fiFTH EDITION InternatiSotnuadle nVte rsion DataS tructuarneds AlgoritihnmJ sa va 'l FiftEhd ition InternatSitoundaelVn etr sion MichaTe.lG oodrich .. ' DepartmoefCn otm puter Science UniveorfCs ailtiyf omia, Irvine RoberTtaom assia DepartomfCe onmtp uStceire nce BrowUnn iversity I \ I JohWni ley & Sons, Inc. I Perafce This internatiDoanStataulr c tsautnruAdedl seg notri iJnvta pehvrrmaoss ­i on of viadne soi dnutetrtdoia sottrnau catnaudlr geosr iintchltmuhsdde,iei nsragi n ganl,­ ysainsid,m plemeInntt earotmfcisu o rnr.i counthl eaI EEbEaIs2Ae0Cd0M 1 ComuptinCgu rcruilutmhb,io soi kas p profporri atuthsceeeo uiCrnSs1 e0s2 (110v/Bei rosnCsS13)0( ,11 0v/Bei rosnCsSll)(l,Av e rsainCodS1n21)(,A II/O/F/H ver)sW.iedo inssi ctuusssf eross uccohu irmnso edrsee tlaaiitthnlei rs f caper.e Thmeja ocrh anitgnhe ese dfiiftathrti ehof lenol owing: Wea ddmeodre ex amapnlddei ss coufds asstitaor nua cnatdlu groer ithm • anyaisls. Wee nhacnocntesedinw scityth hJea C voal leFcrtaoimroe.kwn s • We enhtahdneic secdou afsl sgioordnie tsthiemngciinhcq l uiedksye,n amic • promgmriaanngtd hg er emeedtyh od. We addmeadt eonrniei mwap lrJ oav11ve0amd e tsh.o d • Wec retahtiiensdt enrnaastlti uodveenrtso itfoh bneo owkh,ic cohn tains • contseuancsJth a, iv nat ernatainiodnn taelrniuazntaimittooisrano,­epan l propfrorirea atodeue trssNi odrAetm heo rfai nEcdua r ope. Wea ddade ids coutfsh dseii ffoenbr eetnwarcerevea anyar biimeea- snsaign­ • ment acnldo narirnagy. We_i nclauned xepdad nidsecdou tfsh sDeie oqinun eat ceaern fde LLdiisntk • cliansJsa va. Wei ncrceoavseoerefdan gtoebre jyci ttnsh J ea va CForlalomereckwt.i on • Wef uilnltye aglcrloaf dtareeg dm AePntituos � gee nteytpiecs . • Wea dddeidsi couonsfss Ntvahiegb alteiaMnaatpce� esrw ,fe altslhiemir- • plemenithtnae Jt aCivooaln lse Fcrtaimoeunwssois rnklkgi i ps ts. Wei ncladu idsecdou tfsh Jseai TvoeranMe acpl ass. • Wep rovdiirdsiecpdot fi ostnohsrme te itnhgo dsi tnih Jneacl vliaub dreadr y. • Wee xpaanndrdees dve eidxc eirsceosn,t iounarup ipnrogof da icvhi ding • thienmt oo rercmeecinrntvef,ia attnyipd,rj oeecxtes recsi. Thbiosio rske ltaot feltodlh oehw oionkgs : M.GTo.o dRr.Ti maacshs,ai naDd,. MM.o uDnatSta,t ruancdtA ulrgeos­ • ritihnm sJ oWhinl eSyno sI,n Tch.bi osoh kaa ss· i moivlearr­ C++, & alslt rutctot hpuerr eebs oeonbktuu, ts Ce+sa+ st h uen delralnygiunagg e (wistho mmeo dbeusntte ,cr eyps esdaagdoiegffrnieccreaeslq ubiytr heids appcrh.o) a • M.TG.o odarniRd.cT hina asAsligao,Dr eistiFhgomnu :n daAtniaolnyss,i s, anIdn tEeaxrnientJp olWheinsl ,eS yo InnsTc,h. ii ass tefxoatr bmooorke & advaanlcgeodr idtahstmtasr ucacontudur rseaessC, S 12s0(uT c/hW /C/S versiithnoe In EsE)E I2A01Cc0 Mu rriculum. vii viii Praecfe Usaesa T ebxotok Thed esiagnnda nalyosfei fsf icdiaetsnatt r ucthuarsle osnb ge erne cognaisz ed av itsaulb jiencc to mputfiontrgh ,se t udoyfd atsat ructiuspr aerostft hceo roef evecroyl iecgoiamtpeu ter asncdci oemnpcueet negri neemraijnogr prwoega rraem familwiiatrTh y.p icatlhlieyn ,t roduccotuorrasyre pesr esenatsae t dw oo-rt hree­ coursseeq uenEclee.m entdaartsyat ructaurroeef st berni eiflnyt rodiunct ehde firsptr ogramcmoiunrgos rie n iannt roduteoct oimopnu stceire cnocuer asnedt his isf oliobwyea dm orien -deipntthr oduteodt aitosant ructiuntr heceso urses that follaofwt tehri Fsu.r thermore, stehqiuse insctc oyeu priscfeao lliiyo awtae l da ter poiinntt hceu rricublyua mm orien -despttuhod fyd atsatr uctuarnedas l gorithms. Wef eetlh athtec entrroalolef d atsat rucdteusrieag nnda nalyisnti hse curriculum isf uljiuys tigfiievdte,hn ie m portoafne cffiec iednatts at ructiunmr oessst o ftware systeimnsc,l utdhiWene gb o,p erastyisntge dmast,as beasc,o mpilers, and scientific · simulastyisotne ms. With etmheer geonftc heoe b je-ocrti epnatreadd aisgt mhf er amerwkoofc hoice fobru ildrionbgua sntdr e usasbolfet wwaerh ea,vt er iteotd ak ea c onsisotbejnetc t­ orientveide wpotihnrto ugthhoiutste xtO.n eo ft hem aiind eaofst heo bject­ orienatpepdr oiasct hha dta tsah oubledp resenatsbe edi negn capsuwliatttheh de methotdhsaa tc ceasnsdm oditfhye mT.h aits r,a thtehras ni mpvliye widnagt a asa c oliecotfbi yotnae nsd a ddressweest ,h ionfkd atoab jeacsti sn staonfca ens abrscatdatt tyape ( ADT), whicihn cluadr eesp ertoofmi erteh ofdospr e rforming operatoindo antsoa b jeocftt sh itsy pLei.k ewoibsjee, ct-osroileunttaierodoen f s­ degsnpi aetrnts, teonr ganiuzteidl iczoimnmgo n whicfha cil.istoaftterw eaursee 5 andr obustnTheusss,w. e p reseeanctdh a tsat rucutsuirnAegD Tsa ndt herier- spectiimvpel ementaantdwi eoi nnst urcoeid mportdaènstip gant teamsms e antso organtihzoeis mep lementianttciolo anesssms ,e thoadnsdo, b jects. Pore acAhD Tp reseinntte hdib so okw,ep roviadnae s saotceiJda vian terface. Alscoo,n crdeattseat ructrueraelsit zhiAenD gT sa rdei scusasnedwd eo ftgeinv e concrJeatvceal asismepst ementthieinsnget erfWaeca elss.o Jgaivivame p lemen­ tatiooffn usn dameanltgaolr istuhcmahsss , o rtainndgg r apshe archiMnogr.e over, ina ddititoopn r ovidtiencgh nifqouures si dnagt sat ructtuoir mepsl emAeDnTts , wea lsgoi ve saamppplliec aotfdi aotsnats r uctsuurcaehssi ,nH TMLt amga tching and as impslyes tteomm a intaap ihno taol buDmu.et os paclei mitahtoiwoenvse,r , wes ometismheosow n lcyo dferagmeonfst osmiem plementiantt hiiboson osak n d makaed ditisoonuarcleo ed aev ailoanbt lhece o mpanwieobns itTeh.eJ avcao de imptemenftui:pnqga:n.I, t1lelnd atsat ructiqrnte h�ib so oiks. Q rganiinztaeos d i ngle nte.dattruaess,t ruc Javpaa ckage, whicfho rmacs o herleinbtr oafdr ayt sat ructures anda lgoriitnJh amvssa pe cificdaelsliyg fnoeerdd ucationali nap w uarpyto hsaets nte.adsatrtreusc tu isc omplemenwtiattrhhy Je a vCao llecFtriaomnesw oTrhke. libriasr yrn eoqtu ihroewde,v teorg ,ef tu li use from this book. Preafce ix OnelR isenoruces Thibso oikas c compbayan nie exdt enascmcipovaen ysieontfog n lrienseo urces, whiccahbn ef ouanttd h feo llowweisbni gt e: wwww.iyl.emc/ogojlgolbgjaodoirch Studaerneetn sc outrouas gteeh dsi isat leo wnigtt hhbe o otkho, e wlipte hxe r­ cisaensid n crease uonftd heseru sbtjIaenncsdtti.rn augrcl eti okrewswe ilsceo me tou steh sei ttohe e lplpan o,r ganainpzdr ee,s ent tmhaetierrI incacollusur.ds eed ont hWiesbs iitasec oneeotfei dounc aatiitdohsnaa autlg mtehnteto poiftc hsi s boofkob,ro stthu daennidtn ss trBuecctaoourftss he.ea idrdv eadl suoemo,eft hese onlrienseo uarrpceae sss wporrodt ected. Fotrh Set undte Foarlr le adaenredss ,p ecfiosartl uldywe eni tnsc,lt uhfdeoe l lorweisnogu rces: AltlhJ eva a s oucroedpeer esentbeodo ki.n this • PDFh andoofPu otwse rpsoliin(dtfe osu r-pperro-vptiaoidg neesd)t ructors. • A dataobfha isntetao sll e xerciinsdeebsxyp,e r do bnluemmb er. • Ano nlsitnuegd uyi wdhei,ic nhc lsuodleustt osi eolnesec xteerdc ises. • Thhei nsthso ubleod fc onsiduesrteaoa b nlyeon neee dail nigth tleelg pe tting staorntee edr teaxieor cainstdeh sseo, l utiohnesla pns yhoownuiels dht iosn ege compleexteerdcS itsuedswe.hn oht asv e puarn cehcwao spoeyftd h bioso wki ll gepta sswaocrctdeot s hshe i natnosdt hpears sword-opnrlroietnseeoc uatrtec de s noe xtrcah arOgteh.e r craepnau drecrphsaa ssseaw cocrfedos arns o mifneael. - . Fotrh Iesn tructor Foirn structthobirosso wkuei,s n icnltguh fdeoe l loawdidnigtt ieoancaahilid nsg: Soluttiooov ntesrwh ou ndorfte hdbe o oekx'esr cises. • Ad ataobfaa dsdei teixoenracsliu sietfsaoq,bru l iez azneedxs a ms. • Thceo mpnlteet.aedt suarcttmpeasck age. • AdidtiJoansvaoalu croedee . • SliidnPe osw erapnoPdiD nFt (one-per-page) format. • Self-cosnpteaciinaeld- topiicn clsuuddpiipsnlcgeuo msenscn iotonsnv,se x • hulrlasnt,gr eea ensod,r thosgeognmaielnn tte rsection. Ready-ttuorn--upksreeoy,j ceocmtpswl,ie sttuhep poJratcvioandf geog rr aphical­ • userint(eGtfUaiscsote) hs,sa ttu dceancnto snceonntd rasattrtaue c dteu-re .s ign,illlpalnuedsm aergnaett,ah teiGroUtnlph, ra ong ramming. Thsel iadrefesu leldyi tsaoab slt eoa, l laoniw nstruuscittnhogbir os o fuklf lr ee­ domi nc ustomhiiozsrhi enprgr esenAtlatlth oieno lnrisen.se o uarrepc reosv ided ant oe xtrcah atroag neiy n structtohrbi osaof dkooh rpio tsrhi encrgo urse. Precfea x AR eusrocfeoT raec hgiD tnaaS ttrruueacsnA dl rgtiohsm Thbiosco okn tmaainJnyas v aa-ncpdeos uddeo f-arcgomdeaenn tds ,h oufn dreds exerwchiiascredhesi ,vi indrteoodu 4g0hr%ley i nfoerxiceser4mec0esc%n,r t e ­ atievxcieitrsayen 2sd0 ,p% r ogrparjmcoem.ti sng Thbiosco akbn eu setdh CefSc o2or u ardsse es,ci itnrh 1be798e A dC MC om­ puStceirCe unrcrei ocirucn lo uuCmrS1,s2 0 e( sI /v0re/sBiC oS1n3 0s( )I/,0v /eBr ­ si)oC,nS1 s 1( 1Av e rsainodCn/S1)o2 1,(r A /I/v0e/r)Fsa/,idsH oe nssci rtnih bee d IEEAEC/M2 0C01op mutCiunrgr iwciuitlnhus mt,ru uncaitstoi suo tnliainln ed TalbOeI. . lnstruUcntiito nal RelevMaantte rial PLl. OvoefPr rvoigerwa Lmamnignuga Cgheasp t1e 2r s & PL2V.ri tluM aachines Sect1i.4o1n,1s. 4 11..2,1 .431 . & PL.3 IntroLdauneagtguiTeor snan lttaioo nS ect19i. on PL4D.e cltairoaannTsdy p es Setcio1n.s21 .,42 ,. 5 & PL5A.b stroancM teichanisms Sceti2o.n54s., 51 2.,,5 .631.,. 61.,62 .,4 , 6.731.,7, . 138,.. 91.,91 .,15 41,,. 13.1 & PL6O.bj ect-OPrrioegnrtaemdm ingC hapt1e 2ras n Sdce ti6o.n2s6. .23,, & 7..3781,.2 ., 1.33.1 & PF1F.u ndamPernotmgamrlia nCgo nstrCuhcatpst1 e 2r s & PF2A.l goraintPdhr mbosl em-SolvSiencgt 1i9.o n4s, 2 & PF3F.u ndamDeantStata rlu cturesS etcio3n1.s5,1 . -35..2,36, 1,. ---ó.741.,, 7.31,8, . 893..,91 .-14.0,1 ,1. 31 & PF.4R ecursion Sceti3o.n5 SE1S.o tfwaDrees ign Chap2ta enrSd e ct6i.o.2n26s,. 13.,3 .7, 81.2., 1.331. & SE2U.s iAnPgi s Sect2i.o54n1.,s5, 2 . ·5,.6 31.,. 61.,2 , 6.4, 6.731.,7, . 13,.1 9,81. .9,. 1541,, . 13.1 & ALlB.a sAilcg oriAtnlhamyisci s Chap4t er AL2A.l ghomriiSctt rategies Sceti1o.1n1s1. .11.5,11 ,.23 .11.2,42 ., & 12.2 AL3F.u ndamCeonmtpaulAt lignogr itShemcst 8i1.o4.n,8s2 . .82.,3 9..52,9, .. 31, & anCdh apt1,e11r ,2s 13 & DS1 F.u nctRieolnasta,in oSdne st,s Sceti4o1.n8,s1. ,1 .14 & DS3P.r oToefhc niques Setcio4n.6s31 .,4. 7,� 38..313,.0, 2 1,.0 3, 1.0410, . 15,211 ..'1 .1.3'11 .41.13,3' . 1 131.1,334 .,. 13.5 & DS4B.a soifCc osu nting Sceti2o.n2s. 13.11 5. & DS5Q.r apahnTsdr ees Chap7t,8e r,1s 0 ,1 3 & DS6D.is creotbeaPbrility AppenAd ainxSd e cti9o.n29s.. 24,. 2, 1.121.,1 .15 & 0.M1a:t efroUirna iilttn hs Ie E EEM/2 A01CC0 moputCiunrgr iculum. Table Preafce xi ContentOsr gaanndi zation Thceh apftoetrrh csio su rsoer gaarnteiop z reodva ip deed agopgaittchhsaa tlta rts witthhb ea soifJc asv par ograamnmodib njge ct-doersiiWegennp t.re odva ind e eardliys cuosfcs oinocnsr tertuec ltiuakrreer asan,yld si nlkiessdtoa s st, op r ovide ac oncretteob ufioulopdtow inhn ecgno nstroutchdteairstn tagr uctutrheesn. We adfdo undatteicohnnlaiilqrk ueeec su arnsadil ogno raintahlmy siintsh ,me a ainnd , portoifto hbneo owke,p resfeunntd amdeanstttaar lu catnaudlr geosr ciotnh­ms, cludwiinatdg hi scuosfms eimoonmr ayn age(mtehinasthtt,e a rchituencd­teurral pinnoifdn agststra u ctSupreecsai)l,fi.tl c hyceh apftoetrrh bsio so akro er ganized asf ollows: 1.J avPar ogrammBiansgi cs 2.O bject-nOterdiD eeisgn 3.A rrayLsi,n kLeids tasn,dR ecurns io 4.M athematFiocaulna dtions 5.S tacaknsd Q ueues 6.L isAtb stractions 7.T reSet ructures. 8.P riorQiuteyu es 9.M apsa ndD ictionaries 10S.e arcThr eSet ructures 11S.o rtianngdS election 12T.e xPt roecssing 13G.r aphs 14M.e mory M .·AUs.e f�fathematFiaccatls A mordee taliilseotdfti hncego ntoeftn htbisos oc kab nef ouinntdh tea bolfe contents. xii Praecfe Pereruqiietss Weh avwer itttheibnso o aks sumtihnagt r etahdece orm etsoi twi tche rtkanionw l­ edgeW.ea ssutmhea tthr ee adiesar tl eavsatg uely famaih liigahr- lweivtehl pro­ gramming lasnugcuahas Cg ,eC ,+ +P,y thoonrJ, a vaan,d t hahteo rs heu nder­ stantdhse mcaoinns trfurcostmus c ahh igh-lleavnegluaingcel,u ding: Variaabnldee xsp ressions. • Metho(dasl ksnoo wansf unctoirop nrso cedures). • Decissitrounc tu(rseuasc shi f-stataenmdse wnittsct ha-tesments). • Iterasttirounc t(ufroers- laonodwp hsi le-loops). • Forr eadwehrosa rfea milwiiattrhh ecsoen ceptnso,t w ibtuhhto wt heayr eex ­ 1. presisenJd a vwae,p roviapd rei moenrt hJea vlaa nguiangC eh apteSrt itlhli,s booiksp rimaard ialtysa t ructbuoroekns,oa tJ avbao okh;e nciedt,o �en optrovide ac omprehetnrseiavteom feJ natvN ae.v erthweeld eosn soa,ts sumet htrehe aatd er isn ecessfaarmiillywi iatorhb ject-odreiseinogtrnwe idt lhi nksetdr uctsuurcehs , asl inkleidsf tostr,h etsoep iacrsce o veriend tcohrece h aptoeftr hsib soko . Int eromfsm athemabtaicckag!r owuean sds,u tmhere e adiessro mewhfaatm il­ iawri tht opifrcosm h igh-school maEtvhesenom i,an tC ihcasp.t4 e,wr e d iscuss thseevmeno st-impfourntcatnfitoo arnl sg orithm Ianfn aaclstye,sc itisot.nh sau ts e something otohneeor ft htheassnee v efnu nctairoceno sn sidoeprteido annadal r,e indicwaitteahds tar Weg ivaes ummaorfyo thuesre fmualt hemaftaicctas!, (*). incluedlienmge nptraorbya biinlA iptpye,n dix A. AbotuhtAe u otrhs ProfesGsooordsr iacnhdT amassairawe e ll-recorgensiezaerdic nha elrgso rithms andd atsat ructhuarveispn,ug b lismbaendyp apeirnts h ifise lwdi,t ahp plications toI ntercnoemtp utiinnfgo,r mavtiisouznaa ltiicoonm,p usteecru raintdgy e,o met­ riceo mputiTnhgeh.ya vsee rvaespd r inciinpvaels tiignsa etvoerjrsoa ilpn rto jects spousobryte hdNe a tioSncaile nFcoeu ndattihAoern m,y R esearOcffihc et,h Oef ­ ficeo fN av aRle searacnhtd,h D ee fenAsdve a neReeds eaPrrcohj eAcgtesn cTyh.e y arael saoc tiivnee d ucattieocnhanlo rleosgeya rch. MichaGeolo drircehc eihviePsdh .Di.nC omputSecri enfcreoP mu rdUunei ­ 1987. versiint y Hei sc urreanC thlayn ceilor'si ntP hrDeoe fpeasrstomorfeC notm ­ putSecri enactUe n iverosfCi atlyi foImrivai,Pn ree.v iohuesw laysa, p rofeasts or JohnHso pkiUnnsi versHieti sya .ne ditfoorarn umbeorfj oumailncs o mputer scietnhceeo croymp,u tatigoenoamle trayn,dg raaphl goriHtehi msas n.A CM Dis­ tinguiSschieedn atF iesltl,oo ftw h Aell leriAcsasno ciaftotirho Aend v ancemoefn t Scien(cAeA ASa)F ,u lbrSicghhotl aanrda,F ellooftw h IeE EEH.ei sar ecipoife nt thIeE EEC omputer SToecchineityAc cah!vi eemeAnwta rdt,hA eC MR ecognition ofS ervAiwcaer da,n dt hPeo nAdw ardf oErx cellienUn ncdee rgraTdeaucahtien g. Precfea xiii RobeTmaratsors eicaeh iiPvshe .idEDn l. e catnrCdio cmpaEulnt geirn eering formt hUen ivoeIfrl sliaitUtnyr o biasn a-iC1nh8 a98mH.pei a tsih Pgeln a stech PreosfosCfoo rm pSuctieaernn tdchC eeh aoitfrh D ee partmeonCftmo puStceir­ enacBter oUwnni vHeeri assli tsDyoi. rt eohBcfert oosCrw e nn'ftoGerer o metrie CompuHtiisn gri.en steeiarnrecclshut dse s eicncufrroiyrtpmpytaha,otyn gi,aro lan­ ysdiess,ai ngidnm ,p lemoeafnl tgaotrgiirotadnhpr mhas wa,inc dno gm putational geomeHteir asyn . IFEeElaEln oadrw e cioptfih Teeeen hto Aicchaile vement Awarfodr mt hIeE ECEo muptSeoirce ftoypr,ie oenrthiefin egol gfdr adprha w­ inHge.i a sn e diotfo rsj eomvuaeilrgnsae lo maentgdrr iaaepl hg osr.Hie t hm prveiosuesrlovynte heded itoroiIfaE lETE ran bsoaaorcCdnt o pimuo.tn esr s Ianct ditttohi reoeinsr ea acrccohm plthies hamuethnhatoevsrxe,st eanlssiov e expeirtnihe cenl caes Fsorro oemDx.raG .mo poldherat,isa c uhdg ahsttta r uctures anadl gocroiutirhnsmcesls Du,ad Stitanr gua castf eurhsrmeasn -msoolrpeehv oel couarnIsdne t rotdAoul oegrtiiatoashnnu m pspl eecrvo eulHr ehs aees.a rsneevd­ ertaela cahwiainrtngdh c sia sp aHcitiset aycs.ht iytnliogen vitoshsl etv ueid ne nts livienltyec rlaacstssiervsoetso hibmaor tnio snu gti ntthuaein itdni hsotbinseg hind dasttar uacntadul rgionrtgie thcumheinDscir.T q.ma ashsatisaa u DgahSttta r uc­ tuarneAdsl goraisant ihnmtsr ofdsruehcm-talonecryvo euslri sn1e8c9 8eO .n e thitnhhgaa stse h ti s tsetaaycplhiaeirs nt eg hff eicsut soieifv n et ehryapcetri­ve medpirae seinnttaetwgiirottanhWhtsee be .d Ackngomwneltesd Thearraene u mobifen rd iwvhihoda uvaelc som natdrietb touh btiioosno sk . Wea rger attoe fouaurllre l s ecaobrloclrhaaa trtoicerdhas ia nstgsa inwsthso, provfieeddebodane c akrd lryao ffcth sa patnhedar hvsee l upsie dndve eloping exceirsseosftr,wea a,na dl goarniitmhsamyt sitoIenpnm a sr.t wiecw uolualrd, litktoeh aJneAkffc hVtesesreA,lm ianuJ daomvBe,kas eR ry,aB knae Brej,mna in BeorM,i kBeio len,B roDleaLvnuidbn,oB muoirrdS etviB,inr dag eBmrayna,n CantYrii-ClJhlei,nRa onbgCe,or htDe anvE,il dDl aivsEi,mod ryJ ,o Fdayn Bteon, PinPkeeFtlre,ör hAlsihGciahmr, g , GNealtfMaaasnrHhdkaa, n dy,H oMmi,c hael GreHgo waBrnedoH,îu td sJoonv,anI ngan atowPiawcdizoBt,bza i,PSs ae ptah­ manthJoaumP,ei se cDhaont aP,o livyS,ua snSnReaathuHh ba ,SrP uar kaaeit,o r, AndShycw eMriicnhS,ah aeplMi irSkohe,i M mih,ca SehlGi anl,Si hnuabA imnya , SimpCshorniS,str taYiueaSb nu,N n i,kT iorasn doLpuoVcuials oiDsna,ean nrfga , YoaJ,a sYoe,an nE dr Ziacm ore.B uoLrudbeovDm,ei mrMm MiearkrHke,a ndy, MichHaoem�l,dS cSoeptitg dleevrea lb oapJseaitdvc;u a twohriiaucllh,t imately letdCo h ap1Jt,ae vra SPpreitcmhieaagrnlot.k E osr Ziacm orceo,n trwihbou ted ttoh dee velootfph Jmeae vnate xcaomdipenl betoshao inktsd tho e i nidteisali gn, implemaenntdte asotttfiih noneteng ., ad sattrrelusic btorudfaa srytt ar uacntdu res algoiriJnta hvWmeasa . ra elgsroa ttVoees fsueAll muiadnao nvMd i kSeh fiomr