The Project Gutenberg EBook of The Number "e", by Unknown This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net Title: The Number "e" Natural log Author: Unknown Release Date: June 20, 2008 [EBook #63] Language: English Character set encoding: ASCII *** START OF THIS PROJECT GUTENBERG EBOOK THE NUMBER "E" *** The Number "e" Below is the value of 'e' to about 100,000 places, computed on the NCSA Cray Y-MP using the Brent multiple precision routines (published as Algorithm 524 in the March 1978 issue of Transactions on Mathematical Software). The method used was to compute first the alternating series for 1/e, then to invert this result. The time to compute 1/e was about 594 seconds, and the time to invert was about 97 seconds. No special optimization was attempted on the code, other than the default vectorization that the cft77 compiler attempts to do. 2.718281828459045235360287471352662497 7572470936999595749669676277240766303535 4759457138217852516642742746639193200305 9921817413596629043572900334295260595630 7381323286279434907632338298807531952510 1901157383418793070215408914993488416750 9244761460668082264800168477411853742345 4424371075390777449920695517027618386062 6133138458300075204493382656029760673711 3200709328709127443747047230696977209310 1416928368190255151086574637721112523897 8442505695369677078544996996794686445490 5987931636889230098793127736178215424999 2295763514822082698951936680331825288693 9849646510582093923982948879332036250944 3117301238197068416140397019837679320683 2823764648042953118023287825098194558153 0175671736133206981125099618188159304169 0351598888519345807273866738589422879228 4998920868058257492796104841984443634632 4496848756023362482704197862320900216099 0235304369941849146314093431738143640546 2531520961836908887070167683964243781405 9271456354906130310720851038375051011574 7704171898610687396965521267154688957035 0354021234078498193343210681701210056278 8023519303322474501585390473041995777709 3503660416997329725088687696640355570716 2268447162560798826517871341951246652010 3059212366771943252786753985589448969709 6409754591856956380236370162112047742722 8364896134225164450781824423529486363721 4174023889344124796357437026375529444833 7998016125492278509257782562092622648326 2779333865664816277251640191059004916449 9828931505660472580277863186415519565324 4258698294695930801915298721172556347546 3964479101459040905862984967912874068705 0489585867174798546677575732056812884592 0541334053922000113786300945560688166740 0169842055804033637953764520304024322566 1352783695117788386387443966253224985065 4995886234281899707733276171783928034946 5014345588970719425863987727547109629537 4152111513683506275260232648472870392076 4310059584116612054529703023647254929666 9381151373227536450988890313602057248176 5851180630364428123149655070475102544650 1172721155519486685080036853228183152196 0037356252794495158284188294787610852639 8139559900673764829224437528718462457803 6192981971399147564488262603903381441823 2625150974827987779964373089970388867782 2713836057729788241256119071766394650706 3304527954661855096666185664709711344474 0160704626215680717481877844371436988218 5596709591025968620023537185887485696522 0005031173439207321139080329363447972735 5955277349071783793421637012050054513263 8354400018632399149070547977805669785335 8048966906295119432473099587655236812859 0413832411607226029983305353708761389396 3917795745401613722361878936526053815584 1587186925538606164779834025435128439612 9460352913325942794904337299085731580290 9586313826832914771163963370924003168945 8636060645845925126994655724839186564209 7526850823075442545993769170419777800853 6273094171016343490769642372229435236612 5572508814779223151974778060569672538017 1807763603462459278778465850656050780844 2115296975218908740196609066518035165017 9250461950136658543663271254963990854914 4200014574760819302212066024330096412704 8943903971771951806990869986066365832322 7870937650226014929101151717763594460202 3249300280401867723910288097866605651183 2600436885088171572386698422422010249505 5188169480322100251542649463981287367765 8927688163598312477886520141174110913601 1649950766290779436460058519419985601626 4790761532103872755712699251827568798930 2761761146162549356495903798045838182323 3686120162437365698467037858533052758333 3793990752166069238053369887956513728559 3883499894707416181550125397064648171946 7083481972144888987906765037959036696724 9499254527903372963616265897603949857674 1397359441023744329709355477982629614591 4429364514286171585873397467918975712119 5618738578364475844842355558105002561149 2391518893099463428413936080383091662818 8115037152849670597416256282360921680751 5017772538740256425347087908913729172282 8611515915683725241630772254406337875931 0598267609442032619242853170187817729602 3541306067213604600038966109364709514141 7185777014180606443636815464440053316087 7831431744408119494229755993140118886833 1483280270655383300469329011574414756313 9997221703804617092894579096271662260740 7187499753592127560844147378233032703301 6823719364800217328573493594756433412994 3024850235732214597843282641421684878721 6733670106150942434569844018733128101079 4512722373788612605816566805371439612788 8732527373890392890506865324138062796025 9303877276977837928684093253658807339884 5721874602100531148335132385004782716937 6218004904795597959290591655470505777514 3081751126989851884087185640260353055837 3783242292418562564425502267215598027401 2617971928047139600689163828665277009752 7670697770364392602243728418408832518487 7047263844037953016690546593746161932384 0363893131364327137688841026811219891275 2230562567562547017250863497653672886059 6675274086862740791285657699631378975303 4660616669804218267724560530660773899624 2183408598820718646826232150802882863597 4683965435885668550377313129658797581050 1214916207656769950659715344763470320853 2156036748286083786568030730626576334697 7429563464371670939719306087696349532884 6833613038829431040800296873869117066666 1468000151211434422560238744743252507693 8707777519329994213727721125884360871583 4835626961661980572526612206797540621062 0806498829184543953015299820925030054982 5704339055357016865312052649561485724925 7386206917403695213533732531666345466588 5972866594511364413703313936721185695539 5210845840724432383558606310680696492485 1232632699514603596037297253198368423363 9046321367101161928217111502828016044880 5880238203198149309636959673583274202498 8245684941273860566491352526706046234450 5492275811517093149218795927180019409688 6698683703730220047531433818109270803001 7205935530520700706072233999463990571311 5870996357773590271962850611465148375262 0956534671329002599439766311454590268589 8979115837093419370441155121920117164880 5669459381311838437656206278463104903462 9395002945834116482411496975832601180073 1699437393506966295712410273239138741754 9230718624545432220395527352952402459038 0574450289224688628533654221381572213116 3288112052146489805180092024719391710555 3901139433166815158288436876069611025051 7100739276238555338627255353883096067164 4662370922646809671254061869502143176211 6681400975952814939072226011126811531083 8731761732323526360583817315103459573653 8223534992935822836851007810884634349983 5184044517042701893819942434100905753762 5776757111809008816418331920196262341628 8166521374717325477727783488774366518828 7521566857195063719365653903894493664217 6400312152787022236646363575550356557694 8886549500270853923617105502131147413744 1061344455441921013361729962856948991933 6918472947858072915608851039678195942983 3186480756083679551496636448965592948187 8517840387733262470519450504198477420141 8394773120281588684570729054405751060128 5258056594703046836344592652552137008068 7520095934536073162261187281739280746230 9468536782310609792159936001994623799343 4210687813497346959246469752506246958616 9091785739765951993929939955675427146549 1045686070209901260681870498417807917392 4071945996323060254707901774527513186809 9822847308607665368668555164677029113368 2756310722334672611370549079536583453863 7196235856312618387156774118738527722922 5947433737856955384562468010139057278710 1651296663676445187246565373040244368414 0814488732957847348490003019477888020460 3246608428753518483649591950828883232065 2212810419044804724794929134228495197002 2601310430062410717971502793433263407995 9605314460532304885289729176598760166678 1193793237245385720960758227717848336161 3582612896226118129455927462767137794487 5867536575448614076119311259585126557597 3457301533364263076798544338576171533346 2325270572005303988289499034259566232975 7824887350292591668258944568946559926584 5476269452878051650172067478541788798227 6806536650641910973434528878338621726156 2695826544782056729877564263253215942944 1803994321700009054265076309558846589517 1709147607437136893319469090981904501290 3070995662266203031826493657336984195557 7696378762491885286568660760056602560544 5711337286840205574416030837052312242587 2234388541231794813885500756893811249353 8631863528708379984569261998179452336408 7429591180747453419551420351726184200845 5091708456823682008977394558426792142734 7756087964427920270831215015640634134161 7166448069815483764491573900121217041547 8725919989438253649505147713793991472052 1952907939613762110723849429061635760459 6231253506068537651423115349665683715116 6042207963944666211632551577290709784731 5627827759878813649195125748332879377157 1459091064841642678309949723674420175862 2694021594079244805412553604313179926967 3915754241929660731239376354213923061787 6753958711436104089409966089471418340698 3629936753626215452472984642137528910798 8438130609555262272083751862983706678722 4430195793793786072107254277289071732854 8743743557819665117166183308811291202452 0404868220007234403502544820283425418788 4653602591506445271657700044521097735585 8976226554849416217149895323834216001140 6295071849042778925855274303522139683567 9018076406042138307308774460170842688272 2611771808426643336517800021719034492342 6426629226145600433738386833555534345300 4264818473989215627086095650629340405264 9432442614456659212912256488935696550091 5430642613425266847259491431423939884543 2486327461842846655985332312210466259890 1417121034460842716166190012571958707932 1756969854401339762209674945418540711844 6433946990162698351607848924514058940946 3952678073545797003070511636825194877011 8976400282764841416058720618418529718915 4019688253289309149665345753571427318482 0163846448324990378860690080727093276731 2758196656394114896171683298045513972950 6687604740915420428429993541025829113502 2416907694316685742425225090269390348148 5645130306992519959043638402842926741257 3422447765584177886171737265462085498294 4989467873509295816526320722589923687684 5701782303809656788311228930580914057261 0865884845873101658151167533327674887014 8291674197015125597825727074064318086014 2814902414678047232759768426963393577354 2930186739439716388611764209004068663398 8568416810038723892144831760701166845038 8721236436704331409115573328018297798873 6590916659612402021778558854876176161989 3707943800566633648843650891448055710397 6521469602766258359905198704230017946553 6788567430285974600143785483237068701190 0784994049309189191816493272597740300748 7968148488234293202301212803232746039221 9687528340516906974194257614673978110715 4641862733690915849731850111839604825335 1874843892317729261354302493256289637136 1977285456622924461644497284597867711574 1256703078718851093363444801496752406185 3656953207417053348678275482781541556196 6911055101472799040386897220465550833170 7823948087859905019475631089841241446728 2186545997159663901564194175182093593261 6316888380132758752601460507676098392625 7264111201352885913178482994756824725648 8553335727977220554356812630253574821658 5414000805314820697137262149755576051890 4816223767904149267426000710459226953148 3518813746388710427354476762357793399397 0632396604969145303273887874557905934937 7723201429548033450006952569809352828877 8371067058556774948137385863038576282304 0694005665340584887527005308832459182183 4943180498341996399814587734358631159405 7044368351528538360944295596436067609022 1741896883548131643997437764158365242234 6426195973904554506806952328507518687194 4906476779188672030641863075105351214985 1051207313846648717547518382979990189317 7515506399810164664145921024068382946032 0853555405814715927322067756766921366408 1505900806952540610628536408293276621931 9399338616238360691117677854482361293268 5819996523927548842743541440288453645559 5124735546139403154952097397051896240157 9768326394506332304521926450496517354667 7569929571898969047090273028854494541669 9791992948038254980285946029052763145580 3165140662291712234293758061439934849143 6210799357673731794896425248881372043557 9287511385856973381976083524423240466778 0209483996399466848337747067254836188482 7300064831916382602211055522124673332318 4463005504481849916996622087746140216157 0210296033185887273332987793525701823938 6124402686833955587060775816995439846956 8540671174444932479519572159419645863736 1269155264575747869859642421765928968623 8350637043393981167139754473622862550680 3682664135541448048997721373174119199970 0172939073033508690209225191244473932783 7615632181084289820770697413870705326611 7683698647741787180202729412982310888796 8318808543673278068797716591116542244538 0662586171172949803824887998650406156397 5629936962809358189761491017145343556659 5427570641944088338168411111662007597872 4413708233391788611470822865753107853667 4695018462140736493917366254937783014074 3026684221503351177364718538723240404210 3790775026602011481493548222891666364078 2450166815341213505278578539332606110249 8022730936367402135153864316930152674605 3606435173215470109144065087882363676423 6831187390937464232609021646365627553976 8340194829327957506243996452725786244003 7598342205080893512902312247597064410567 8361870877172333555465482598906861201410 1072224659040085537982352538851716235182 5651848220312521495070037830041121621212 6052726059944320443056274522916128891766 8141606391312359753503903200775295873924 1247645185080916391145929607115634420434 7133544720981178461451077872399140606290 2282766643092649005922498102910687594345 3385833039117874757597706595357097964001 2224092199031158229259667913153991561438 0701292607801970225896629233681543124994 1225946002339947222817105660393187722680 0493833148980338548909468685130789292064 2428191747958661999444111962087304980643 8500685262025843284208558233856693664984 9720817046135376163584015342840674118587 5815465145982702286766718553093119233401 9128617061336487318319756081256946008940 2953094429119590295968563923037689976327 4622839007354571445964141082292859222393 3283621019282293724359028300388444570138 3771632056518351970100115722010956997890 4849644534346121292249647323561263219511 5570156582442766159932646315580667205312 7596948538057364208384918887095176052287 8173394627476446568589009362661233111529 1081604152410021419593734978643166155673 2702792109593543055579732660554677963552 0053783046195406369718429161685827341222 1714588587081427409024818544642177487692 5093328785670674677381226752831653559245 2045780705413525769032535227389638474956 4625594037892492500762438689377647531010 2323746733771474581625530698032499033676 4554303052745615129612145859444321507490 5149145395098100138873792637996487372839 6416897555132275962011838248650746985492 0380976919326064376087432093856028156428 4975654930790973385418558351578940981400 7691892389063090542534883896831762904120 2129491671958119357912031625143440965031 3283521672802137241594734409549831613832 2505486708172221475138425166790445416617 3032008203309028954888085167972584958134 0713218053398882813934604985053234047259 5097214331492586604248511405819579711564 1914588428330005256847768743059163904943 0687134311879618963747550336282093994934 3690321031976898112055595369465424704173 3238953940460353253967583543953505167202 6164796134779091232799526492904515114830 7923369382166010702872651938143844844532 6395173941101311525027504657493430637665 4186612891526444692622288436629946273246 7958736383501937142786471398054038215513 4632237020715331348870831741465914924063 5949302092112205261031239068294134569678 5958518393491382340884274312419099152870 8043328091329930789368671274139228900330 6999587592181529761248240911695158778996 4090352577345938248232053055567238095022 2667904396142318529919891810655544124772 0450851021007152235234279253126693010827 0633942321762570076323139159349709946933 2410139087791616512268044148097656189797 3504315139606691325837903374862083669547 5083280318786707751177525663963479259219 7335779495554986552141933981702686399873 8834701025526205231231721525406257163677 1270010760912281528326508984359568975961 0383721577268311707345522501941217015413 1879365181850202087732690613359218200076 2327269503283827391243828198170871168108 9511878967467070733778695925655427133400 5232670604000434884343290276036049802786 2160749469654989210474443927871934536701 7986739208038456337233119838558626380085 1634559719444199434462476112384461761573 6242015935078520825600604101556889899501 7325543372980735616998611019084720966007 0832028056991704259010387692865833655772 8758684250492690370934262028022399861803 4002113207421986429173836791762328264446 4575633033655677737480864410996914182777 4253417010988435853189339175934511574023 8472929090154685591637926961968410006765 9839974497204728788183120023338329803056 7865480871476464512824264478216644266616 7320960125647945148271256713266970673671 4461779564375239174292850398702258373406 9852309190464967260243411270345611114149 8357839017934997137909136967064976371272 4846661327990825430544929552859493279381 8341607827091326680865655921102733746700 1325834287152408356615221655749984312362 7828710664940156467014194371382386345472 9606978693335973109537126499416282656463 7084905801515382053383265112895049385664 6875292113593222026568185641826082753879 0002407915892646028490894922299966167437 7313477761341509652624483327093438984120 5692614510885781224913961691253420291813 9898683901335795857624435194008943955180 5547465540000517662402028259448288338118 8638174959428489201352009095100786494186 8256009273977667585642598378587497776669 5633501707485790272487013702642032839657 5634801081835618237217708223642318659159 5883669487322411726504487268392328453010 9916775183768315998212632371238543573126 8120244517540185213266374053880290124972 8180895021553100673598184430429105288459 3230647255904423559605519788393259303395 7293466305516043092378567722929353720841 6693134575284011873746854691620648991164 7269094289829710656068018058078436004618 6622356287459138518590441625066322224956 1448724413813849763797102676020845531824 1119639279410696194654264800067617276181 1563006364432111622483737910562361135883 6334550102286170517890440570419577859833 3484633179219044946529230214692597565663 8996589374772875139337710556980245575743 6190501772466214587592374418657530064998 0566883769642298255011950658378431252321 3530937123524396914966231011032824357006 5781487677299160941153954063362752423712 9355499267134850315782388995675452879155 7842048310574933006019795820773955852280 7307048950936235550769837881926357141779 3387502163443910141875767119389144162771 0960285941580971991342931329514592437363 6456473035037374538503489286113141638094 7523017450887848856457412750033533034161 3809656004310586054835577394662503323003 4341587814634602169235079216111013148948 2818953910289168163287093097131841398154 2767881806762865097808571826211700314000 3377301581536334149093237034703637513354 5376345210503709954529420552320788174493 7093767705600930635364551091348162737820 4985657055608784211964039972344556458607 6895155696868993848964391952252323097033 0103727722771087056491296612106149407278 2442033414057441446459968236966118878411 6562903551178399440709617725671649197901 6819523452380744629987766482487375331301 8142763910519234685081979001796519907050 4908652374428416527766114253515386651627 8131609096480280123449337242786693089482 7913465443931965254154829494577875758599 4820991818245224493120777682508307682823 3500159704041919956050970536469647314244 8453825888112602753909548852639708652339 0529418296918023571205453282318092703564 9174337193208062873130358964057087377996 7845174740515317401384878082881006046388 9367116404777559854812639075047472950126 0941999037372124620167703051779035295279 3168766305099837441859803498821239340919 8050551038215398276772913731380067153392 4012695458637642206509781085290763907972 7841301764553247527073788764069366420012 1947457023582954813657818098679440202202 8082263795700675539357580808631893207586 4444206644691649334467698180811716568665 2133896861735924509208014653125297779661 3719869591645186943232424640440167238197 8020728394418264502183131483366019384891 9723178171543721921039466384737156302267 0180134351593044285384894182567887072123 8520597263859224934763623122188113706307 5069182601096890692514171425142181534915 3212907772374850663548917089285076023435 1768218355008829647410655814882049239533 7022705367056307503174997881870099892510 2017801560104227783628364432372977992993 5160925884515772055232896978333126427671 2910939931037734259105923032776526676418 7484244107656444776709779039232495841634 8527735171981064673837142742974468992320 4069325060628344689375430167878153206160 0905769340490614617660709438011091544326 1929000745209895959201159412324102274845 4826054043618718363302689928586235821456 4387969521023526667337243442309157718327 7565800211928270391042391966426911155333 5945696857828170203254955525288754644660 7462029476611600443555160473504429212791 6358748473501590215522120388281168021413 8658651684645699648100156337412550984797 3013865627546016127924635978366148016387 1602794405482710196290774543628092612567 5071817736417497632544367735036325800040 4291990696311739778787508156022736882496 7077635559869284901628768699628053790181 8481488108339469000163807910759607455046 8891268679281239114888003672072973080135 4431325347713094186717178607522981373539 1267728125939582205242899913716906856504 2157505672999127417714927960883150235869 7816190894908487717722503860872618384947 9397574406649127605188781242336831254672 7833151318675891566830067921021594733685 8591201395360301678110413444411030903388 7615204882969091046891676715553733466225 4557597520262477124279622598327840583358 5897671474205724047439720232895903726148 6883880031741464902038435903585279931238 7104284598160899610194569164698383771826 7264685264869172948414153004604004299585 0351641018990275293668674318349554474581 2414019075468160777097792057938389537819 2128847409929537040546962226547278807248 6855080465710431238548733516530705707845 8424333555095822191286279720545546626709 9131902370311779690892786623112661337671 1785129430593232816058265356238481641921 4473254373100206273846681235169101635925 2588256806438946389880872735284406462208 1495138622752399389387349050826254724177 8170258204412985376049982789902008349838 7362992498125742354568439023012261733665 8205467856711479730650770354756205674283 0018747301919731088115751677700507143201 2726354601912460800451608108641835539669 9469369473222716707489728504641953929664 3472525472435765919296994906167018906143 3616907056148280980363243454128229968275 9802266940456421813286245175496521472216 2083982459457661334271056495719356443156 1774500828376935700995419541839029151033 1879339076142074670288679685949854397894 5730076893989007007392469746181285576466 2265412913204052279071212820653775058280 0408971634671637090249067747363091369040 0261564643215956091085109244516245442014 1442641660181385990017417408244245378610 1584333617772925806111591920084140918881 9120885820762701148367176074904698091444 3057262211104583300789331698191603917150 6227929862827094462759150096832263450737 2545136685817248349847008084016386820972 6371345205439802277866337293290829914010 6455897616974559784092114091676840202693 7022923174333449998690184151088899316512 5090001163719114994852024821586396216294 9817530946230476048323993793910021425329 9647623516356900944508605809120245990461 2118623318278614464727795523218635916551 8830579306577033314985100683571356243418 8188440578002884401812903137865379486961 4630467726914552953690154167025838032477 8422724179945136535822609716525883567121 3351954683833534980150326935979816746323 1847628306340588324731228951257944267639 8779467131210427633808726957386093146315 3914854879251402888502518978807602383899 5615684850391995855029256054176767663145 3540584962967967813494201160033258744314 3874624831385021498040168194079568721926 8462617287403480967931949965604299190281 8105976032632517464050164546062667655290 1063986870366826329905057770626639786845 3584384057673298268163448646707439990917 5040188923192675575183540549560177329071 2721913457752490577151277335842331400835 6080926962298894163047287780054743798498 5455628707299684073829372186238317665247 1609096719200723765889422618655048755261 4557855898773008703234726418384831040394 8187436162244552861632876285411759464604 9702772449079927514644579298254980225860 1001772437840167723166802004162547244179 4155478105541780367735533544670303264696 1944756081283193309567968558277193203120 5941616693902049665352189672822671972640 0294933073847175447537619370178829763824 8723336181349941454169473654925484063379 3674361541081593464960431603544354737728 8023610477431153307851599029777714996102 7462776975961248887944860986334942285284 7651310277926279743981957617505591300993 3773682405109025837593451700153405222661 4407723705089004449661329585953602055603 4009492820943862994618834790932894161098 8565949542131143356088102394237060871080 2646591320356012187593379163966643728283 6752328391688865373751335794859860107569 3748896456571872925404485086244499478162 7384251722934396013721240628678363667584 5331904743954740664015260871940915743955 2827739043038687727282620656631293874598 7531774997379929304329437176380185628006 1141619563942414312254397099163565102848 3157654270379068371757648702300523881974 9874663685629265505822288771322178144048 9538099681072143012394693530931524054081 2157054022744145218765419014283867442600 1188904172457053747075555058163283168724 7110220353727166112304857340460879272501 6947010678311789270955272532221252243616 7334336638475659094972822180941868407423 8351567868893421148203905824224324264643 6302014417879820221162484716574682911463 1540756377022274013584110907607846478007 0182766336227978104546331131294044833570 1348695851652674595151876800333955224105 4818176786777215279827025011719581657760 3549732923724732067853690257536233971216 8843908788792621882023055299371323971943 3308353623124887038641619436150652955126 7334207198502259771408638122015980894363 5618085970100800816225574550391013219819 7904552004961858377772104804663553380661 6517023595097133203631578945644487800945 6203697849734599020046068865727018658677 5784275853064570661712719496737108395060 3267501532435909029491516973738110897934 7822976841001176579870981857251313722677 4970660925048187683551600371463868591891 3011736805218743265426063700710595364425 0627604582523368805525211815664175534306 8118154826784416931528440846108758821431 7641649835663127518728182948655658524206 8522218307553061183933269341644594153426 5177865339798058082815880630074995289755 8204686612590853678738603318442905510689 7786984177356031181116775638725899115168 0323654700298798962898618101459647130791 6144369564690909518788574398821730583884 9808095230775693588516160277195214889983 5863232312730890986156077738600698403526 7826785387215920936255817889813416247486 4564332110431948214212997931881046363995 4149653944150138386874838487022468182939 1860319598667962363489309283087840712400 4310227061375913680565188613134583079907 0500360758832724886787932409338007186415 2853317943535073401891193638546730000660 4537837844724692888305469790001312489521 0044694903205883829492361391928430524916 7833012980192255157050378521810552961623 6375236479626857516600665393641422730630 0164865261389184224350179745599361679406 3303522111829071597538821839777552812981 5385701687022026202746786479166440307290 1844549795639984483680785199708820140776 9199261674991148329821854382718946282165 3870648585886462216114103435703428788629 7908341887160621443001453327502971510467 3156021000043869510583773779766003460887 6248616409386452521779352899475784962552 4392559862052140905234625084783048704649 2688313289470553891357290706967599556298 5866695597216865060520728013421043557627 7918402179762665648458026159140717347700 9039475168017709900129391137881248534255 9493128666534650337288463906499684606447 4190752431332390340490819523304438955906 0547854954620263256676813262435925020249 5162756070809004364604214970256914885552 6502281032776211584228243326952862913766 2675481993546118143913367579700141255870 1433194347640357253769143888996830882628 4461642557503400142898255762038636438413 7906519612917777354183694676232982904981 2617176761915542925704384322399184822617 4435047019917125821468768317264607895969 0569981353264435973965173473319484798758 0641379268854135525232757204573294772157 0685001695004695975838937352753862266494 3456437071610511521617176237598050900553 2321548960628177943022686405795558457306 0059837648270333985942009858235140017950 7104569019191359062304102336798080907240 1963126752689163621363510326480772329149 5085915126581214382337107294914808847235 5286394195993455684156344577951727033374 2381299032601981605719711839506627582203 2183713605971802594087061553471310448227 2716848395524105913605919812444978458110 8545112316681735348382537248253476367775 8171286720586514828531727356906983993511 0763432091319780314031658897379628301178 4098064101750165110729329078321774875662 8931065038380609337284139922673338477820 3302020700517188941706465146238366720632 7426443366121740117669149192355709056448 0301634229430183765526310845017251030754 0942604409687066288066265900569082451407 6325991581644993614551724520570204430937 2230555021722229970620974926860976278740 9626448772056043078634808885709143464793 2415362143031999656956107535704172072853 3425017132555881811329550409521783013946 5216436594262960768570585698507157151317 2629289600725876015648405560886131654118 3595862871066549628259953512719324463579 1046554389165150954187306071015034430609 5823022574559749442750676309263225299663 3821939520292791797324709455969101640298 3683080426309910481567503623509654924302 5895752735214124451495424629722585101207 0780211018810672234797257933065318771343 8466713807546383471635428854957610942841 8986017946587214444951988015508040425064 5219148498992040000731067236994465524602 0908767882300064337725657385010969899058 1912909570798666994537650804079178524382 2204107059927888926774575208428752637798 6730360561230710723922581504781379172731 2612348783340344738335736019732359466042 7370463520132718259241090604009763858585 7716958419563109577748529579836844756803 1218748182028339418870763117316152898117 5642971133418149721807804046507765720445 7082859417475114926179367379999220181789 3994333377311469119707378610419639864221 6604558896568320670133750574503887211133 2436739840284188639147633491695114032583 4758415141703256901617849314557069041698 5805021779849763701475891481054320585491 4100662201721719726878930012101267481270 2359408551626016894251114584996583155896 6046009152579788167038462590538325692052 0425791378948827579603278877535466861441 8268277976512589535637614859944850497066 3840626612195714191106324606177418057721 2381659872472432252969098533628440799030 0075945462815492355060864815579289619696 1706071520158982529977280352000261088881 4176506636216905928021516429198484077446 1436178914151915179765378482826870187500 3026486760843320465852547055588241025465 4806040437372771834769014720664234434374 2555141291785030324712634180765251878029 2553477400110485399696054992650809391069 1337614841834884596365621526610332239417 4670643683405047499433398022856103130830 3848457129476738985629393764191440703650 7544622061186499127249643799875806537850 2037531899726180144046677930501403015807 0926621322927364971865395286656753857211 5133606114457222800851183757899219543063 4136923022931397511437024048302273576290 3991179449924848091507100244407848286659 8579406525539141041497342780203520135419 9259776281781828253720229201081864494483 4925542179398272327935709582874859712678 0783134286180750497175747373730296280477 3769089325589145981417248526582995108822 3005522324221858619139479518422013155331 9634363922684259164168669438122537135960 7100317436519590277125716045884860448206 7441093521532790681603205421596795906641 1120187618531256710150212239401285668608 4694359374081585364819125280049207240421 7217091398312311805404327701583562951365 6274610248827706488865037765175678806872 4988616570948466657706745770002071443325 2555573655708315032001908299209654549873 7419756608619533492312940263904930982014 7003711618294859399311999550704553811967 1128936773524995818201177479978863639328 6405807810818657337668157893827656450642 9173966855795550531887153145523530703559 9474018622598814985466073778769878154236 0397080977412361518245964026869979609564 5238285842359535646151854481657999664606 4826139661872030483911956025038111155093 8420209894591555760083897989949964566262 5405141956107800902986670146352385320660 3257446682025943061880177309110921274113 8269148784355679352572808875543164693077 2353637682260360801740406609971511768804 3492748919713308782295112374663263563532 8517394189466510943745768270782209928468 0346841574431277398110441867620329544754 6807751112666368547994446093480999295187 5666499902261686019672053749149951226823 6378958652454628134392893383651565369924 1310963810255911464392380521390786289356 1660998836479175633176725856523591069520 3268959900548847534241605866898200674831 6317428632911963339913270908606507459526 0357157323069712106423424081597068328707 6244371655327502287978025986909811112265 5888815152083748245003446304650598456969 0276166958278982913613535306291331427881 8882493421364424178335193197865439402014 6532808341034178527248987905091993236927 0996567133507711905899945951923990615156 1654803001453592125506964053452638234521 5599921057819137103018897920640888397476 7667144727314254467923500524618849237455 3075757349027073424962988799969420945959 6100870250132945332535804568928570724120 7965919809225550560061971283541270202072 5839941711755209208201510965095266851138 9757715081084944350828545874991294385756 3115668324566827992991861539009255871716 8404956639919591540342183645372120236786 0865536474517565487931892564408527448919 0918193411667583563439758886046349413111 8752410384254679379992035469104119354431 1321913606812965756858361177456465467486 1061988591414805799318725367531243470335 4826375270813531055708180496424985846461 4797346759931594651478702506527108350878 2350656532331797738656666181652390017664 9884854560549613002157761152558133961840 2706781490035025287682360782210739710233 9146870159735868589015297010347780503292 1540143595952986834046574717562321966405 1540147795316746172620872730482063465246 9109953327375561090578378455945469160223 6876896414259601646896471063480741099285 4648235308354013233292486403731800319520 2317476206537726163717445360549726690601 7111767610477749716668901521638389743117 1418062222234571856794150729952620108620 5084783127474791909996889937275229053674 7850205000386300365262188006709266741048 0602734199775666002942794109040006465428 1074454007616429525362460261476180471744 3228899532858283977621846009676692675812 7030280651953545205317353680895458990218 0783145775891280203970053633193821100095 4432412441979491929162052344213463956538 4078120941621483500115588361842116428399 2454027590719621537570187067083731012246 1413620489265556681094670763865360830158 4761451258158856961003033708119705834445 2874666198891534664244887911940711423940 1159869707957459463371702432684848646320 1898635282709231304708921568475820775303 4387689978702323438584381125011714013265 7693205549118601535195516546279411755939 6794795881033393541328970252889353374810 6257875620364294270257512121137330213811 9513957564191226851559624762032820387263 4206622734786822303652201965572932590506 8134849292299647248229359787842720945578 2673299758538185364423706173535176530603 9680108789949050665449154457795216603855 2398013798104340564182403396162494910454 7121048394392009459146475424247859910969 0004654137109163009678595156394733219093 4511838669964622788855817353221326876634 9580591237612512030109838678411957258877 9920604126004986589502724713314676372220 4388398558347770112599424691208308595666 7875319424651314443899711959681059379575 3215552420465941008141835112017419685343 2672343271868099625045432475688702055341 9691995453009526443984463843465988304182 6293223929561261004588464424428501155155 7765935780379565026806130721758672048541 7971578964015542768810904758995646054883 6298914022658002613415803948035797101900 4151547655018391755772677897148793477372 7475257438981587050407019682151012188260 8804008455133279516284128067967896557016 3917067779841529149397403158167896865448 8413190463683321791150591078138982610262 7197969682641117991865603899389541892848 8851750122504754778999508544083983800725 4314688429884126160426822488230977885564 9576542401711451039392798029099760490442 8832198976751320535115230545666467143795 9319152726802782102415406297958288284663 5562358098672563820056521551995179355106 9127710538552661926903526081367717666435 0712134539837113575009758544059395586617 3782829712054469318226040167030853091165 7973113259516101749193468250063285777004 6869871772552265257084287457330398597442 3063975183720997533905509588362364281449 3247460522424051972825153787541962759327 4362788192837402531856685450408939294010 4056166686766440286821160729483030523646 5560955351079987185041352121321534713770 6676813962114438916324032357415737737879 0883826761845875636102643518295181539245 5211729022985278518025598478407179607904 1144720414760917658043029845017468679812 7758497173173328730528113496959166838787 7072315968334322509070204019030503595891 9946666520375302719237642525529103479503 4381635772169811546432924560895115873201 2675424975710520894362639501382962152214 0336210654228218767395801212864427885474 9192897695931576689198730517638869846150 3354594898541849550251690616888419122873 3855226999768226096450075045000961168661 2917109318028235504255365399716605475390 7348915189650027442328981181709248273610 8638015760072406016495470823313493615824 3512829905040540533399257707132101150371 3898695076713447940748097845416328110406 3508048633935552384057355808637187635302 6186797172560815532871643611147487510703 3512913923595452951407437943144900950809 9328721532351959996167502975324759319099 3801296864037978355355907135570836994731 1923538531051736669154087312467233440702 5250069180267477250789589034488566730814 8729946480778649770936196938929089171822 8134002845552513917355978456150353144603 4094412115120017386972614667869337331543 4100758751490829582275691935054218410644 8264951943804240543255345965248373785310 6579790379775050314364746514224847688313 2347976267368985547494427794991656010852 8257618964374464656819789319422077536824 6611104276719364818363605341087489710668 6631880502655592956812395968044929516661 5409802610781691689418764353363449482900 1259293668405913700595269149344218618917 4214256107189684662633587441497697392156 6392767687720145153302241853125308442727 2457711615055505190762762500165221662747 9625742442542054678576747819095948650057 5711016264847833741198041625940813327229 9058914864221279680429847253562372028878 3005178853973790945526513514407313004986 9453403245984236934627060242579432563660 6405975494712390923724581261545825266673 0470231935986652337885624422918827843644 0434628094888288712101968642736370461639 2974856167800797799596968433677303524830 4747824066992827714006903166070995147315 4191919911453182543906294573298686613524 8865005747802519776074426607983002915730 3052319905218571862854368757786091572692 5232573171665625274275808460620177046433 1012124434092813146597602213604162230311 6775008596012847528925946334831240876674 0128170543067985261868949895004918275008 3049989264720349869653633262109198306214 9509587722826081556670215569348463407977 6879525038204442326697479264829899016938 5115521246889358732898783362678193617640 2368171460649518550878059663535469878820 5094762016350757090024201498400967867845 4053541300504824049966469785580026289318 2651870871461390952145498799230043177950 0489569529280112698632533646737179519363 0943996091763545687990028145151697437175 1833063223294219913213761450641139126983 7128970829395360832883050256072727563548 3742054978566598954690899385589184410856 0511151035436747781077850057271818080966 1542709143010161515013086522842238721618 1090431831637960464315231844346697999048 6533637531929596772608085345765227471404 7941973192220960296582500937408249714373 0400873769880687970380472234888258198190 2564408684774976750899916415350216022396 7816357097637814023962825054332801828798 1600469103366024159045046373335974881199 9866399561717108991180985119761648649923 3594328274275983382931099806461605360243 6040408483796190725421658694094866820923 9614308381730362152064229783998253369802 7039931804024928814430649614747600087654 3055716726972591146319906888238930053800 6156800773098441606135584370127757346370 8822073792921409548717956947854414951731 5618281763439295702347104600882306375098 7752139122341954847119698230316954446804 5517922669260631327498272520906329003279 9729329068272046476503669697652276736454 1903163988743304222632202132536817604416 9612053532174352764937901877252263626883 1078793451941338259963687950209850330214 7230760337544234687164722379550779413030 4865403488955400210765171630884759704098 3313061095102941408655740710746404019373 4771881533990204703674908435930908635477 7210564861918603858715882024476138160390 3785326601858425689141091944645661626677 5371236599283248186573925142949855514151 2136758288423285957759412684479036912662 0153084180417376989637590025469994541316 5934198562478071443497720199170266538071 4107259910648709897259362243300706760476 0976904563415765733955495884489480936040 7715568874728845183810606903802652831827 5560395905381507241627615047252487759578 6507848945473890965733127638529626645170 0445962632793463772115102854547231288003 9058405918498833810711366073657536918428 0846558989823492193152052574783638552662 0540070356131026040514507932592579822740 6012199249391735122145336707913500607486 5616573018540492174771620516784865079135 7333633425768598836125272025094401943067 4728667983441293018131344299088234006652 9153857637791109557080006001435799563518 1159676472507566836772605235293977301634 8235753572874236648294604770429166438403 5588464223707601117748210796259011802655 4886899518123947062595425458449134020340 0196442965370643088660925268811549596291 1661686120361953192532626622711081421498 5613264646721195480114245513394638238590 8540917878668826947602781853283155445565 2659339124878856395046441960224751860114 0523918754374252658168500305230187709615 2411653980646785444273124462179491306502 6310629034027372604799401819299544542972 5637750717270565927177928553719554743385 2182309492703218343678206382655341157162 7886039901574952080654434094624466346532 5358157481402247126061897306086055906508 2163068709634119751925774318683671722139 0630930610193031823266664206281551296476 8531386101867292188934703934207224555679 1239578260248978371473556820782675452142 6873142522526017958897591162387208075805 2722103132744475408331921513593452696139 7220564699247718289310588394769170851420 6315571927036363450395296043628850885551 6000837197352638383899678918460032707368 2083234847108471706160879195227388252347 5063808116060908401242224314761035633289 4060928243012546201380603260812194287684 7907192546246309055749298781661271916548 2296443172635875245486075630206676569423 5534277461763554923181745615918566806168 6428714964129290560130053913469569829490 8910039912590882903487919433686969426206 6294694851493147268892357161503240554226 3391673583102728579723061998175868700492 2274186290770795088093362153463038429675 2560436960611019384272388310758777165359 4778681499030978765900869583480043137176 8329548717526047141130648472708872466971 6458521877444210090009091618981941345630 5028950484575822161887397443918833085509 9085660085431027963752474762653530315586 8451512028339664054749694634398628829195 7510384781539068343717740714095628337554 4135679554246646013356636173058117116460 6271785407889849533432910031598567393230 5693426085376230981047171826940937686754 3018370155575408223715380378383833427023 7953593440354945217396032709540771210733 2936507766465603712364707109272580867897 1811824937995404770083693488892209638142 8156159561093181518370113510479017638359 5168144627670903450457460997444500166918 6756610358893134838005127364111573045992 0595547112244390319647664276103816428591 8037488354360663299436899730090925177601 1620437614116166881281782923823112217458 5023808073372720490888009518188957631410 3157447684338100457385008523652069340710 0789559165498130372929444623063712843579 8480987196414308514687852503312898931950 0645722582281175483887671061073178169281 2424836137964756924820763213564273572616 0982514244526251595251487527380563315096 4052552659776922077806644338105562443538 1362589418097880156773789513103131573611 3602604789076194559182028936577011641688 1703644242694283057457471567494391573593 3537631148302466687547275666530598197468 2234657869997229179241615604355766518338 2167059157867799311835820189855730344883 6819344183059870218805022591928180477752 2388440716789478041470141465107358045202 1499197980812095692195622632313741870979 7313208708645522367404161855907938167456 5823435303728330950372902242980276845155 9528656923189798000383061378732434546500 5827227123250314207124881002906972263111 2906762908095114575806027080609280150440 6139446350643069742785469477459876821004 4414534380337597173847772320520653010378 6132641882358603656905477334307091175915 2582503029410738914441818378779490613137 5367946548933752603229062776319833379768 1664172108314055186413330222478711851181 7036598365960493964571491686005656771360 5331924231852621667602220733688448444092 3447094856802790589419182996946772445626 9443308241243846160408284006424867072583 6610114334042144736834536384965447010678 2731316953843591912044028394954195687445 3676459875488726170687163109591315801609 7223820497725773074545629791279061775316 6325285720585876637675428291793354992367 8212008601904369428956102301731743150352 2046656750884915930259266188165810087016 5849945649558685562820874724831835151633 9189292646558880593601275151838235485893 4261652230866973145114120356599169341030 7697477445194704383673960007657862824547 2064617380804602903639144493859012422380 1733770381546752976455965184926760393001 7194304251179404567986211463013840237109 9347243455794730048929825402680821621522 3465602742584865956870745103527942916334 0591502507599239861122434031205699978051 6223878772230396359709132856830486160362 1275795616013285618663881460047222005800 1758028227927216784272064996695684090575 2590774886105493806116954293569077377792 8210841597374696131432918085104469539734 8506759050366239172210873233316990960336 3771705474725026941732982890400239372879 5493865404638285967422163182015301396297 3439847958862863293474665069028406671901 8081265539973675916799759010867483920062 8778885311027816950875457403846075946169 1958461065596332728348560957030557250249 4416337066573150237126843581984154103154 4010084303806314421837767503498134081693 2520124081345228597462671517715222306374 1359255747513535160669108359443999692315 8981567320330271292842412196519363037344 0798120465679532298635737458903165400701 6472204989445629050395873788912680565516 4642744601747381752963134587393904845604 1420342646556042211223913463102316129083 6446988901247285192778589195228773637440 4326592646722399821864527976648266730701 6880272205233860037284290315582845459385 4349099449420750911108532138744823216151 0078089225162851232757243551019990381959 9335003264144605347035729307391257848175 7987468353429629749652545426864234949270 3363994275193542400019731250988824196000 9576625721762186047457376957764958220179 6258392376391717855799468922496750179251 9152182196246535755705642282203995466826 4832982299616721708015680108079977712651 7156274295763666959661983507435667132218 3833585095366658066055971483767738669225 5160346364438626997729575065846892959980 9168949981898588529537874489519527097766 2626841770885902843216763521326308388127 6633536331900413433284434763006798202371 6933653652880580156390360562722752187272 4547642588409952164825544536620838117891 1772522568261147801424289697096712196750 2094421226279437073328703410646312100557 3767274502716389752341114262878287367583 5881905674216306152341678947605687927715 4789714326222041069587947186435439940738 6399489868361689193778366483271373636546 7690117376024664308228536249471260517329 3777247276797635865806019396287718060679 1224268139228721340616948820295068316545 8970762366830255616755947749871518342698 9208952182644710514911419441192277010977 6166458500689638494261655934731129610642 8237904821605621009426507617383808247903 0510998790719611852832556787472942907151 0414689481049167510352958972423818022881 5127658225719070553765245528551159863642 1244284176256230139538669970308943645907 6006849380408752108541598512780703332077 7986563590796846219153494458767717006377 8573171211036517486371634098385626541555 5732926646164022797911959752485253003767 4177405612570030362581170483838539120727 3191845064713669122576415213769896260940 3518041474320536003692341790354407357030 5831474162345284018894080898312519130774 1823338981880316339159565954543405777784 3316811625518980604091830189075121701929 8362289709959898340548496228428939846984 7938668614293324543983592637036699355184 2316616152445059805767457653355523387156 7821146668999684522704295458971092216365 2573965950289645637766038988037941517917 8679106751990099661392062387323187867584 2054427939636675910412682184337501574306 9045967947046685602358283919759975285865 3843381891200428537875493027689721681991 1334069728225553530004474395883007979973 6518459131437946494086272149669719100359 3999747352627641261259953509026095400486 6939895589948742137959080289319691484582 6873123710180229775301190684280440780938 1565980816946116793744256632446567996063 6375154630483311272223181233837177980043 9731087402647536582575657351059978314264 8318796198437654958778036852617518353918 4492048819862978632974313694851178057929 8636452193232481339393090754566368038513 6306197180339579795225395086974325465026 5912358504928302883293448928459137362162 4852528877442891851104093746333590660233 2397119228144507355883733240578148626622 0748621551337503677558549413867835292827 3109003823116855374520901095101174796663 0033303525341432300242882480513966314466 3265608158204521688392231202567106538845 9503224002320453633895521539919011035217 3627209095655008464866053689754984789958 7559610316769658716128195191966889332664 1203784750417081752273735270989343717167 6423299569356971662137827361388995305157 1182296089639405538043193939845397086441 8654291655853168697537052760701061488025 7007853871508357794809523131527477357117 1364335641324297420813726689614910956421 4803567792270566625834289773407718710649 8661504474787261642499766714813830539479 8495893806420288666795194348275016819202 3591633247099185942520392818083953020434 9799193618533802014070724816273043134189 8594250385840436599328165194149737728672 9589582881907490040331593436076189609669 4948000671943714240581053275177219524743 4498341419197991817990986463158324602151 6575531754156198940698289315745851842783 3905810294116004986993077514285130212862 0253950873238877935740978128818700082994 4831476678183644656510024467827445695591 8457680687049780448241057997107715775790 9352580382422737761243690870987518914904 9904225568041463131309240101049368241449 2534279922013463805383423696437674288625 9514014617820181073410056546670823685431 2816339049676558789901487477972479202502 2272181694051590421708921042875521886583 0860845270842392865259753614629003778016 7001654671681605343292907573031466562485 8096395500800233476761870680865268787227 8317742021406898070341050620023527363226 7291964034093571225623659496432076928058 1655144286432049552568385430792542999093 5319932943296601822078793312232322592827 6556048763399988478426451731890365879756 4982076074782702588614099760507880367067 3226819247351364635675861121295307464477 7149423343867876705824452296605797007134 4589875941266546094142114475400072117906 0745833068686623130915578000596652273618 3536340439991445294960728379007338249976 0206304488060645748927405477306939713370 0796274613553444251474542365466275225262 4869916077111131569725392943756732215758 7049524172324282065553228088686701536814 8291173854273579715415794368949106375974 9151524510096986573825654899585216747260 5404683423386107608236057829419480093343 7004686656825857982732387515830256672015 2604684361412652956519894291184887986819 0882773391472820637945122602945157073671 0563772002342781180262150269179040048800 1808901847311751199425460594416773315777 9517354444909657521310263068360471403314 4231429807789561705125693005180428747236 8435536402764392777908638966566390166776 6256785753542399474279194425446646433155 5413826554338848777885997206367966069232 7601733858843763144148113561693030468420 0174340613952200724036588127982491432617 3161781389497095503836947959461797982925 7740992171922783223006387384996138434398 4685022347804387337844709287038905364205 5747483628461680936365097379090020411852 5835525201575239280826462555785658190226 9583763453426634209462144266724539871710 4772148212815760727530517333096345590932 3664528978019175132987747952929099598069 7901485158395404442839883817975112453555 4842612678421779772826898973500795450583 4273726937288386902125284843370917479603 2074795540809114918662086871848995504452 1061615543708329950285490365961736272655 2868081324793106686855857401668022408227 9924333943609362233903214993572625074806 1740917363606236546445847638464786952054 7719533384203403990244761056010612777546 4714641774126255485198301446274055386018 5570835998154489128686348072071006178705 9669365218674805943569985859699554089329 2195072693375502358215614249945382347811 3831659166268310306519473023341938416407 6823699357668723462219641322516076261161 9760347088440464730831726826112777236133 8193849060653440404390490986412690347926 3503943531836741051762565704797064478004 6843230694302417490297311819511329357468 5455048471107874290549987060037398311376 1544808189067620753424526993443755719446 6654535240882872675377591970745262863228 4021962955724793298713285247999463893892 4943286917770190128914220188747760484939 8554711685248105599915744415515074312144 0612033376286953379243954715539421312102 1954430556748370425907553004950664994802 6147945247390128028426466892294556649586 2130811891350027965491034480615017040726 8010067948926855360944990373928383520627 9928201815764270549629974019008374934449 5060075436552575890554655240210341286212 4809003162941975876195941956592556732874 2378561126697417713671044248219166714996 1172890394439366534029422651457568290749 0402153401026923964977275904729573320027 9828160621305231306587315130769138323171 9362666446550229073501734765629303331852 0949298475227462534564256702254695786484 8199775133263932215794782124933070511073 6747491801634566788881078210115182631487 8755138027101379868751299375133303843885 6314151759089289869561975611230253108750 5718896253576322583427576334842101666810 9884514141469311719314272028007223449941 9990039649482454575207049220916206142229 1279532268823904649823908159296111100375 6999529251250673688233852648213896986384 0524370494021521875478251633470824303035 2103692784976251731782586086221561451916 5573478940019558704784741658847364803865 9951196514095426150266151476512208202458 1601080121827598257747765239385915916506 7449846149161165153821266726927461290533 7531630556544407934278765502673012145783 2488594873689907351216611839787734271587 2870912311383472485146035661382188014840 5607160746524411188418007340678985871592 7398245214732831721462190733049206081744 0914125388918087968538960627860118193099 4892408117023504135541268238637443412092 6778172979069471475901826482476111241455 6423937732224538665992861551475342773370 6833441730731508054401388940840872531975 9553889761398640016563990693460067078050 1058567196636796167140097031535132386972 8990017498629488833623898586321271765713 3014207133017999232638198209404299337779 0345261665892577931395405145369730429462 0794880331410992499071132416945042413912 6539727407898495307373036413489368806034 0009640631540701820289244667315059736321 3119262311791427949448972814772640383210 2172071801756160102511117902216370347629 7572233435788863537030535008357679180120 6530166683167802698738607554237482985482 4636098160895767042190314568494296728664 6362305101773132268579232832164818921732 9415531513869887818372322713640117558813 3252429413534869938465813717585761433095 2147617551708342432434174779579226338663 4549594387368078395699119870593880855008 3750798405112665897301814932106195076900 7587519836861526164087252594820126991923 9167222737184303852631072660000473678724 7491582860169443992004157110270608150727 0147619679971490141639274282889578424398 0014979856581303057406200285540973826878 1989115895548758648664570923172182587034 2960508203415938806006561845735081804032 3477500842141005745773428029854040495555 2921598640493324648104077307661169160558 6804857302606467764258503301836174306413 3238877079996986413722755263176496628824 6790109453111712024389032341025993751158 4651917675138077575448307953064925086002 8356296970450161379356962667597759234361 6636937503536869945455039287444994032832 8128905560530091416446608691247256021455 3812482853076135561496184443649230142909 3828937321531281879754113921941560663162 2784836152140668972661027123715779503062 1329160019888063691276474165670674854907 9534276233825394399002249897288366026392 0518704790601584084302914787302246651371 1443954182534412690033311819142680707351 5928418041510055519914656493487279696935 1992963117195821262627236458009708099166 7528203658186991119483658661027583758633 2299322554147747921042132416684826495311 1826527351008031659958888814809945737293 7856814114380215238767064550632330672339 3955196426039744382987482232266203635286 1302543796600943104500158604854027036789 7119346955799891891123022333816023022362 7772608484629618955073085069806150028143 6425336666311433321645213882557346329366 8709567084322525643338959978124021641899 4697834832037601161391385549993399078665 2305860332060641949298931012423081105800 1697459750385168871120377476315773118313 6000274250272245157090630449636923093838 2329175076469684003556425503797106891999 8123196025337336774379706877138147475521 9014292858678172404424804932375033095700 2929126630316970587409214456472022710796 4847786573106608321730937680338217421564 4660219033520398153161893578708356160330 2255162155107179460621892674335641960083 6634838358967034091155130878201387234947 1432140045051394142899835057603879934335 5677628023346565854351219361896876831439 8667357260408695111366498812299578016188 8283412400412614225147518455250250264089 6823664946401177803776799157180146386554 7332652785694180055013634339535028708362 2060512183941851623915370979076808490967 4194289061134979961034672077354959593868 8624279864114379284356205759555001443080 5126766443218368832143458370854908224001 4585748228606859593502657405750939203135 8817224421649554168897855582651980462455 2789834328957841696889075623746728104480 3018524217706136533236073856228166664597 6540768447159639307820910170907633779177 1148520549336793686843083240412678922092 9930411890501756484917499452393770674524 5780191718416795418255543779302992492778 9241627725778814797477044600542366934615 7135208417428211847353652367573702352791 4598376457122576461226056281278521695808 9280898839459440616534052193251484330610 5322700231133680378433377389724881307874 3256149527442435847530111503451037376882 2383757380428200735858693804433152925312 9961025096113761670187568525921208929131 3544731963084400668351551609139256929121 7578437917900480884802302930439263092134 2768601226558630456913133560978156776098 7118092384406563531361826769237616133892 3780297272073624396723985414448075728681 3436768000573823963610796223140429490728 0585514447713386823144995479293381312599 7199689407223384740454259231663978160820 9399269744676323921370773991899853301483 8146223642994939020732850720980409053000 5916009164171017560540981430190644437990 5831277826625762288108104414704097708248 0779051682258572357326652344149561690079 8552084884188602735278086121804941806001 7941147110410688703738674378147161236141 9504740565210410022689878585254706890316 5709467713182211320550504657970186933776 9278257145248837213394613987859786320048 0117928145468590965326166160684031600779 0158494684022434416393831361874227541771 2170336151163782359059685168880561304838 5420875051269331441717058805172781279175 6405328292942735797182336084278467629232 4980318169828654166132873909074116734612 3671090592361551138604472463787212446125 8040693172476915221921740909688020900880 1535633471775664392125733993165330324425 8998525989667247441265036084164841607244 8212598055075485123231333130062149004270 8542735985913041306918279258584509440150 7192176047942740477402533143054513677103 1194754452132173222587555048979926746854 1529538871443696399406391099267018219539 8906851867558685744344692137920945906836 7792952824679543730226347249535946630023 5998990248299853826140395410812427393530 2075751287742739928248669212856372400691 8485977112648035237602546971430931663653 9718514623865421671429236191647402172547 7872389640431453641905411015143717737977 5246363274161926999046159589579394062298 6041489302535678633503526382069821487003 5780611015522102244866332471843670355023 2667274978773047021616501971193744250562 9639916559369593557640005236360445141148 9161551477763018763021360688252962744602 3807752318964689404303318214865563701469 2476427395401909403584437251915352134557 6106980464697394245117979990487549514220 1004309023571363689261949376360267364587 2492900162675597083797995647487354531686 5319001764272227510394460996414393226725 3210866604791259893835192669449755356809 6931962642014042788365702610390456105151 6117920186989006730270823841032802134874 5672006283974482871329822395757910542081 9286308176631987048287388639069922461848 3239929026853924998123670914216134887815 0123409338799977609743361575091099258546 8475923085725368613605356762146929424264 3239066267086028461633760515735990508698 0031423973536892843529495809943446541431 6189806451480849292695749412903363373410 4809435794073212660124507966137894422084 8584053644602161651788556896930268518895 0832476793300404851688934411125834396590 4222111527362762786723666658457575595854 0948624826169448020179174822308583500786 2255216359325125768382924978090431102048 7089757150333309636515768045019660252155 2708035210384817616700444374057213129425 2820989545456276344353575741673638980108 3105799316979179167182711458374352220263 8777180525029079164541479117361625315584 0768495583288190293564201219633684854080 8659280951315050126029195625760329325128 4725046988190814647532434236386386024794 3921015193235101390117789997483527186469 3460245542470283753000337254039100859976 5098764283280290844566202167836226727229 2737780213652404028817217012490974899454 4308268617722393852508837607497421959426 5521730173335585138940745734814416151138 0845358039740277795072051893487170722955 4276836558267067663139119722118115284665 0222338349090667655416833690795940940457 6472940901354356409277969379842065738891 4819902253990223159133881458514872251265 6092757679587375920701391502921651372085 1137197522734365458411622066281660256333 6320744499185114691744550622971460865787 3631358538902366255728542451601808048716 7823688885575325066254262367702604215835 1601748519818854608600365976067432333464 1047199102756235864534174863172655639132 0606407754779439671383653877377610828300 0199373597603704672457378809679398944937 9582960291074690160945128845655007145809 1887879542641820145369659962842686882363 4958792770070252989609967989759419557352 5391423778244330274670828200872260205341 5292735847582937522487377937899136764642 1537278435539862440158564886921016447816 6160296211357005663834799033404962387594 1092886778920270077504951511405782565295 0150244849682047443797108729431085416845 4051301631090226711295195914052082754686 6418137305837933236150599142045255880213 5584747515162678153094655412405240916638 5755129889483479742332285450414052735423 5070335984964593699534959698554244978249 5869291791824150680530025533704127787034 7644624432920590683290188669240022239191 8714603175399666877477960121790688623311 0029086683054317870093550669443891319133 3358636803744753066450241843713603085228 8582121720231274167009740351431532131803 9780336802281542234901837374941179732544 7859415796210437878707215481409172516361 5415163381388912588517924237727229603497 3055338409428899189191611862495805600735 7052722787494032125064542620630446947080 4277945973817146810395192821550688079136 7012101099442207370246136871960314911623 7096793935463639644813902571176805779975 1751298979667073292674886430097398814873 7807673637928867677811705205343677057315 6689589918153082576160659184376050505170 4242093231358724816618683821026679970982 9664362247236448986489768571001736435473 3695561934763859818775685591237623258084 9341570570863450733443976604780386678461 7115203251155282371614692006347135703833 7722987732136502886886885943405120579838 6937002783312365427450532283462669786446 9207809440521385286533846279707480178724 7798846114601507761711626180078155791547 2305214759943058006652042710117125674185 8602741888013779312799381537276926121140 6681015652144190356733392611669714045381 2010040811760123270513163743154487571768 7615755549162366017628802206010686555241 4161931431267153558715486674789939868551 0873576261006923021359580838145290642217 7929877487841615163494973097007943683050 8095562126459279533369063193659441326111 7944256602433064619312002953123619348034 5045030043150967985881118969505373356710 8633688694466556411266228792181211412142 5167348136472449021275252555647623248505 6383913916307609763649902889305880534066 3135247099699336256810236039226404358878 7550723319888417590521211390376609272658 4090238735534185164264448652478057638261 6002385828069314892223145775878379156490 2227590699346481624734399733206013058796 0681363781529646159632606987449611053683 8420310536418367537359417637395598808859 1188920114871545460924735613515979992999 7222980417071122569963109459450977655664 0997272282401529366309489106796329673550 5830412258608050740410916678539569261234 4991028197595639557117530118234803041810 2908971965527824577028308532173374159393 8595853203645590564229716679900322284081 2595690328869282912601392675878582847655 9907582801661112006314541131514410887576 7081854894287737618991537664505164279985 4510774007719463980462650777766140535248 3109049789985951087311262061301875710864 3735744708366215377470972660188656210681 5163280009080861985543035979484798697894 6643402702929089914343222392033348710826 1968698934611177160561910681226015874410 8330930703775068769774858403241324746437 6308788966615197255618037147259002955071 8424245405129246729039791532535999005557 3346001116935570202257224427729502638405 3830943399938338801883955382154037144739 4465152512354603526742382254148328248990 1340230545508113902367680386497238999242 5780031580372555541017846186347869064604 5865826036072306952576113184134225274786 4648523633247591026705624663508025530581 4220155228205098919781842042502825952188 0098846231828512448393059455162005455907 7761219812979540401506539853415790536291 0177793977695789208451097926538290562673 6402636703151957650493344879513766262192 2371856429991508288980809041891810154508 1314503438573403257954970781938528569992 6238835221520814478940626889936085239827 5371744909037699041455552602491901263414 3132737382707595039088253122353687638981 4182564965563294518709637484074360669912 5500260804241605625335918562309553765668 6612402787588310102149528460080480502804 5254063691285010599912421270508133194975 9171467622673050442250759152902517427746 3649455505232518632241138840619125701291 7881384181566918237215400893603475101448 5542546989378342396064608136668297500193 7911506170945268098478515286212317137789 7417492087541064556959508967969794980679 7709616830579416743105192544863273588851 1843659714358334875602740540016557117830 9126113117314169066606067613797690123141 0996720131237303297076789887400993173096 8738012674053892361223037077972702519134 0850390101739924877352408881040807749924 4126353464131818587924807605532681228815 8430747132676828309720314904986888445618 7976015468233715478415429742230166504759 3933121322565101891753685663381397368363 3612601090841959021558211181667741384396 9205870515074254852744810154541079359513 5966536300491887695236775791473191842258 0680253981841892988894303822476618640585 6591859943091324575886587044653095332668 5322613212098258391805383608141447913203 1969927603719476019128667430861521724304 9852806380129834255379486287824758850820 6093892146686937298811915601156337012486 7540420591146493088821905024885764575208 3363921499441937170268576222251074166230 9016658670677145688627933431535135056882 1616511280731852933312407091234383250230 2341169501745502360505475824093175657701 6048845770177621831846155679784275410884 9950161091272081791353240678426716179201 3428902861583277304794830971705537485109 3804180914917502454334322174459241330379 2838169433097501291854459692338873328861 6144238100112755828623259628572648121538 3489006985115034853695444615421612832417 0053358318052008291572290469636555317815 2398468725451306350506984981006205514844 0207695393241550967626808876035724639139 5527822224643912259265192128844696110746 3586148252820017348957533954255019475442 6431489032333739267634091155271897684298 8778361734661353538850765632710781431243 5018965109238453660236940276060642119384 2276657552106636718796032175271844046515 6042728986956020699701290636784716165479 3068868305846508082886614111979138822898 1124982614345594089618135092268576114746 0940614793724000884215353586205278012501 4270055274468359151840373309373580494342 4839404675057083479279483381332762379378 4462920932399941759337491789978648495814 8818865149169302451512835579818112344900 8271686445483065466339752560796159358308 2140002195161134233705835911154521729372 1664061708131602078213341260356852013161 3451368716009803787125567661439231464580 8565208403974421735274481374121527747520 2259244561520365608268890193913957991844 1099715883127800208982759358981064821179 3615795183793702674145140090283306446620 9280549839169261068975151083963132117128 5132574349645106814796947826197014832043 9220614010952345320926931176229813942204 4308117317394338867965739135764377642819 3536214678374361361615911679265787001377 4812784851004144784541646456849660669913 9509524527949914769441031612575776863713 6346444770067871310668324178715562817791 2233907784127518419316118815588722967674 9605752053192594847679397486414128879475 6471330495435550447902771286900956433579 1340512737557039180682234471816793932912 1448449553897728696601037841520390662890 7812182401412993685904651465192091986053 4778857684269653845944570016975842253124 1268031418456268722581132040056433413524 3021027392137884152504757045338780024673 7857147002108731469325455792313475724364 0544448132093266582986850659125571745568 3288314403227980492741044039217614384057 5075028860842353696671519166851042800174 8971774811216784160854454400190449242294 3336663383476844380726243073190193635710 6744736341369846732852260557012645012334 8367412135721830146848071241856625742852 2089091045837273862273007815666689142507 3345637325956725335431617158653333984332 1723688126003809020585719930855573100508 7715337374464652118744817488687106523111 9869111405850349223915675546214246755049 8676710264926176510110766876596258810039 1639483978119866155851962164876959363989 0450038325804105442059548285995523906575 8108017936807080830518996468540836412752 9051828137448787696395483063850897561464 2187488927129489039802562304681217514550 2330254086076115859321603465240763923593 6999491804707804967644868899809021237357 8045704038082077035738758852597604243460 8851075199334470112741787878845674656640 4719016196335467707140905908269542251964 0944631954765865303210472380462524997191 0690110456227579220926904132753699634145 7687952422445639730183112914511513227578 4132037622586245822478469666978594791498 1610522628786944136373683125108310682898 7661237826975063430472632784537190244479 7097501739683121449335729079164877991508 9163278018852504558488782722376705263811 8037924778355400181174529577473397140123 5201145990198475335843486129709292852942 4139865507522507808919352104173963493428 6048713423704295727578625493659178054016 5253633041069203370469109309758878293829 1296447890613200063096560747882082122140 9784723016806008358123369570514546501812 9269436457835781560850330339246603955379 7630836137289498678842851139853615593352 7821037407330768184330408936244605767060 9618829452917136294096759250763134863660 6011346115980434147450705511490716640635 6887390206902794534382369305311334409013 8139284916350748444907682838668747666361 9303412376248380175840467851210698290605 1961123571888111507236073031585066225745 6636674072066899906132062779399411280575 9798332878792144188725498543014546662945 0796707076881350222305805622259429830968 8773285678897149462388827218464761815304 5844390967248232348259587963698908456664 7957542001959919192407076158230023289774 3974811269047654625687368435222906321788 9227643289360535947903046811114130586348 2445664891592113822588678809725643516464 0436432841607624776611434988031979223053 7889671148058968061594279189647401954989 4662329621625672647390158186929567656014 4424850182171330052799555131253984991993 3907083138030214072556753022600033565715 9342831826509089793508696989505426358430 4676514566899762798960629592511976367290 7762567862769469947280606094290314917493 5905115232356987153971278667180775786719 1038036899144538148456268260400345679824 8689847811138328054940490519768008320299 6317570430114850873840485918501572643921 8741459246461740473527525050678399227312 1600117160338604710710015235631159734711 1531981987106161098503757589655767289040 6038716811431308417289371081741276458120 6119054145955378853200366615264923610030 1570446272317777886498067007235988895287 4748137219017507470000557110817893035489 5017924552067329003818814068686247959272 2055916279022926005921077105104481033928 7899128682070544897997731969557437452970 8195463942431669050083984398993036790655 5415960993248678224754243617589443717914 0378716816618909390024386203861000136219 3667280872414291108080291896093127526202 6678819020855957081118538361661288487295 2787514320295639329591050834968702906069 2838441522579419764824996318479414814660 8982817256904841843260619462542766936889 5354073236342830218969494776612607834632 8490315128061501009539164530614554234923 3938062140077792563376193730520256993190 9978940439084744359697205206599901782853 7676265683558625452697455260991024576619 6140375378595945063632270951224892419318 1372814166842701309605073457865904790424 3852086508154491350136491698639048125666 6108437022947302667214991648496107468032 6158335258035285827579903858409166761887 7199539888680431991650866887781701439663 1768155922620169913966131537380212941600 0690694753343167780263220722626588184275 7216055461439677336258462997385077307751 4738333151014683952964113973296724579335 4039013610739524568624300809672046099554 5708974893048753897955544443791303790422 3460377687292360013865695939523007680913 7776884778974629969948994901614186613155 2200856673695770822720338936659590666350 5943300403637625911891956915616261227047 8869651035606274842310060547209143706947 1661080277379848576543481249822444235828 3298135436451240922208966439872019979456 1903039732725461782313636337592762265630 1565813545578319730419339269008282952718 2521388551265830376304774906259955149259 4310530747890104300987658081650814486260 7975129633326675259272351611791836777128 9310531444716688351829205143436092924931 9118024936605179148533042104389977301926 7686085347768149502299280938065840007311 7678954912860981123113070025356003478986 0065380508453257243155365442206766135233 7408211307834360326940015926958459588297 8456494622713008555942933445207270077182 0639888740474218669770934964775817368358 0193168322111365547392288184271373843690 5266386076624512842993684350826128813673 5853629387379236992883704790048472224037 0919885912556341130849457067599032002751 6325139266942494856923209045968977756767 6268422476812003327957705939461318525235 6456291805905295974791266162882381429824 6226541410672464872161743513173976971222 2801010066817878677611982596153764364182 8573481088089988571570279722274734750248 4390226078804480757248077016210646701669 6510020265437126004664193554616583894595 0143502160890185703558173661823437491622 6690773118001211882997373198910060609668 4119326607516545274182945954118927726419 2546108246351931647783837078295218389645 3762363048580427744179071691463565462012 1512541866488539616154205515237500042679 4253417764590821513675258479774465114750 4384605963258204688096677957090446458846 7384748163804563518818321038659479820437 6334738389017759714236223057776395541011 2945234880983414766455593422094020597334 5233795630944144669822245702636711949328 6653989491344225517746402732596722993581 3331108317118072340443268137372312096690 5241185673489739223415275070795413745346 0386506786693396236535556479102508529284 2942277105930566606251522909241480570809 7115978345835117316820412964596707063330 3569271821496292272073250126955216172649 8218957909088650853824908489044217555309 4683205563631643189391762626993103428948 5184392539670922412565933079102365485294 1621322002511937952724803401331352470141 8219561841905576103019019952164745973440 1211601239235679307823190770288415814605 6472914817451053880601097875059255371523 5611229018128471013791721512466742850006 1818271276125025241876177485994084521492 7279025670059258544310277046369110988005 5431245722968383698047086404170601096696 2231877065395275783874454229129966623016 4080547697058214171286363296501304165012 7815639779963195741262763401113013508272 1772287129164002237230234809031485343677 0165449593807506342852930531311279659452 6665196042635040645486254338377220942848 2543536823186182982713182489884498260285 7056906990457909981446491936545632594965 7004468901104992393921808815562619183440 4362264965506449848521612498442375928443 6426120042566286021578011404678796623392 2819080457762410907648708740615707048665 8398144845855803277997327929143195789110 3735300198731104868956562819173620367030 3917971064630990628548370283611848667221 9457621775034511770110458001291255925462 6805374277273788637267830165683510923322 8064990845917962030569156680618082658692 3920561895421631986004793961133953226395 9997495267988010745764665383774004374636 9513368567136255318405463847519164673794 8743270916620098057717103475575333102702 7063173956124484137457827343763301018534 3849745023626573319174244656778749966500 0938706441886733491099877926005340862442 8334504869073382793484253056987374694973 3336426719196899284953456104571933866522 2471536681145666596959735075972188416698 7673216493318989671829786579746122165739 2240485690022532416036780532999092543896 0169901664189038843548375648056012628830 4094213213002061645408219861380994627212 1432723445780681992582320285139823711892 6541234460723597174777907172041523181575 1947935274564429846308888463853810686217 1527453161230316570584897431620983140132 6306699896632888532682145204083110738032 0527846692799840031378789965256351268853 6843555962059805727895175449869421932697 2133205286374577983487319388899574634252 0482133375525845710566195869320315632994 5150251919455969123143757999113830165611 7185508816658756751184338145761060365142 8584278721902325981078345939707382251471 1187831154087577756002066412456229323911 6606733386480367086953749244898068000217 6666748274269259686864337319165487177501 0634360830737628161398410739241003719675 4833838054369880310983922140260514297591 2211591485059387706790687013510298622075 0228772112334562442102471516394125125895 4337788492834236361124473822814504596821 4522535500359683253374891862786783594439 7904159804399212488984866079504501170116 9092519383155609441705397900600291315024 2538482827828262233041513709295021921965 0837471469784580555061591453950643731640 1173317807741497557116733034632008408954 0665416946657467357854831337701336289489 0439767002586300254063526400660163171288 3920305576358989492412827022489373848906 7643853399318786080192231083288474598164 1770126408907855177783013161616204979277 9670521847212730327970738223860581986744 6686109943830499604374073231957844732548 5741623973885201620238478425616351259716 1783106850156299135559874758848151014815 4909373809333940744557008420901559038534 4496212836831368737516678051308259459977 1257467939781491953642874321122421579851 5844916693625515693709168552526447207865 2797146647676032847133298550194568977275 8983450586004316822658631176606237201721 0079222164101882993308084093840142137596 9718597689704275904150094659525276348762 8135867117352364964121058854934496645898 6518265456343828511591376315695198952302 6288179495997154522125066746117439488443 3312659432286710965281109501693028351496 5240828501201908310786780670618511457409 7078756311761074642883559391598542167311 5153096948758378955979586132649569817205 2842910381727212131386815655244281098711 6886274396802188558151536753121837411997 2919471325465199144188500672036481975944 1679508874879344167595983619600109948387 4470907910409978597465611245985197215755 8134628546189728615020774374529539536929 6554490129530972889637677133538424297153 9417954717909558012013421017515093149166 4699052366350233024087218654727629639065 7233414550059039138902536993171559171798 2306516267974471185795150657386850408822 9934804445549850597823297898617029498418 3762552587574553031129919143411094130882 3811444306884306265530560165880140856102 3324210300218460588586954418502977463085 8584961300372381903251622255707299757107 2730606607291692297803364704884095871122 8045188511908718588299514331534128549297 1738497685231362760768684947803649482999 0447571577114108095805814120895605947166 8626290036145602625334863284986816039463 3724366671129644602929157461811177891696 9583994708095478886350328112962689923111 0099889317815313946681882028368363373822 2814149740069179421928888171391162839102 9568491823335893081336013148874836646422 4381776081007739183393749346933644748150 5649336493231572353061093857968399021533 8144912692535076821109873835219750773665 3475499431740580563099143218212547336281 3594883176814891943065304260297738854929 7457056944878307794587886506297089549984 3760181694031056909587141386804846359853 6840341059483417884389631799564688157919 3717465670504744152802771254156940136586 2097760735632832966564135817028088013546 3261048927687318299179503799444463281585 9518138014471681728499679306181417713191 2099236282922612543236071226270324572637 9468635333917587374465520060088199752940 1757242129972354206963042785795060891111 3416534893431149175314953530067419744979 0172351816715687541634849494912890017393 7745143192838243118326326507953037117780 6185851153508809998200482761808307209649 6364769430661725491861437009713875679402 1869671014854030747156109135893316560016 7252126542502898612259306484105898847129 6492309412151445639478899993271458759695 5573709085515064800232147644303723246614 7111552578583071024936898814562568786834 7455188933851817916675790542104210363493 1625787047654312679066121664414228501744 6278477132740595579600648343288827864837 0434560669664568997469103739877128915933 1327126624750558225863492842771835583164 1593667712218537642376222104779338956378 7229025095430141822571803313001481133777 3694150848886750189315699484983893605266 6818012783912005801431596441910546663236 8101482077993565230564904207113641922001 7718910793524323432276178771256825112648 1332974354926568682748715986654943041648 4682205939216733594850578496228079324226 4981270527139840772099570723622700924506 7665680069149966555737866411877079767754 8670287864318179415217961783106550302871 5727228225081201706071338033964184121125 3856248920130010782462165136989511064611 1335624438381853662735637834369212793547 0923011965591491580056170725851850316728 9370411936374780625824298250726464801821 5234302680814869781648243493534568558436 9637838415383805118440604369687166641651 4036129729992912630842812149152469877429 3323052149999818290461194716767275037422 2136718661465404253446314166064987149900 1000660041544868437352208483059495953182 8722805208286763003610917345086321330336 4728958417658875534522793848029772448571 1815574893561311524926772006362198369980 6641595493886838364118914304437677154980 2654495906173826559117854599937851086144 6014967645550103653971251138583505085112 4425177729238143962330437240360326031814 4299136575024601278751411794490130580345 2199992701148071712847770301254994886841 8675729751892142956525124869439837290474 1036312189912421733955068877864313075002 4823361832738729697376598820053895902935 4860549798023204004722368735574118581327 3433797893158203941287898972897329881255 3514507641535360519462112217000676321611 1958410292525685365618131387840864771470 9972455301317076171216318660029146450137 8587854802096244703771373587720086738054 1081400423114185258032932673963245969140 4483466572204288067928061602988404340053 6534009706581694636096660911110968789751 8013252244782469579132518921226530560858 6654111537358491279025465436902086941987 1125588453729063224423222287139122012248 7699768371476455985267392259049978855142 5004758526029792930615991344489834197358 3316070107516452301310796620382579278533 1251617607899846301034934969814942610553 6783636602256121376708142109137353178068 2420175737470287189310207606953355721704 3575351774615735248384321015713998137985 9660712966443831479129635927542962712943 6142685922138993054980645399144588692472 7675985442715277884438367601499128973582 5996186972975658897874108218942233734454 7375227693199222635973520722998387368484 3491768411910202466274795795643496150126 5743384575863883473583224253532814204782 6934473129971189346354502994681747128179 2981674396445249566555323116499206771636 6458031820584962613223465260617541353244 4702007661807418914040158148560001030119 9941095954923214344060676347697130895133 8917105050385633650354516643177448964006 1738861761193622676890576955693918707703 9423049400384406226144495725166310170806 4292334517042242667960707540402855118239 8361531383751432493056398381877995594942 5451967565591819686908852834348860508285 2964243757871292943936617736283013659587 2723080969468398938676366226456791132977 4698126752265956210093183220817546947788 7875535618833508387024829534607859702360 9865656376722755704495258739871812593441 9037852755713334098424501272585966924343 1768901896614540445367904713629423815612 7656824247864736176671770647002431119711 0900074740659456503153750441779821923063 2370087203921208549956968106137918902996 1178936752146022386905665481382858280449 5375301609214221959406387870747879911949 2089837409178853441752306471503027839797 9864517336625329511775105559014160459873 3381868879778588172919766045163533535560 4764842052088881172283199004450428448685 2338334530105533929637308039738230604714 1045254700948994076012152476028199638463 4355485293237716141086959195078687327607 5400085220065031871239272857835807010762 5427696553559647894501660138162951779085 3113981109283158321693156386745974744958 4385282701658246192092219529134323496779 3455856131402077659961425464632886773568 9178557683516960839286418883009488332470 0447958316931533832382377876344426323456 3016795136710475104696690012177771280655 2245368937187145156739473344044728045095 9433090683667110655953338602938000999949 0106427698596232604018637335728466795312 2968315635814542089054065122641916201550 4500430562136991850941034609601030543816 6947959645858044251949051107333876799467 3447171861564772381173703565491762870758 9456035519195603962301157866323750234725 0544610739794024751844155581780879628222 3197269298451668330691950507999335725916 5675557294585962182052650473353712351623 6627704793332893221361418587859727716856 8272530373483689191184719713375308844677 7943274857148827821608844765700041403499 9213767942096275608830815094380307056660 2276467811753336102818780071021979442877 7313146387857817205661409023041499923248 2689824772221098521897581408797634861467 6360636867461196662034730460891727724004 5953051376938375381543486981101990651706 9617740522182474226576521381527406126990 1270688087538640866990146174089054098187 7671880076124151967064152117653084325544 2610175363482811968374933958257425412446 3424723358636077798096019974518775884545 9645895956779558869098404768259253477849 9304578831285417470790597959094316277223 2784457891869421492945154017421462324030 0841907975296782445969183509474202123617 9403090486349605340549312999194960879579 5258697717023668003386250576493808874099 4009589948109397983231108838769236490221 4991111208706392028924906984353331527279 9133098633545432497144137805913224081496 0156485679843966464780280409057580889190 2542366067745004134157943121125012752322 5014806723297965223048849375116608497611 6412777395311302041566848265531411348993 2437478902689351739040432948516106597858 3225316820420283499364159598019734388988 3020994152152288611175126686173051956249 3671800538456378551291718484178415947974 3558061785668075849108018580569556799018 5198397660693358224779136504562705766735 1709615504933383904526124043955174491368 8511598745434093204010221898270753921240 3241042424451570052968378815749468441508 0111386125611641024771909030500402406622 7894560706151210826614609866204042501058 3978098192019726759010749924884966139441 1841597346103824011785567390805664833210 3907386708329869107809349582888870711065 1559651222542929154212923108071159723275 7975108599113980768447326394264194520631 3821786226099916008675244626545702896906 7192282283045169111363652774517975842147 1022190999062573733834727264986782444010 4899850763163066805026711594463629352512 0269424810854530602810627264236538250773 3405754757017043670395964677159592610294 3831307489724550572908568849609134632316 5819468660587092144653716755655531962091 8659526284482537313536981625173519301153 4158117135329203587316416883910799400067 7266031617527582917398395852606454113318 9855057478471210535057956490959316721675 6562481878200276996373415588000086785256 7422461511406015760115910256449002264980 0394984033580913091401978778436501679601 6746537028746606258434632970830372598049 4653589318912163976013193079476972058034 7105531111172158592190662310280992120840 6928309190601737076465465568341320755631 5315006453462321007133584907633048328153 4586984973325998011874796642731402793812 8996172052454067469527194807993039673019 4274036466594154400092799908634806622334 9066952240446521589928642034350988584226 9201934057549684090481295552265475465071 3532842543496616084954788090727649930252 7028150678628108252432229799853917598451 8886838700447710186677215943970851466461 2871148749531862180941719676843144666435 1758376884367860814463196419125665740477 1869916091555091087891943125367194565126 1878486910876729910565595155159739659034 3836281246291181177609494118801059463366 7103904977731200424357811579042982304507 2038322781246413671297959415082918378213 2128768905459635863693448797497848411232 7492133166316281245638823828871564844788 3142417650147980187858215768793063001153 7889980146236901358037533062461485760749 3256780768265104573805901883123761727188 9933790487113395588485234240255002352200 6135749143182591424798293677754904963993 5075583966896757836431661836930762560352 8602940662803255416535431518013714821941 7726722440052684019965333341840043455252 9659291850294013160065112439529787436422 2806977720437363717873457948420238745151 2491579131394111486084164293479587936818 6860968968464085833413101785814271095541 6293375915178392341303110543328703526599 9939049668221127681583165112468664511673 5137821434533665059832834744353629031239 3672084593164394941881138607974670134709 6403785349071490898423178917397836506547 5198288336739571436000000343986336321209 1718954899055748693397700245632475954504 4114225824107838668376554674001373243228 0911369267068280539754911116617110239743 7749479335174036135005397581475520834285 7728009861894019843754464350814982183601 1257763244738945205163693858513648425996 4518361856989088721789764694721246807900 3309250834966458416565542612941951088471 9720910660510554093373195488840644408028 0579549008076040034154662137669606444293 7749858973536255919596185524481879403173 7450825607289512094545656215954040542581 4886929842786582357673195799285293120866 2759223661151374457679160636216752674404 5122105105209083470744398613782908235277 2895849625656881972792768694795806100573 7870841214448150347974223121032953592978 2237713407754954547779181382354260718461 7108389097825964406170543546968567030745 4116342441344863086763279491776829230931 8322134145548259136720282328439654900180 5653203960795517074496039006696990334199 2782126967677718352090839595453418667779 4487274038373338198523588420284015098157 9594685874537989503257362809837592216229 2585985991238439935755732850286131559703 6293424981417805646161586341533863507722 3269996508860870999964899373049307170967 8887401497461475428803874212506892121558 7669224238743470112099085908216407357638 0817386959755176083877600277517253037133 4456548526356617201975630015800497902234 1958673806144240150243628895750320653369 0825756785507020555105572381878574650371 0863081581858628158830545646622976948039 7061826549138518132673748522718826791791 9091354407852685476254126683398240534022 4699899666525731556376458622518628230920 8542441280599762850548891309833176188498 3352975136073772030571342739638126588567 4050138410747889433939966035918539341984 1632261765485737667194313284005062629514 0357877264680649549355746326408186979718 6302187600258139957199236013453742297589 1828516751135817147262582859694079851857 1870075823122317068134867930884899275181 6613996097531052957735846185258652118933 3937577185991633511216344103791045184501 9023066893064178977808158101360449495409 6653636603700758810044502657349351277074 2674257860878489818562886998085166571332 0835842613381142623855420315774246613108 8731063181119898802897228497905510751484 0370229058048305273188495999415660653731 4021296702220821915862905952604040620011 8152696649100685875926556605675629633614 3423023281074748839504038098498186005616 4646099819257616235478710913832967563761 5067325508606834337204387481867916689757 4656345602000256288960119110098045335042 3842063824039434163502977688802779835087 4811782983494172116749194256016086853324 3538595115206180903124169818207931461506 2073826097180458265687043623935757495737 3327815789043860113780785081102730494466 1182195745017010605938433651945862836068 2108585130499820420578458577175933849015 5644473058345152914125616799705696574261 3990168193205624192797728202671429725870 0193234337873153939403115411184101414292 7417035375420036987606087655001093452990 0703403240133480638851409576955714719036 4152027721127070187421548123931953220997 5065530226468442277000205890459227424239 0493705150736776462984497168212199419827 4794049092601715727439368569721862936007 3870778107974409755566278073712280303500 4882984391954643375335578789506401899868 5060281902452191177018634505171087023903 3985505407044541890884720423764997490350 3851894950589797128663164469940749095947 3411581934618336692169573605081585080837 9520363356199476919379650650168087102507 3507082526004682124282043436724582447885 9256555487861614478717581068572356895150 7076022174335116273317094727659324132491 3270242551939150908360134623961233500108 6614623850633127072987745618984384288764 0998361649647757146385732473332266538945 2358836597295515990518741177928860876023 9306160016168434070611663449248395156319 1528827288228313754586782698306966912201 3095481593545075492355416776687645521254 5681242936427474153815692219503331560151 6144922475124889575348359262262635454067 0476703386641002527727680088638326662948 8582740369655329362236090572479794734434 0777042843185079019734690711412303641117 2922492930773193930979545287741245118395 3480382210373644697046967493042810911797 2324486154132640315784309553966710614680 8381554894714673365248367913856643108474 7848676243012018489329109615281108087617 4227791316293454944253954227273096450579 7612288534739318960081096520209015110457 9377602529543130188938184010247010134929 3174435628835786098615456911616698573880 2497375694055813863058109982337256516492 0155443216861690537054630176154809626620 8006330593207758971755899258621954620964 5546462439953539174322822543326717430849 2508396461328929584567927365409119947616 2251559647040612970477598185518784414199 4861401315385932206074518590960888428021 8943358691959604936409651570327527570641 5007762613237836481490052454814131959892 9639844137178140276412208764498968862979 8910870164270169014007825748311598976330 6129511956804274853178863330411697671750 6382213521383977913844332564428849087291 9067009802496281560626258636942322658490 6286280350572829831012669191096372583781 4936377496059451521693264494518829263952 5772348420077356021656909077097264985642 8317786947778049643439917625492165006086 2628532947105560267041338450050782739064 0287529864161287496473708235188892189612 6412795535364422869554305513087000098785 5753422310054715341281095702487081265431 9123261956462149376527526356402127388765 1038832550073648999371671832800283988323 1937330156412327718539565493242297795301 6534830128490677845037490891749347389015 6495885748021949967226211858743610397749 4633863305788748740554000544043934488819 2044102134790034598411927024921557026873 7009709952053919309793194958832659221715 0832462194230018597439670649114955941173 3728199869021311629886680267446443489233 0206070038212628417236796273071914050080 8408570397815199814882239005994891194647 4438682533745889962375133378280532928272 0168159779700664883944824463322109283205 0404598300894356595426725687971491870344 7338237767914829203283196838105907715727 1919030423653156509574645496434253280695 1039655873354980385099514346350617536148 0050195045201350200180281506933241918267 8557377644140970809457456248548677049043 6836871759091805726979401046501948485314 6726642978667687697789291431128505043098 1929497361659442594717547651352052450725 9753857795837279770297223143519995849952 2344049394502115428867244188717409524554 7718674849114750318017733046899093179744 7295703519238768640554427813416980724938 2219749124257510162187439772902147704638 0107314706531542013005838104589050067645 5733299814994585465510552637491435419586 7992595981412218735238407957416123372264 0638604319889362498676496935925695921284 9590625444647433175999968516366030521642 6770428154681777589339252115538590526823 3116083027511943848238615528524650103294 6729719811210531412589816510012074268814 3577590825227466863206188376830450921784 5825262395941896730036408086242336576209 7911164176633132885235206248792297895945 6450333733139422384778582717195412347860 4343761652415687179435625702156366666800 8853100672894703307954080458332419218848 8870712275670333173939262509073556164513 6770641995391119488812406598216857871313 8505685062309415520687798753974065848425 0135205615103489821873770245063583314243 6248074325424641959846474115756254410103 8967157667726319644252493194180647242378 9334668561083789808830313571333157729435 6649560781253049175940158951469549652231 1855966904855946760796819016726663465018 6182955669893965019614544401768162810604 4650684481395616672207292612101646923390 1679339963283301316385083096794279293455 1268435760356901970523138364640961311774 9046007728408622147475476532215055181164 8988787908778091800905070604006122001005 1271575991225725282523378026809030528461 5817395581981223970100920172022516063529 2246478161553353227545326454308709332092 4631855976580561717446840450048285353396 5468626788523300449677955807616618018336 6879231251046080977389556548896281508951 9622093675058841609752282328250433712970 1866081937489686999613014869246944824207 2363291236705254214546416296891044298163 3373266871675946715392611950649224725627 2545432741934959955695902432790971743922 5809810360148636440910149173418307964634 5064833303404765711827040276868271418084 5749984933920393174454026166636746466687 5438509396712991806747190988531271072672 4428584870694307099756567949198418996425 7488847646220303256377511125340600879369 0456577927203520592134592427296520668333 8510673615276261016026647772485083344719 8919868026561972364208475049626616077970 9290684475779825179556975823508437174610 3310387911789239441630112634077535773520 5580400669825231912255705191336314072113 4972322654915106296173905061785712750940 3623146700931176133132018631158730886798 2392980098050894915107883711940997503754 7367430574518726541401644692457679218575 3680363289139664155342066705623272936001 1777814988861008308778495717098808586670 2310404324252678595556207731054307229803 2125941107957349146684680220501816192150 7666491068620333787138260589876552104236 6819867017786167267197237415691788000169 0656659046965316154923604061891820982414 0061037794071663420027358289119941826478 1278265966620703038479588144279024666926 4032799404016800137293477301530941805070 5874211532846422030065507639667561683188 9700515202665664992941738284032730594074 0147117478464839241225676523593418554066 4409837060836364576570818016642850442582 2455165080886442121211391435245393522552 2162483791737330329812349528984098613273 7099574077867893493119752042379250228513 7588043679185454783641677315182145722650 4640800104202100410766027807729152555503 2181823872217081127662086653176519264584 5249526968537631443799834033694712444724 7796973890514941120010934140073794061859 4471655166126749307993747057729305217504 2638379836766815918358904965216372649296 0837147204067428996276720315410211504333 7420571828540901363257214375920546404718 9432854869688359978512226213081298958157 1391597464534806099601555877223193450760 3154116631129638437194003337360133055263 5257149045432792519079400711150478537803 6370897340146753465517470747096935814912 7971881878543767977516759278223003129455 1859504288390273549467266764750607264369 8761394806879080593531793001711000214417 7015044954964124543616562101509199978629 7249590580919182525548635870352932014200 5857057855419217730505342687533799076038 7466896842834026487332908888817454530471 9474093925840736205824284934902475688335 2446212456101562729065130618520732925434 1792522994174478551899950989599998774109 5146417007698930562016350219269265316659 9093238118295411937545448509428621839424 1862180674571280993852588426319306701820 9800805090001981962175845893251687769859 4110522845465835679362969619219080897536 8132104845187845162306239118780246040508 2490933606999809477625379297359703775906 6145994638578378211017122446355845171941 6703447321627224432659148585957978237529 7632344291124231136860372451443876580127 1594060878788638511089680883165505046309 0061488325454528199082562388058720428439 4183468786514254137768605429107972100427 End of the Project Gutenberg EBook of The Number "e", by Unknown *** END OF THIS PROJECT GUTENBERG EBOOK THE NUMBER "E" *** ***** This file should be named 63.txt or 63.zip ***** This and all associated files of various formats will be found in: http://www.gutenberg.org/6/63/ Updated editions will replace the previous one--the old editions will be renamed. Creating the works from public domain print editions means that no one owns a United States copyright in these works, so the Foundation (and you!) can copy and distribute it in the United States without permission and without paying copyright royalties. Special rules, set forth in the General Terms of Use part of this license, apply to copying and distributing Project Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm concept and trademark. Project Gutenberg is a registered trademark, and may not be used if you charge for the eBooks, unless you receive specific permission. If you do not charge anything for copies of this eBook, complying with the rules is very easy. You may use this eBook for nearly any purpose such as creation of derivative works, reports, performances and research. They may be modified and printed and given away--you may do practically ANYTHING with public domain eBooks. Redistribution is subject to the trademark license, especially commercial redistribution. *** START: FULL LICENSE *** THE FULL PROJECT GUTENBERG LICENSE PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK To protect the Project Gutenberg-tm mission of promoting the free distribution of electronic works, by using or distributing this work (or any other work associated in any way with the phrase "Project Gutenberg"), you agree to comply with all the terms of the Full Project Gutenberg-tm License (available with this file or online at http://gutenberg.net/license). Section 1. General Terms of Use and Redistributing Project Gutenberg-tm electronic works 1.A. By reading or using any part of this Project Gutenberg-tm electronic work, you indicate that you have read, understand, agree to and accept all the terms of this license and intellectual property (trademark/copyright) agreement. If you do not agree to abide by all the terms of this agreement, you must cease using and return or destroy all copies of Project Gutenberg-tm electronic works in your possession. If you paid a fee for obtaining a copy of or access to a Project Gutenberg-tm electronic work and you do not agree to be bound by the terms of this agreement, you may obtain a refund from the person or entity to whom you paid the fee as set forth in paragraph 1.E.8. 1.B. "Project Gutenberg" is a registered trademark. It may only be used on or associated in any way with an electronic work by people who agree to be bound by the terms of this agreement. There are a few things that you can do with most Project Gutenberg-tm electronic works even without complying with the full terms of this agreement. See paragraph 1.C below. There are a lot of things you can do with Project Gutenberg-tm electronic works if you follow the terms of this agreement and help preserve free future access to Project Gutenberg-tm electronic works. See paragraph 1.E below. 1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" or PGLAF), owns a compilation copyright in the collection of Project Gutenberg-tm electronic works. Nearly all the individual works in the collection are in the public domain in the United States. If an individual work is in the public domain in the United States and you are located in the United States, we do not claim a right to prevent you from copying, distributing, performing, displaying or creating derivative works based on the work as long as all references to Project Gutenberg are removed. Of course, we hope that you will support the Project Gutenberg-tm mission of promoting free access to electronic works by freely sharing Project Gutenberg-tm works in compliance with the terms of this agreement for keeping the Project Gutenberg-tm name associated with the work. You can easily comply with the terms of this agreement by keeping this work in the same format with its attached full Project Gutenberg-tm License when you share it without charge with others. 1.D. The copyright laws of the place where you are located also govern what you can do with this work. Copyright laws in most countries are in a constant state of change. If you are outside the United States, check the laws of your country in addition to the terms of this agreement before downloading, copying, displaying, performing, distributing or creating derivative works based on this work or any other Project Gutenberg-tm work. The Foundation makes no representations concerning the copyright status of any work in any country outside the United States. 1.E. Unless you have removed all references to Project Gutenberg: 1.E.1. The following sentence, with active links to, or other immediate access to, the full Project Gutenberg-tm License must appear prominently whenever any copy of a Project Gutenberg-tm work (any work on which the phrase "Project Gutenberg" appears, or with which the phrase "Project Gutenberg" is associated) is accessed, displayed, performed, viewed, copied or distributed: This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.net 1.E.2. If an individual Project Gutenberg-tm electronic work is derived from the public domain (does not contain a notice indicating that it is posted with permission of the copyright holder), the work can be copied and distributed to anyone in the United States without paying any fees or charges. If you are redistributing or providing access to a work with the phrase "Project Gutenberg" associated with or appearing on the work, you must comply either with the requirements of paragraphs 1.E.1 through 1.E.7 or obtain permission for the use of the work and the Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or 1.E.9. 1.E.3. If an individual Project Gutenberg-tm electronic work is posted with the permission of the copyright holder, your use and distribution must comply with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed by the copyright holder. Additional terms will be linked to the Project Gutenberg-tm License for all works posted with the permission of the copyright holder found at the beginning of this work. 1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm License terms from this work, or any files containing a part of this work or any other work associated with Project Gutenberg-tm. 1.E.5. Do not copy, display, perform, distribute or redistribute this electronic work, or any part of this electronic work, without prominently displaying the sentence set forth in paragraph 1.E.1 with active links or immediate access to the full terms of the Project Gutenberg-tm License. 1.E.6. You may convert to and distribute this work in any binary, compressed, marked up, nonproprietary or proprietary form, including any word processing or hypertext form. However, if you provide access to or distribute copies of a Project Gutenberg-tm work in a format other than "Plain Vanilla ASCII" or other format used in the official version posted on the official Project Gutenberg-tm web site (www.gutenberg.net), you must, at no additional cost, fee or expense to the user, provide a copy, a means of exporting a copy, or a means of obtaining a copy upon request, of the work in its original "Plain Vanilla ASCII" or other form. Any alternate format must include the full Project Gutenberg-tm License as specified in paragraph 1.E.1. 1.E.7. Do not charge a fee for access to, viewing, displaying, performing, copying or distributing any Project Gutenberg-tm works unless you comply with paragraph 1.E.8 or 1.E.9. 1.E.8. You may charge a reasonable fee for copies of or providing access to or distributing Project Gutenberg-tm electronic works provided that - You pay a royalty fee of 20% of the gross profits you derive from the use of Project Gutenberg-tm works calculated using the method you already use to calculate your applicable taxes. The fee is owed to the owner of the Project Gutenberg-tm trademark, but he has agreed to donate royalties under this paragraph to the Project Gutenberg Literary Archive Foundation. Royalty payments must be paid within 60 days following each date on which you prepare (or are legally required to prepare) your periodic tax returns. Royalty payments should be clearly marked as such and sent to the Project Gutenberg Literary Archive Foundation at the address specified in Section 4, "Information about donations to the Project Gutenberg Literary Archive Foundation." - You provide a full refund of any money paid by a user who notifies you in writing (or by e-mail) within 30 days of receipt that s/he does not agree to the terms of the full Project Gutenberg-tm License. You must require such a user to return or destroy all copies of the works possessed in a physical medium and discontinue all use of and all access to other copies of Project Gutenberg-tm works. - You provide, in accordance with paragraph 1.F.3, a full refund of any money paid for a work or a replacement copy, if a defect in the electronic work is discovered and reported to you within 90 days of receipt of the work. - You comply with all other terms of this agreement for free distribution of Project Gutenberg-tm works. 1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm electronic work or group of works on different terms than are set forth in this agreement, you must obtain permission in writing from both the Project Gutenberg Literary Archive Foundation and Michael Hart, the owner of the Project Gutenberg-tm trademark. Contact the Foundation as set forth in Section 3 below. 1.F. 1.F.1. Project Gutenberg volunteers and employees expend considerable effort to identify, do copyright research on, transcribe and proofread public domain works in creating the Project Gutenberg-tm collection. Despite these efforts, Project Gutenberg-tm electronic works, and the medium on which they may be stored, may contain "Defects," such as, but not limited to, incomplete, inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other medium, a computer virus, or computer codes that damage or cannot be read by your equipment. 1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right of Replacement or Refund" described in paragraph 1.F.3, the Project Gutenberg Literary Archive Foundation, the owner of the Project Gutenberg-tm trademark, and any other party distributing a Project Gutenberg-tm electronic work under this agreement, disclaim all liability to you for damages, costs and expenses, including legal fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH DAMAGE. 1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a defect in this electronic work within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending a written explanation to the person you received the work from. If you received the work on a physical medium, you must return the medium with your written explanation. The person or entity that provided you with the defective work may elect to provide a replacement copy in lieu of a refund. If you received the work electronically, the person or entity providing it to you may choose to give you a second opportunity to receive the work electronically in lieu of a refund. If the second copy is also defective, you may demand a refund in writing without further opportunities to fix the problem. 1.F.4. Except for the limited right of replacement or refund set forth in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. 1.F.5. Some states do not allow disclaimers of certain implied warranties or the exclusion or limitation of certain types of damages. If any disclaimer or limitation set forth in this agreement violates the law of the state applicable to this agreement, the agreement shall be interpreted to make the maximum disclaimer or limitation permitted by the applicable state law. The invalidity or unenforceability of any provision of this agreement shall not void the remaining provisions. 1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the trademark owner, any agent or employee of the Foundation, anyone providing copies of Project Gutenberg-tm electronic works in accordance with this agreement, and any volunteers associated with the production, promotion and distribution of Project Gutenberg-tm electronic works, harmless from all liability, costs and expenses, including legal fees, that arise directly or indirectly from any of the following which you do or cause to occur: (a) distribution of this or any Project Gutenberg-tm work, (b) alteration, modification, or additions or deletions to any Project Gutenberg-tm work, and (c) any Defect you cause. Section 2. Information about the Mission of Project Gutenberg-tm Project Gutenberg-tm is synonymous with the free distribution of electronic works in formats readable by the widest variety of computers including obsolete, old, middle-aged and new computers. It exists because of the efforts of hundreds of volunteers and donations from people in all walks of life. Volunteers and financial support to provide volunteers with the assistance they need, is critical to reaching Project Gutenberg-tm's goals and ensuring that the Project Gutenberg-tm collection will remain freely available for generations to come. In 2001, the Project Gutenberg Literary Archive Foundation was created to provide a secure and permanent future for Project Gutenberg-tm and future generations. To learn more about the Project Gutenberg Literary Archive Foundation and how your efforts and donations can help, see Sections 3 and 4 and the Foundation web page at http://www.pglaf.org. Section 3. Information about the Project Gutenberg Literary Archive Foundation The Project Gutenberg Literary Archive Foundation is a non profit 501(c)(3) educational corporation organized under the laws of the state of Mississippi and granted tax exempt status by the Internal Revenue Service. The Foundation's EIN or federal tax identification number is 64-6221541. Its 501(c)(3) letter is posted at http://pglaf.org/fundraising. Contributions to the Project Gutenberg Literary Archive Foundation are tax deductible to the full extent permitted by U.S. federal laws and your state's laws. The Foundation's principal office is located at 4557 Melan Dr. S. Fairbanks, AK, 99712., but its volunteers and employees are scattered throughout numerous locations. Its business office is located at 809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email business@pglaf.org. Email contact links and up to date contact information can be found at the Foundation's web site and official page at http://pglaf.org For additional contact information: Dr. Gregory B. Newby Chief Executive and Director gbnewby@pglaf.org Section 4. Information about Donations to the Project Gutenberg Literary Archive Foundation Project Gutenberg-tm depends upon and cannot survive without wide spread public support and donations to carry out its mission of increasing the number of public domain and licensed works that can be freely distributed in machine readable form accessible by the widest array of equipment including outdated equipment. Many small donations ($1 to $5,000) are particularly important to maintaining tax exempt status with the IRS. The Foundation is committed to complying with the laws regulating charities and charitable donations in all 50 states of the United States. Compliance requirements are not uniform and it takes a considerable effort, much paperwork and many fees to meet and keep up with these requirements. We do not solicit donations in locations where we have not received written confirmation of compliance. To SEND DONATIONS or determine the status of compliance for any particular state visit http://pglaf.org While we cannot and do not solicit contributions from states where we have not met the solicitation requirements, we know of no prohibition against accepting unsolicited donations from donors in such states who approach us with offers to donate. International donations are gratefully accepted, but we cannot make any statements concerning tax treatment of donations received from outside the United States. U.S. laws alone swamp our small staff. Please check the Project Gutenberg Web pages for current donation methods and addresses. Donations are accepted in a number of other ways including including checks, online payments and credit card donations. To donate, please visit: http://pglaf.org/donate Section 5. General Information About Project Gutenberg-tm electronic works. Professor Michael S. Hart is the originator of the Project Gutenberg-tm concept of a library of electronic works that could be freely shared with anyone. For thirty years, he produced and distributed Project Gutenberg-tm eBooks with only a loose network of volunteer support. Project Gutenberg-tm eBooks are often created from several printed editions, all of which are confirmed as Public Domain in the U.S. unless a copyright notice is included. Thus, we do not necessarily keep eBooks in compliance with any particular paper edition. Most people start at our Web site which has the main PG search facility: http://www.gutenberg.net This Web site includes information about Project Gutenberg-tm, including how to make donations to the Project Gutenberg Literary Archive Foundation, how to help produce our new eBooks, and how to subscribe to our email newsletter to hear about new eBooks.