35435285619633477188657", "012044528760580027637144", "7710192790346334577205575", "6855547943705919236443310083011132111970859", "0033564893567", "43729123722978785352940649623", "494604565572561680374314794972111", "06911244394519155259394124859520454557345139196", "9024371", "065192738336", "76399843676373836006722388728485255309418", "355011", "11435697586459582852251135763390670801396", "4308555011999980526471746699745903129", "057388383453923922016848076865", "8587070648375857677457", "019468573032582161353549580128270540", "96635413975074416", "23350023603772132", "3111908867238265728612022070205960892", "2648797175877297388985897569800", "141776567964", "738747257922952925554360881055303092075", "7136199183466452228297001628268076079322881", "88058331507359152250701110582429695987827201", "74169499928564383714986243057903", "980393533477798748243684853701947208367523", "16408966083831598379", "236260567730", "2862922150322582699958171946696016", "7447844856955492486547711257758380699240257"}

854

Returns: 1462.7335126521937
{"1036289617", "9", "384291788", "96335541573832682", "4", "1145886696298818414409133853", "14003669829889666632945210664529577317996900453", "82693945549422703149770409756645099919935", "63848", "54920232068520940146620831532", "7972648441263043822510844454622945596963728168", "77924812773987462545137418685572685085149", "9598902647806463326698034850", "469219720257361086076072438401", "4608219002506398", "295887240155846949391897815", "313541402779220386738561", "449204598080091286340588122261239768475745", "004580988", "64297948069966", "38", "99634652276403970661097710570754719", "0900457768474418456", "702766459586239506910468", "966801", "7190", "83", "30584", "41406007382355862157884964760302924733292", "222545775097", "33815114706414507938", "982760962164611308051945360486494228129358", "69572722063648288572177822973844324122", "283406552987622181313437819833302", "480561611800320964348782093106451343386"}

6491

Returns: 1209.7331644291628
{"838247705932267198570661460474752119466", "172891", "67863605462357189612108993057539297584", "714125177040828966", "4231065554403276916540488948", "18113238711437003882249855050342015581582", "522542486837916367956231067933396", "3685739565315296084722680"}

6799

Returns: 347.3538011695906
{"69278405853158124638120914", "8983658629366349642785931436685876574488", "274466367193455752", "6990", "17739", "257020151741933456820100642075456726450", "7592568494932531863458386777", "930788498559945648523559056064180263035992599", "46492690331652032", "2991100755474202188063493", "9256201", "319709108381301578204588649556156986794337185", "0414933567648414268365758087", "1662526", "8735812038669910449934", "02485486", "783151674041479", "78798", "5813855100465408673907745961503719014103", "1339492822022683257344", "917074984523152384501095786", "9996138678622894935145757540553475217415796544", "478868905", "11873099891526193114937789648327683529116", "433347", "206504728324689215908815", "63706", "6", "8209877114319", "14853"}

620

Returns: 978.4448380181036
{"90316333741484937626385333299453659180159552453", "435689", "988936595646979236000544528542", "89435582277345565", "8762532351241553408971693655"}

1659

Returns: 208.20312500001918
{"93630469914685", "3739", "33655835162497144", "97789981789381505914627", "52302443463205648296", "1167495845109765927105394865734265921", "31112177585868573848341111", "39531783584037520277701325583569106", "12183576508469465623664474137690306575", "3167985367132405956609665793312", "7930760", "13986858739369799570672685794269958112", "943789", "7467816339675208", "88782386873459529010875769527", "4338333048937840962909133", "5594072", "05852861049111757", "2582765453926897625323", "09917550284329460730207484429", "44714489892860739115", "9943792892627", "56525241691571695481640927", "2010833819", "7721886", "7859565054879555", "899998582285644", "0772892882226544970660894266729559", "5719334258967790526841", "973638010877503496", "974258438773692286727954969041993552177", "4366245200475942984242", "47305990042126427", "13154755539627458511", "9006850993", "7009044775309553426566", "8199494444703550744", "25011356197149642", "74406135853050087895855704061148652535141311696", "62", "29314148601885", "2982562635754917982010612692010046", "23778708647219392155101284799488973017490", "6"}

7366

Returns: 1473.8396287936769
{"12337", "0853342", "145359537576160485096925282232496830216", "69", "39293592005809669409002690865", "7420618377798", "1461084513826363533892465051550722675168094453", "185952942", "238", "66079802104546380809853722873781004636", "784580431464263446210119830158090", "2793800567913899015277", "52322299708638499690730618403146404", "5684546926920865899", "840333414480982", "00144", "3340420170661045107849609064", "1300814375749543743931490863", "5200942786745188924411", "0805936", "63423623482874159848313452480588800552", "195066199042144340708162792096", "662325553675039851350388238905956012214254", "74029156", "67774810886265844454993204175034", "8", "188046270895902495526892636674478", "81769", "36203895134", "905183937414663258914887049", "69881046911442351235006626962495271702875985", "0849884062314397", "62795280724706946164453454326274059147519781", "542789876713982476452452", "97805390261658918360480782596937", "1015705", "667046407617838104015547", "6469241002846333383277386715693", "1", "2513463514549755228406740", "22255256568090", "1", "7092487694635"}

2283

Returns: 1356.328204186212
{"34941882972476102294537781268121091", "8684632448", "6111547997548790315197967348873514311743682818", "0484758707", "405893154740236338914009056742813", "77034427053332720010927786624230644", "0313505517688308969954784", "88219718555583226452086761", "91", "52265631750", "54434", "30733282692684319", "930720134317905620727333632240584603", "39360337904054098599292", "3664599086955014286502607655130926070", "13563563", "89", "49530000524", "8195459497097815138361610959107", "6824488650737404953840162341592966544691"}

9777

Returns: 656.6177577125657
{"673109048460888361333296515215598192550533", "9500081822673715987383149112057995239334562", "1278219819968639727", "68", "769570748265697766855", "61340981864527595", "391318297723705165", "79874263516221213732750914137881573324379819", "854162550157062931278480300348540025895740851", "63188309407", "0991447111500599857033273558962671562", "16559749585181756269", "7120559", "55421497411697140019509682250450078288707594", "29952752154714390119408957446538813313635730", "800355260309773659", "172695048159084993251213815415842", "8", "839501208276872834068309110703288752", "7635", "190119646979666740111935079150960", "377", "82727775071553", "8858607518649", "367981765543790658705712520801205", "47224730975618986995275815", "550531628573", "825", "2357951471768502811786812879705599234458", "4931662374", "31871295073186067678143188054226", "5286", "506292342427153394750316", "992285196789221415937", "992656885252665609"}

125

Returns: 1212.247260247146
{"713923863890517", "8818071503507751370880905240514633642886", "0", "576264814404", "613196331757229834515656202365178923924131"}

2903

Returns: 158.4969696969697
{"327572235098", "5981444810131", "5678699519345371656000740283198", "540262407801318002568"}

56

Returns: 110.09215386372018
{"89553895", "39106", "65411161862834", "55212430245767638914267"}

5451

Returns: 78.34666666666668
{"46212371765408169585132046922683794996900674993", "27688925333034400560025639304935300696056937014", "14423959843570928029824898117163088549991411471", "15439924261242257781547329569119494229039150740", "41862614771600731802162787936320342057148255367", "66662240583955658109899910512772750573406652086", "99037051615491378519012573141462645027503712043", "70506225877329084810791400553211207076029095930", "71972695321963505373038861376687659952936530513", "89737303175230445694413231148255347840052210852", "04345970843536594632322936759609997922555035291", "91174328017324490159787525705316475153661354352", "56196334771886577012044528760580027637144277101", "27903463345772055752685554794370591923644331008", "01113211197085920033564893567343729123722978785", "52940649623849460456557256168037431479497211100", "91124439451915525939412485952045455734513919619", "24371806519273833677639984367637383600672238872", "48525530941823550118114356975864595828522511357", "33906708013966430855501199998052647174669974590", "12930573883834539239220168480768657858707064837", "85767745780194685730325821613535495801282705408", "66354139750744167233500236037721323311190886723", "26572861202207020596089212648797175877297388985", "97569800614177656796477387472579229529255543608", "10553030920753713619918346645222829700162826807", "07932288128805833150735915225070111058242969598", "82720177416949992856438371498624305790329803935", "34777987482436848537019472083675239164089660838", "15983799236260567730128629221503225826999581719", "66960167744784485695549248654771125775838069924", "25730910362896174913842917884963355415738326821", "71145886696298818414409133853114003669829889666", "32945210664529577317996900453182693945549422703", "49770409756645099919935163848654920232068520940", "46620831532179726484412630438225108444546229455", "69637281682779248127739874625451374186855726850", "51490959890264780646332669803485044692197202573", "10860760724384017460821900250639852958872401558", "69493918978152313541402779220386738561344920459", "08009128634058812226123976847574500045809881642", "79480699660380996346522764039706610977105707547", "95090045776847441845627027664595862395069104686", "66801471902837305848414060073823558621578849647", "03029247332923222545775097833815114706414507938", "98276096216461130805194536048649422812935846957", "72206364828857217782297384432412272834065529876"}

275

Returns: 3352.2818372553234
{"81313437819833302548056161180032096434878209310", "45134338628883824770593226719857066146047475211", "46671728916678636054623571896121089930575392975", "49714125177040828966542310655544032769165404889", "85181132387114370038822498550503420155815820522", "42486837916367956231067933396536857395653152960", "47226806916927840585315812463812091448983658629", "66349642785931436685876574488827446636719345575", "46990717739125702015174193345682010064207545672", "45057592568494932531863458386777493078849855994", "64852355905606418026303599259994649269033165203", "42991100755474202188063493192562016319709108381", "01578204588649556156986794337185804149335676484", "42683657580873166252618735812038669910449934702", "85486478315167404147957879855813855100465408673", "07745961503719014103013394928220226832573446917", "74984523152384501095786099961386786228949351457", "75405534752174157965448478868905511873099891526", "93114937789648327683529116843334722065047283246", "92159088157637067678209877114319314853787903163", "37414849376263853332994536591801595524539435689", "98893659564697923600054452854248943558227734556", "38762532351241553408971693655453936304699146850", "73943365583516249714409778998178938150591462715", "30244346320564829651167495845109765927105394865", "34265921931112177585868573848341111439531783584", "37520277701325583569106812183576508469465623664", "74137690306575831679853671324059566096657933123", "93076021398685873936979957067268579426995811239", "37891746781633967520838878238687345952901087576", "52794338333048937840962909133555940722058528610", "91117573258276545392689762532350991755028432946", "73020748442944471448989286073911549943792892627", "56525241691571695481640927420108338193772188687", "59565054879555389999858228564460772892882226544", "70660894266729559257193342589677905268412973638", "10877503496597425843877369228672795496904199355", "17754366245200475942984242847305990042126427813", "54755539627458511490068509934700904477530955342", "56638199494444703550744625011356197149642174406", "35853050087895855704061148652535141311696262929", "14148601885029825626357549179820106126920100463", "37787086472193921551012847994889730174906632712", "37808533420145359537576160485096925282232496830", "16269539293592005809669409002690865274206183777", "81146108451382636353389246505155072267516809445", "01859529422238266079802104546380809853722873781"}

563

Returns: 3476.6851728427337
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401

Returns: 3319.740276278519
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40

Returns: 3367.6895292237045
{"68187039961248098458610044521194341681532390154", "74791808997682320379379673720362635546472431789", "37736270441978263574152590390531009650133011882", "46048126895072547808811585565925742950429934183", "89017999057283422723226780970553938944309271344", "96619343703733392282161084770663204281840914261", "58204513193471619762763253709442456933258578079", "47830735285543259545420294913010340193759253534", "62227444201962300882803629956082986867815310993", "73269094999818600109958940368913414521152238690", "93456022521712185267319992359943406030460151499", "32881871279982881462250799945953494206583754922", "69203983665488937909533286584967346962623833785", "62458773527151010027362281778736708476756595244", "97022781511037130702821859525244810416850438269", "33431792289825847405682490143458424545537375598", "82813784851143525682521743792283156007639155371", "61482050506694424142940168046859372959388042698", "76676841902664348809017161877423602777246521931", "78287019354340091940034415272759230220108480338", "65227887686670373660591612666182928962479680645", "44058413852718016601116887237710170936115145080", "53240306592363920540253466445364458856610022743", "38083110566083823083464353802079048524910562928", "60633188050135345785701117654449338421205045845", "65600139600591641786006922669071322659569204476", "88033681174605538249201263007427176527200125755", "57011051554562218505512670654494270029356823976", "10826209080872111282773078068146208439477144493", "08256412856218625189296261031338170918711407282", "89857066988700902184257748811565504026870865589", "92409376910807246296794937668995047564984142128", "19578541898437325913743994073767651332488425401", "41702357466181031896604818611433905435505380566", "62123741030627370734881683882806515981473166972", "73715123786757972155983268834088009529816643897", "50966836328336405690584237685818005097150366874", "29948460050868569535891778283925773775271482717", "29797870660782264455654902696937163286585127738", "16381229990972562210333527220701999296282906209", "59574391328698856179656018447735661112502083204", "72957909400723775473421079277508641602259909905", "23167179476443817114504001848816331602373266126", "89596386722455168435961606212242361539610685293", "52112132370513240898860537659031097215318187296", "59345284084842985392623314965861017307429632997", "46339459609824043015176753914019181125587571452"}

604

Returns: 3274.6826282405914
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95

Returns: 3405.683866777557
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510

Returns: 3268.267676387547
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295

Returns: 3321.9673783446306
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77

Returns: 3406.278465412515
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271

Returns: 3447.155443637532
{"46212371765408169585132046922683794996900674993", "27688925333034400560025639304935300696056937014", "14423959843570928029824898117163088549991411471", "15439924261242257781547329569119494229039150740", "41862614771600731802162787936320342057148255367", "66662240583955658109899910512772750573406652086", "99037051615491378519012573141462645027503712043", "70506225877329084810791400553211207076029095930", "71972695321963505373038861376687659952936530513", "89737303175230445694413231148255347840052210852", "04345970843536594632322936759609997922555035291", "91174328017324490159787525705316475153661354352", "56196334771886577012044528760580027637144277101", "27903463345772055752685554794370591923644331008", "01113211197085920033564893567343729123722978785", "52940649623849460456557256168037431479497211100", "91124439451915525939412485952045455734513919619", "24371806519273833677639984367637383600672238872", "48525530941823550118114356975864595828522511357", "33906708013966430855501199998052647174669974590", "12930573883834539239220168480768657858707064837", "85767745780194685730325821613535495801282705408", "66354139750744167233500236037721323311190886723", "26572861202207020596089212648797175877297388985", "97569800614177656796477387472579229529255543608", "10553030920753713619918346645222829700162826807", "07932288128805833150735915225070111058242969598", "82720177416949992856438371498624305790329803935", "34777987482436848537019472083675239164089660838", "15983799236260567730128629221503225826999581719", "66960167744784485695549248654771125775838069924", "25730910362896174913842917884963355415738326821", "71145886696298818414409133853114003669829889666", "32945210664529577317996900453182693945549422703", "49770409756645099919935163848654920232068520940", "46620831532179726484412630438225108444546229455", "69637281682779248127739874625451374186855726850", "51490959890264780646332669803485044692197202573", "10860760724384017460821900250639852958872401558", "69493918978152313541402779220386738561344920459", "08009128634058812226123976847574500045809881642", "79480699660380996346522764039706610977105707547", "95090045776847441845627027664595862395069104686", "66801471902837305848414060073823558621578849647", "03029247332923222545775097833815114706414507938", "98276096216461130805194536048649422812935846957", "72206364828857217782297384432412272834065529876"}

833067

Returns: 3335.350384789501
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196301

Returns: 3444.44907197827
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765090

Returns: 3311.662290629243
{"73910676541116186283415521243024576763891426782", "81574902863259743062852337989711258026300441358", "56980434314959264237824707917275730722001257921", "28896651812838823775693754061225675049426890711", "70400381171271738368053760411583709264507147730", "65950601275734555743826072111016042724560122302", "71578517348232854212636808389076522063695353797", "09286755246569095094209431696964273146896259837", "13272066522648936221285001244272793385113450028", "80324980611842609600636779818314872047156667057", "50914954377587864979806100318545334906883882821", "44692054674422523370445992544023441689262718080", "55686966512907342104877742498979925147501171896", "29758229041469039005824938280999062586580568087", "59780873587422010878234607918247776467625821627", "25024171468783739053293475714384250508918498634", "32456005910609596856886245460270315408517894282", "20202414619962093504698274816474813125670641853", "38158394935387262701475240144168926764695120073", "23584006618666985158247598306803060886170157044", "99824342540342908897672928070877169509963952092", "63010792241821285689646937662179251694824646817", "57561815127520882048925167292663710457245441060", "86799543493724115453399475106131610999306268652", "56427189774621016356744686946174591854993079649", "28669231776522896161924880296684707531453755843", "81951377679663517323577238022344840617890102658", "99743424147543564832989068370950742812751741288", "23693648684944603659376193360893031997574654609", "19659534704463624668938163066783937814001851015", "86241602291125921484105931478801239790502665286", "32337647599624560769518384180095796431721684256", "06149111690869031594538398992531060056226393499", "53697059392100258115521222232226549994487552245", "63655989085860111440517436862444225231758929678", "53363161523125554668382047914130556976713505930", "87577636880858011675940099563462874731414662789", "90285734790456706212153723515500195891073091796", "00297540456577967305381356633195673538964632382", "70579280977090624926564586023477724619507740723", "89307332257115229532176310317125684971266743773", "99471697386571954879545104585187181178221956180", "81809629660832933482195033617038015271902315784", "75583769529515638627578421079950957574411880715", "06113633455437271843561033969642656436492022183", "74183268936770152176133040515406572775531673530", "00893320254759507197750118041790465516996912758"}

621852

Returns: 3332.3476686283416
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537970

Returns: 3283.3033046627374
{"46212371765408169585132046922683794996900674993", "27688925333034400560025639304935300696056937014", "14423959843570928029824898117163088549991411471", "15439924261242257781547329569119494229039150740", "41862614771600731802162787936320342057148255367", "66662240583955658109899910512772750573406652086", "99037051615491378519012573141462645027503712043", "70506225877329084810791400553211207076029095930", "71972695321963505373038861376687659952936530513", "89737303175230445694413231148255347840052210852", "04345970843536594632322936759609997922555035291", "91174328017324490159787525705316475153661354352", "56196334771886577012044528760580027637144277101", "27903463345772055752685554794370591923644331008", "01113211197085920033564893567343729123722978785", "52940649623849460456557256168037431479497211100", "91124439451915525939412485952045455734513919619", "24371806519273833677639984367637383600672238872", "48525530941823550118114356975864595828522511357", "33906708013966430855501199998052647174669974590", "12930573883834539239220168480768657858707064837", "85767745780194685730325821613535495801282705408", "66354139750744167233500236037721323311190886723", "26572861202207020596089212648797175877297388985", "97569800614177656796477387472579229529255543608", "10553030920753713619918346645222829700162826807", "07932288128805833150735915225070111058242969598", "82720177416949992856438371498624305790329803935", "34777987482436848537019472083675239164089660838", "15983799236260567730128629221503225826999581719", "66960167744784485695549248654771125775838069924", "25730910362896174913842917884963355415738326821", "71145886696298818414409133853114003669829889666", "32945210664529577317996900453182693945549422703", "49770409756645099919935163848654920232068520940", "46620831532179726484412630438225108444546229455", "69637281682779248127739874625451374186855726850", "51490959890264780646332669803485044692197202573", "10860760724384017460821900250639852958872401558", "69493918978152313541402779220386738561344920459", "08009128634058812226123976847574500045809881642", "79480699660380996346522764039706610977105707547", "95090045776847441845627027664595862395069104686", "66801471902837305848414060073823558621578849647", "03029247332923222545775097833815114706414507938", "98276096216461130805194536048649422812935846957", "72206364828857217782297384432412272834065529876"}

1000000

Returns: 3335.350384789501
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1000000

Returns: 5159.0
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557

Returns: 3787.6662334200705
{"6656654455545476467475554574774575767444565655", "447645667467464577446755477666664544665477766", "75767466656666645767554665556665467465665664556", "674467675774576754775445644767477446744564744", "44655764655565764464474465545574447556576", "45644674754555666757447566544544564657574", "474766777477777475544577654755764464676456", "756475566454747565466665665567774745576754", "5444665477456744457565564454656466665775474", "55667544557757477445577567555656646746664677656", "64674555767464567447764656747664556476766676", "5756764474567544664456464767557455756647567", "5757565766657574555547664476666465747456445", "777545666767567776674747647776756566656575", "6766654557567664476464567775477576445465655", "47645646775546755656666544665657774566676", "5574756654754757446654466575455674455457776566", "5675756566447444456755446557646564567774766544", "575464777654666764447675774546474777567745745", "45774666544465756774756574577545654547757676", "44664467457764457547476454577654674547774", "477747766546664747557677557465554776574755565", "44456644567755675477675564775574775767446", "474455457746457767464454674456644767556467", "54774656744674757765575766755677477675776544455", "466765755677675657544555574677745744765647", "457746675547666674454454446747754447776754", "54766576575645557646775657657455776744475", "464565775455455455746657546457765545565745547", "5646777454444546746564667677545677665545565747", "457566677744657675555747777456465756467677774", "755774754465776645774554576754574645474557", "5646676456654666565556545667776556774576577446", "55464564575575457754544475564676775547777", "74476645776445574754776754555645454775477", "667645465666576755454546557677675655657744", "7756447667455775555445646547446764575577574744", "676575646756677677455575744645674645544476", "46476665746454766667577776756777445646575676", "46745555765746766654746476457655775474466747774", "4546577557657756766645646667544746466467645764", "46546665475574555777447674575474646547576564744", "77476767756656674757654644545556565465775", "74755567444474464555645644466477475564445"}

383

Returns: 3542.5544569534864
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456

Returns: 3772.0945750778915
{"46212371765408169585132046922683794996900", "749937276889253330344005600256393049353006", "60569370148144239598435709280298248981171630", "85499914114718154399242612422577815473295691194", "4229039150740041862614771600731802162787936320", "4205714825536706666224058395565810989991051", "772750573406652086799037051615491378519012573", "41462645027503712043570506225877329084810791", "005532112070760290959301719726953219635053", "303886137668765995293653051328973730317523", "44569441323114825534784005221085280434597084", "5365946323229367596099979225550352910911743280", "7324490159787525705316475153661354352856196334", "7188657701204452876058002763714427710192790346", "3457720557526855547943705919236443310083011132", "119708592003356489356734372912372297878535", "9406496238494604565572561680374314794972111006", "11244394519155259394124859520454557345139196190", "4371806519273833677639984367637383600672238872", "48525530941823550118114356975864595828522511", "57633906708013966430855501199998052647174", "699745903129305738838345392392201684807686578", "8707064837585767745780194685730325821613535", "958012827054089663541397507441672335002360", "77213233111908867238265728612022070205960892", "264879717587729738898589756980061417765679", "4773874725792295292555436088105530309207537", "361991834664522282970016282680760793228812", "805833150735915225070111058242969598782720", "7741694999285643837149862430579032980393533", "77798748243684853701947208367523916408966", "838315983799236260567730128629221503225826999", "81719466960167744784485695549248654771125775838", "699240257309103628961749138429178849633554157", "8326821471145886696298818414409133853114003669", "29889666632945210664529577317996900453182693", "45549422703149770409756645099919935163848", "5492023206852094014662083153217972648441263043", "225108444546229455969637281682779248127739", "7462545137418685572685085149095989026478064", "3326698034850446921972025736108607607243840174", "082190025063985295887240155846949391897815", "3135414027792203867385613449204598080091286", "40588122261239768475745000458098816429794", "069966038099634652276403970661097710570754", "195090045776847441845627027664595862395069104", "86966801471902837305848414060073823558621578849"}

41897

Returns: 3122.6925315227872
{"6030292473329232225457750978338151147064145079", "829827609621646113080519453604864942281293584", "95727220636482885721778229738443241227283406552", "876221813134378198333025480561611800320964348", "82093106451343386288838247705932267198570", "61460474752119466717289166786360546235718", "612108993057539297584971412517704082896654", "310655544032769165404889485181132387114370", "3882249855050342015581582052254248683791636", "95623106793339653685739565315296084722680691692", "84058531581246381209144898365862936634964278", "9314366858765744888274466367193455752469907", "7739125702015174193345682010064207545672645", "575925684949325318634583867774930788498559", "4564852355905606418026303599259994649269033", "65203242991100755474202188063493192562016", "1970910838130157820458864955615698679433718580", "1493356764841426836575808731662526187358120386", "991044993470248548647831516740414795787985581", "85510046540867390774596150371901410301339492", "22022683257344691707498452315238450109578", "099961386786228949351457575405534752174157965", "48478868905511873099891526193114937789648", "276835291168433347220650472832468921590881", "76370676782098771143193148537879031633374148493", "626385333299453659180159552453943568929889", "659564697923600054452854248943558227734556", "38762532351241553408971693655453936304699", "468503739433655835162497144097789981789381505", "1462715230244346320564829651167495845109765927", "053948657342659219311121775858685738483411114", "953178358403752027770132558356910681218357", "5084694656236644741376903065758316798536713240", "95660966579331237930760213986858739369799", "70672685794269958112394378917467816339675", "083887823868734595290108757695279433833304", "9378409629091335559407220585286104911175732582", "654539268976253235099175502843294607302074", "44294447144898928607391154994379289262735652", "24169157169548164092742010833819377218868785956", "0548795553899998582285644607728928822265449706", "08942667295592571933425896779052684129736380108", "75034965974258438773692286727954969041993", "52177543662452004759429842428473059900421"}

10268

Returns: 3010.8015843770886
{"278131547555396274585114900685099347009044775", "09553426566381994944447035507446250113561971496", "217440613585305008789585570406114865253514", "3116962629293141486018850298256263575491798", "010612692010046323778708647219392155101284", "994889730174906632712337808533420145359537576", "604850969252822324968302162695392935920058096", "940900269086527420618377798114610845138263635", "389246505155072267516809445301859529422238266", "798021045463808098537228737810046366784580431", "6426344621011983015809042793800567913899015", "779523222997086384996907306184031464047568", "54692692086589938403334144809829001444334042", "17066104510784960906411300814375749543743931", "9086375200942786745188924411608059366634236", "34828741598483134524805888005522195066199042", "44340708162792096566232555367503985135038823", "90595601221425487402915666777481088626584445", "993204175034086188046270895902495526892636", "744786817694362038951349905183937414663258", "14887049869881046911442351235006626962495271702", "75985108498840623143976627952807247069461644534", "43262740591475197819542789876713982476452452", "978053902616589183604807825969378101570556", "70464076178381040155479646924100284633338327", "386715693113251346351454975522840674032225", "25656809071970924876946352643494188297247", "10229453778126812109128684632448161115479975", "8790315197967348873514311743682818204847587078", "05893154740236338914009056742813877034427053332", "20010927786624230644303135055176883089699", "47841882197185555832264520867611912522656", "17503544341307332826926843192930720134317905620", "273336322405846034393603379040540985992924366", "599086955014286502607655130926070113563563389", "495300005248819545949709781513836161095910786", "2448865073740495384016234159296654469174867310", "04846088836133329651521559819255053399500", "8182267371598738314911205799523933456201278219", "19968639727868676957074826569776685556134098186", "52759563913182977237051653798742635162212", "3732750914137881573324379819685416255015706", "9312784803003485400258957408517631883094073", "991447111500599857033273558962671562216559749", "85181756269571205590554214974116971400195096", "2250450078288707594629952752154714390119408957", "4653881331363573078003552603097736593172695"}

38497

Returns: 3088.983083615271
{"1590849932512138154158423818395012082768728340", "830911070328875217635819011964697966674011", "93507915096083770827277750715531885860751864", "33679817655437906587057125208012054472247", "09756189869952758158550531628573882502357951471", "685028117868128797055992344582493166237463", "8712950731860676781431880542264528675062923424", "71533947503166992285196789221415937699265", "885252665609127713923863890517288180715035", "7751370880905240514633642886902576264814404", "613196331757229834515656202365178923924131", "56327572235098159814448101318567869951934", "37165600074028319885402624078013180025688", "78955389573910676541116186283415521243024576763", "9142678278157490286325974306285233798971125802", "3004413583569804343149592642378247079172757307", "2001257921028896651812838823775693754061225675", "4942689071127040038117127173836805376041158370", "264507147730265950601275734555743826072111016", "4272456012230267157851734823285421263680838", "0765220636953537977092867552465690950942094", "1696964273146896259837113272066522648936221285", "01244272793385113450028780324980611842609600636", "79818314872047156667057950914954377587864", "79806100318545334906883882821144692054674", "22523370445992544023441689262718080055686", "66512907342104877742498979925147501171896629758", "2904146903900582493828099906258658056808705", "78087358742201087823460791824777646762582162", "62502417146878373905329347571438425050891849863", "4324560059106095968568862454602703154085178942", "2520202414619962093504698274816474813125670", "41853538158394935387262701475240144168926", "64695120073323584006618666985158247598306", "03060886170157044999824342540342908897672928", "7087716950996395209246301079224182128568964693", "66217925169482464681725756181512752088204892516", "29266371045724544106008679954349372411545", "399475106131610999306268652456427189774621016", "567446869461745918549930796490286692317765", "2896161924880296684707531453755843981951377679", "6351732357723802234484061789010265859974342", "14754356483298906837095074281275174128892"}

47294

Returns: 2840.346964064433
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22734

Returns: 2974.3210993813427
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41897

Returns: 0.3336378864017059
{"1000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "00000000000000000000000000000000000000000000000", "0000000000000000000000000000000000000000000000"}

38209

Returns: 0.33363677742375947
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4242

Returns: 3301.7182154243324
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1000000

Returns: 3296.3150746944284
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1000000

Returns: 3336.6849253055716
{"5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646339803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264746332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850850959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5750851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485048", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669885044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890260646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490990264780646332669803485044698", "5726850851490959890264780646332669803485044698", "5726850851490959890264780646332669803485044698" }

1000000

Returns: 3412.6807396498166
{"59740026857326999213276424915873807807757969041", "76325111473316427435586471205449571521208941901", "74101775210470704392116136581057441900584145640", "51780397228255532056413465348877751825665361973", "74886148403546184021427937386532806502073147383", "89153897699493763171797766720125349265183589745", "68923536027786731244719755503971909108500012661", "89998679183547557319346168839316866786360096022", "94153866972178755972002348080497632465823127535", "56455068339768984497947361930431115753240688039", "59920829666413356956428624621685227152778992158", "74314872386067406215342129486676613521011763949", "82222542681898525646312052660209656792992103773", "26496900757583488017220408253693417912146313071", "60736176736918215150165903830252354261935489429", "73192807429930134038045703279518027853424745652", "04685087651331938304361539626298890182579663694", "95313014466954297013180095664280178176712118126", "06964908464998284496730275211096850003711640555", "42112377798643051325616450858093168921062710830", "74493063939069429028940393013017778211155144957", "34185211986692305367264545810994490211377918257", "18162321552009266418277933815167152822564590492", "61436321795869390621020112512194264635280761323", "95348027952359872891733045921297253864590272119", "54791112675531386585963797432427784982304922161", "70920653750014050077035816801957647232971116195", "10154524189669373118075054509857790560065721109", "08575777218121914024192682008235162775006074041", "20504783424831817755790316386406085280375105117", "64990052497738418593250271621080207102512560680", "61474598961014634025792018930211710271740363657", "73622013960339597810288084103114394204003330426", "92006101901894976777076784573053616171858530394", "25640263974341206837064962449004834299836506168", "29726450247058380887379160346853932560626200413", "80627425185088150633621825066852221148565217335", "93156898756817911741127457871596856667746879045", "81297751285081646013251454525520020238787552926", "85768334388896767229842748186084577900332961856", "84254842866278006374209928169755166607482796967", "40237046605467768698382333453673655284318417144", "23087284179146529594739167858922434086534492359", "86640810679750081380872884085958980530257720477", "15126311287548960691087429985797870213637724380", "22588257971141634398129568363475292540866777385", "60579393962188793782148473743816003617247098307" }

1000000

Returns: 3273.9615210502475
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1000000

Returns: 3261.6170212766037
{"12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222", "12345678912345678911222221235689124567891122222" }

1000000

Returns: 2979.361702127671
{"123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789", "123456789123456789123456789123456789123456789" }

1000000

Returns: 3378.3333333333335
{"12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567", "12345678911234567891123456789112345678911234567" }

1000000

Returns: 3324.340425531918
{"11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111115111111111111111111111111", "11111111111111111111111111111111111111111111111", "11111111111111111111111111111111111111111111111", "22222222222222222222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222992222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222222222222222222222222222222222222", "22222222222222228822222222222222222222222222222", "22222222222222222222222222222222222222222222222", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333377333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333336333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333", "33333333333333333333333333333333333333333333333" }

1000000

Returns: 1597.5435203094798
{"21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199", "21231232321312322123123232131232212312323213199" }

444444

Returns: 1724.8936170212828
{"91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111", "91111111111111111111111111111111111111111111111" }

1000000

Returns: 862.4468085106414
{"12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955", "12345678912345678912345678912345678912345678955" }

1000000

Returns: 3685.0
{"123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111", "123456789876543211111111111111171111111" }

1000000

Returns: 1636.863247863253
{"32777583035609148423614342460717037227836774709", "42723660528505188596592220484154823845459300198", "46740431516192807325583368066051243563157917436", "16411596421534672240606236080764125715673613918", "37038634431149673457784793542131598134832602412", "07484409650856483050833390427590089099059731373", "88945470700542125167182726907655080398627243954", "11805063528483252226461715310936265809628241831", "10371762289819308441635970702315916518432758837", "47813489405661797036191224822748456857880744023", "15040616443345907296800630957462102717343288780", "05316242190460048164129554407065690792012352497", "95937062972976190513821026624948836568999719553", "27206911827175206914670084151102406546804083550", "22455304072506673547094142558984072334792980478", "90086642688135810554756072792026841537584105142", "98310923435777671630728858921730781648653065287", "68075381327186655345644594984512749943680489584", "06837401081660264546774190065209820836345152814", "69553920070969174057095891882376051229976919618", "14622819291596227081208949055364436248980958505", "59579955540789187514293887373583940624648474865", "51723687061337559111919476710351511831302173031", "79147651301626883307512722246907316381458016204", "12301395905198928121666458840334303033223067082", "07385441143629383549911106767791759478921437224", "51333966364286432873227655671717162740839520235", "01597199973107590157243977190067262213198061454", "05971172196133984426759620682185748096254970313", "81360933033459746414348140057732716121689458864", "15097277040317819399976502926674048043642603738", "81501141292341775710824378030730336454524943431", "36266306561620357566760493244174089938269065978", "59152911945216598065813623246291721654414777928", "08802670176852628171468127488932387648309859610", "48208651116389173513718975233830558936588962283", "43110730256916949864397360365990346905943662109", "93147660156055037819070295406529290897466984600", "91708166257873209480326307343033314864731771058", "21997987547670998755179831870001097472979248014", "57249385895811525639709342192706817769301425056", "91921007500499846237597710347586769258551150311", "73396394370916708911367110173471368166533708018", "90363935247216462864346388826376041029688270408", "21595028634350896428576692660994514320264875295", "68135702662379522555067329261877292830413035787", "08150802473898664511051598333822387363245848387" }

1000000

Returns: 3268.289723856948
{"1232439479864973924823094793275983284023", "347982374982374837849372980473473", "3493274923740987390573984793247398479234", "4923798739873294759345793470397423947", "237498723957239570934875394793847", "4354324913874923748932748932748362583254732894", "3249732857329847982374923749823759823", "394879327598327498327592375392572398", "2359873295639847398275983275983275893", "239748932749837598237498723984798324", "23957329857392489023759238749327598237", "2375985923759823759287598237", "2359723957398275982375893275" }

1000000

Returns: 843.5820895522388
{"07570467078484696920428046317340357568851192388", "41295759899052433645905658305524691310191503119", "70244405815769917581290600439433211130863305398", "63721221990871846311367313037084218242168058243", "10221343806306788445922487753307172120294378089", "62452965808768483687825006527141174169512978578", "18899983779581233848930838502747563265865242545", "40159246365330307054947396855242258624049133741", "82953430021644977437089077687635366124135981708", "47876912725140545891014713684866470366582444817", "39880631585801138895823722875194629311707328250", "01445779352899008163200395785472580732004121879", "20260372965213137120939373235351299035272442761", "20986327198289844681137701214905932334746519015", "74426180389111603238300791853373627964302341269", "51480706181225564010958968260798946341468578010", "30773930887897946219869230808680939504721110775", "76924752877869468556531329193872906393040607156", "06661936118838688246560696545097817269461103049", "20527149627660096380191904925377134007658198522", "13916757185931877249880415337867242680799480346", "47271565728190765024775931321447695181486949752", "48899081935670954522032825089774585858484161191", "45816542799013892347036581326142593007162653361", "79034650885185447091169004426173439752057224021", "70102739385056051518949479069657227726943588031", "76975425493929457271438811113356206092545479551", "34028666282639959488999626225021382165048136518", "60446008766613981623731783041988550658731567332", "76835397792703574043408437019526314442693110533", "90793108757904919353692978922174912139566295794", "70394057119679729956048736355719750939624848342", "00118980991128047023277434728226383406443122813", "08776817506956405215014656961468120095925982810", "56670327553461264357989229413460459194251925976", "76380787130655463933376324327945685349131657768", "83970182412386732843753882556892540832973447360", "44532233457416014193510126562398296587758126144", "02179604537819067878617660645829804055330731290", "13515164196904098051889425173811804391708924894", "01402884039892765377615705385518709855312844883", "20770447798086757134066018801596264877717957488", "62699942239138851365880357343699764671155785514", "13668369227776360829262725631763023441415209425", "14909676943271196138797391195196688160595943902", "73341550525982623803479134971793614585260610513", "29274060443620699308324759443425110953820125505" }

5001

Returns: 3331.2129095757473
{"7938024839052273790239970398657627039991", "7236558147138480460326941378838153543659", "5491755418835226678417187877449155582982", "0748583062252271521101876009562859439056", "3630840464643840093757297565304855542192", "4586251397375021871558567941612044597539", "0556326891488719311495909340757506478400", "6247418589993377325634060405685376867184", "9731023718937480405700567806573430487595", "3273977953338589604233700103003836040924", "9291093003019869016448614081031150849305", "2387804571060335023271009717451782545301", "9459396640820607298116118115008370134377", "5126654171348615065310195768547966667041", "0814884579845889470406538512467550520779", "7539949159830907683861967897552494479556", "1591388943951745146032214770957297682998", "3712617650451237241826039496513269003953", "1126919061738703691414610240431794701152", "2249772090716092960284480151115170853796", "3158092433905544382264000817671481853193", "9104900032824835006707332140087384529098", "0535545116193479807584250707682390383100", "8047616149642844981037434812839996173984", "0634697494196709731564512880779601232110", "1380094240297922313216810604994506908828", "0209535989128401081495902359013690402441", "9021549020382168329734861156980226761213", "6573632503735918408958232666344292892567", "2800825803233219163917966644457677021143", "7443079994412947309031153963181308762914", "1250426763419598887388968695968694768138", "0811876188356889937238351542291588040855", "9577376435456943634740750254215160023050", "5748060592837629859255911442636910458216", "0847817046953294166023358181130723583561", "7924839647731749698036654231212564801054", "2679591089979690572201505645230647118520", "1124552323119809524235845110416145233684", "8392309272279309015825028399301527396492", "3597242467592629699803637587716134322111", "2330045701863096284662517184077122747573", "8937157572449960162359191636408195517780", "4453965372184210603784795336089745975745", "8795966852839333914452695030283178686740", "0876463784682304433297971339047418088172", "3060480394511070451424067159150059434444" }

1000000

Returns: 2782.2900709219907
{"572685085149095989026478064633266980348504469", "19720257361", "9", "69", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361", "572685085149095989026478064633266980348504469", "19720257361" }

1000000

Returns: 1873.1721798133992
{"572685085149095989026478064633266980348504469", "19720257361", "9", "69" }

7

Returns: 98.3238536775161
{"028602486509006", "138934460661849" }

1000000

Returns: 45.51111111111111
{"111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111", "111111111111111111111111111111111111111111111" }

1000

Returns: 600.6666666666666
{"01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456", "01234567890123456789012345678901234567890123456" }

1000000

Returns: 3151.85106382977
{"1", "1", "1", "1", "1", "1", "1", "123213", "897412398721", "4123678126312", "321312" }

1000000

Returns: 48.090909090909086

Statistics

Problem Statement for "TheSwapsDivOne"

Problem Statement

Definition

Notes

Constraints

Examples