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Uci ~uyex djei hl uci pqi~ilu h~ gl`x eirguie ug eij` vhuc uci eiri`gpdilu gb uci nglnipu gb vgq`erhiv vhuchl uci H~`jdhn uqjehuhgl jle ngluisu eyi ug= :, Uciq Uciqi h~ j ~cgquj ~cgqujfi fi gb ~uyehi ~uyehi~ ~ gl uci eiri`gpd eiri`gpdilu ilu gb &vgq`erh &vgq`erhiv& iv& bqgd bqgd aguc ch~ugqhnj` jle nglnipuyj` piq~pinuhri~ vhuchl uci H~`jdhn ngluisu $ lg ~pin ~pinhb hbhn hn eh~n eh~nhp hp`h `hli li jle jle lg ~pinh ~pinhbh bhn n aqjl aqjlnc nc gb klgv klgv`ie `iefi fi nj`` nj``ie ie & vgq`erhiv ~uyehi~& 1, Uciq Uciqi i h~ lg ~pin ~pinhb hbhn hn aqjl aqjlnc nc gb qi~ij i~ijqqnc ucju ucju eij` eij`~ ~ vhuc vhuc uci uci ch~u ch~ugq gqhn hnj` j` eiri`gpdilu gb uci nglnipu gb vgq`erhiv hl ngluidpgqjqx H~`jdhn ibbgqu~ uci djmgq vgqk~ ehe lgu eh~ny~~ vgq`erhiv ch~ugqhnj` eiri`gpdilu jle nglnipuyj` ngl~uqynuhgl ayu bgny~ djhl`x gl uci h~~yi~ jle ugphn~; if= H~`jd Hdjl Hc~jl Fgedjl `hbi rhnifiqilnx iun, Uciqi viqi viqi ~pinhbhn juuidpu~ yleiq ~ync j bhi`e nj``ie HVR ~uyehi~ ~uyehi~ jbuiq uci jppijqjlni gb niqujhl ~pinhbhn vgqk~ ~ync j~ uci vgqk gb ^jxxhe Zyua gl uci &Ncjqjnuiqh~uhn~ gb HVR& Dg~u Dg~u gb uci ~ncg`jq~ ~ncg`jq~ cjri pqgrh pqgrheie eie djlx heij~ heij~ jle hl~hfcu~ hl~hfcu~ gl HVR dy`uhbjniuie j~pinu~ Jlguciq fqgyp gb ~ncg`jq~ eij`u ehqinu`x vhuc uci h~~yi~ gb HVR ayu lgu vhuc hu~ hlnipuhgl jle eiri`gpdilu j~ j nglnipu jle j ~ipjqjui bhi`e ∑
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Uci~i Uci~i cjri ~cgvl uci isuilu isuilu jle juuiluhgl juuiluhgl fhril ax Dy~`hd Dy~`hd ~ncg`jq~ ~ncg`jq~ ug qi~ijqnc gl uch~ jqij ayu uci vgqk~ gl`x eij`u vhuc vgq`erhiv h~~yi~ hl filiqj` uiqd~ qjuciq ucjl ~x~uidjuhn jle gaminuhri hlzyhqx hl vgq`erhiv
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EIBHLHUHGL GB UCI HVR ‡
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J@$ UJVCHE J^ J KIX I@IDILU HL UCI EIBHLHUHGL JLE NGLNI_UYJ@H]JUHGL GB UCI HVR Ylhux gb Fge j~ j rh~hgl gb ish~uilni jle rhnifiqilnx ngqi gb HVR vhucgyu; H~`jd `g~i~ hu~ gqhfhlj`hux jle j le exljdh~d j`$Ujvche h~ j filiqj` griqrhiv gb qij`hux gb uqyuc gb uci vgq`e gb ~pjni jle uhdi gb cydjl ch~ugqx jle ei~uhlx jlx eibhlhuhgl jle nglnipuyj`h}juhgl gb uci HVR ~cgy`e qirg`ri jqgyle j`$ Ujvche jle hu~ hdp`hnjuhgl~ ug ai`hib jle `hbi HVR idjljui~ bqgd uci ai`hib aj~ie gl `hbi jle ish~uilni njdi hlug aihlf j~ j qi~y`u gb uci vh`` ei~hqi jle ei~hfl gb uci Gli jle Gl`x Nqijugq
EIBHLHUHGL JLE NGLNI_UYJ@H]JUHGL _QGB LJZYHA LJZ YHA J@$J J@$ JUUJ^ hl~ipjqja`i `hlk aiuviil uci ~iil jle yl~iil j~pinu~ jle aiuviil uci pqi~ilu vgq`e qij`huhi~ jle uci ciqijbuiq gli~ ‡
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h( uci HVR eij`~ djhl`x vhuc ish~uilni hl hu~ uguj`hux vchnc hln`yei~ uci ~iil jle yl~iil vgq`e~; hh( uci HVR rh~hgl h~ j diujpcx~hnj` ~yqrix jle qirij`ie klgv`iefi ucju j~phqi~ ugvjqe~ n`ijqhlf ugvjqe~ n`ijqhlf uci nglby~hgl jle ~iuuhlf uci uqyuc~ jagyu ish~uilni; hhh( uci lgl$ehj`inuhnj` ljuyqi gb uci HVR jle lgl$ch~ugqhnhux gb hu~ ~gyqni vchnc h~ qirij`ie j~ ngdp`iui jle ngdpqicil~hri uisu pqgrhehlf n`ijq jle pqgbgyle hluiqpqiujuhgl~ jagyu uci uqyuc gb ish~uilni ∑
bhqd`x ~uqi~~i~ gl uci diujpcx~hnj` gb HVR
_QGB NCGYECYQ NCGYE CYQX X idpcj~h}i~ aguc uci ehrhli ~gyqni~ hi Zyqjl jle uci pqgni~~$gqhilujuhgl gb ylhbhie klgv`iefi vchnc h~ eiqhrie bqgd uci ehrhli ~gyqni gb HVR j~ vi`` j~ uci hlui``inuyj` pqgni~~i~ qizyhqie hl hu~ ngl~uqynuhgl hl `hfcu gb uci qirij`ie vgqe gb Fge qi~y`u gb uci Dy~`hd&~ ileijrgyq ug ngl~uqynu ch~ rh~hgl gb qij`hux hl `hfcu gb uci qirij`ie vgqe gb Fge uci HVR ngdi j~ j qi~y`u gb uci Dy~`hd dhle&~ hluiqjnuhgl vhuc uci vgq`e qij ij`hu `huhi~ hi~ hl `hfcu `hfcu gb uci uci uijn uijnch chlf lf~ ~ gb uci uci Zyqj Zyqjl l jle jle uci uci pqjn pqjnuh uhni ni~ ~ gb _qgpciu _qgpciu Dycjddje ∑
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vgq`erhiv h~ gyq rh~hgl gb uci vgq`e ayu ax hu~ ljuyqi h~ lgu uci pqgeynu gb gyq bii`hlf~ jle idguhgl~ qjuciq hu h~ uci qi~y`u gb gyq ucgyfcu~ jle ~piny`juhgl~; qi`ju qi`jui~ i~ ug uci vi``$kl vi``$klgvl gvl zyi~uh zyi~uhgl gl gb klgv`i klgv`iefi efi;; isn`y isn`y~hr ~hri`x i`x cydjl cydjl pqgpiqux j~ gppg~ie ug bii`hlf vchnc djl ~cjqi~ vhuc guciq jlhdj`~; vgq`e klgv`iefi h~ isn`y~hri ug djl jle h~ j bylnuhgl gb ch~ qib`inuhgl jle hlui``inuhgl
J@_JQ^@JL vgq`erhiv h~ uci diluj` bqjdivgqk h~ uci uguj`hux gb nglnipu~ jle diluj` juuhuyei eiri`gpie ax uci hlehrheyj` ucqgyfcgyu ucqgyfcgyu ch~ `hbi; uci y`uhdjui bgylejuhgl gb j`` cydjl ngleynu ∑
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_QGB DGCE KJDJ@ CJ^^JL uci uci HVR HVR h~ j ngdp ngdpqqicil icil~h ~hri ri ngln nglnip ipuh uhgl gl gb uci uci ylhr ylhriq iq~i ~i jle jle djl& djl&~ ~ qi`juhgl ug hu bqgd uci H~`jdhn piq~pinuhri idpcj~h}i~ gl uci H~`jdhn piq~pinuhri jle gli&~ pch`g~gpcx gq gyu`ggk gb `hbi H~`jd H~`jd aingdi aingdi~ ~ uci piqdjl piqdjlilu ilu qibiqiln ibiqilni i jle ~gyqn ~gyqni i bqgd bqgd vchnc vchnc uci Dy~`hd ~iik~ fyhejlni jle ehqinu ch~ hlui``inuyj` ibbgqu~ jle hmuhcje ∑
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DYC^HIL JAEY@CJDHE $ HVR h~ uci H~`jdhn piqnipuhgl gl h~~yi~ piqujhlhlf ug uci Ylhriq~i jle Hu~ Nqij Nq ijug ugq q _qgp _qgpci ciuc ucgg gge e ~gnh ~gnhiu iux x djl djl ciq ciqijbui ijbuiqq j~ gppg gppg~i ~ie e ug guci guciqq vgq`erhiv~ ucju jeeqi~~ uci ~jdi h~~yi~ ayu bqgd ucihq ~ujle piq~pinuhri J RH^HGL GB @HBI JLE _IQBINUHGL NGLNI_U GB HVR= :, Ng``in Ng``inuhr uhri i Yddjuhn Yddjuhn ljuyq ljuyqi i gb HVR 1, _g~hu~ jle eij`~ vhuc ish~~uilni ish~~uilni hl hu~ uguj`hux= uguj`hux= ~iil jle yl~iil vgq`e~ >, Qi~y`u i~y`u gb uci Dy~`h Dy~`hd d hluiqj hluiqjnuhg nuhgl l vhuc vhuc `hbi jle qij`hux qij`hux hl jnngq jnngqejl ejlni ni vhuc vhuc uci uijnchlf~ gb H~`jd 5, HVR HVR pqgr pqgrhe hei~ i~ uci uci lini lini~~ ~~jq jqx x fyhe fyhejl jlni ni bgq bgq uci uci Dy~` Dy~`hd hd ug gyuq gyuqhr hrj` j` hl ch~ ch~ gaminuhri~ hl uch~ vgq`e jle hl ciqijbuiq hi Kch`jbjc ‡
J NGD_QICIL^HRI ^UQYNUYQI GB HLUIFQJUIE KLGV@IEFI HVR h~ j ngdpqicil~hri hluifqjuie jle ngl~h~uilu ~uqynuyqi gb klgv`iefi piqujhlhlf ug uci qij`d~ gb uci ~iil jle yl~iil; hu h~ i~~iluhj` jle rhuj` bgq aguc djl&~ yleiq~ujlehlf gb chd~i`b jle ch~ ~yqqgylehlf~ j~ vi`` j~ ~ynni~~ hl ch~ dh~~hgl j~ j rhnifiqilu gb Fge jle nglrixiq gb uci qirij`ie fyhejlni ug cydjlkhle
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J RH^HGL GB @HBI JLE _IQBINUHGL J^_INU^ GB HVR= h( ui``~ djl jagyu jagyu uci ng~dg~ jle jle ng~dg``gfhnj` uqyuc~ uqyuc~ jle pjuuiql~; pjuuiql~; hh( isp`jhl~ uci iph~uidg`gfhnj` qy`i~ jle pqhlnhp`i~ ucju liie ug ai ngl~heiqie vch`i eij`hlf vhuc h~~yi~ gb ish~uilni jle `hbi; hhh( isp`jhl~ ucig`gfhnj` djuuiq~ piqujhlhlf ug uci ai`hib ~x~uid jle djuuiq~ gb bjhuc jle vgq~chp; hr( isp`jhl~ uci iuchnj` ~x~uid lini~~jqx bgq aj`jlni jle ~ujah`hux hl cydjl ‡
`hbi; r( pqgrhei~ `ifj` jle `ifh~`juhri hlmylnuhgl~ bgq uci qyllhlf gb cydjl jbbjhq~ jle myefhlf gb cydjl jnu~; rh( pqgrhei~ djl vhuc j nhrh`h~juhglj` rh~hgl ~g j~ ug j~~h~u chd ug jnchiri isni``ilu jle piqbinuhgl hl ch~ ileijrgyq~; rhh( &&iriqxuchlf ucju cjppil~ hl uci vgq`e egi~ ~g ax Ch~ ngddjle~ ax Ch~ jnuhgl&& - HVR h~ j ~uqynuyqi gb hluifqjuie klgv`iefi jle j rh~hgl gb `hbi ucju gbbiq~ djl uci lini~~ lini~~jqx jqx klgv`i klgv`iefi efi jle gqhilu gqhilujuhg juhgl l qizyh qizyhqqie hl ch~ ileijr ileijrgyq gyq~ ~ j~ j rhnifiqilu gb Fge gl Ijquc ‡
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J DJLH DJLHBI BI^U ^UJ JUHGL UHGL^ ^ GB QI@H QI@HFH FHGL GL,, ^GNH ^GNHIU IUX X, ^U ^UJ JUI UI,, JLE JLE NHRH@H^JUHGL ilujh` ilujh`~ ~ jle ~x~uid ~x~uidjuh juhnj` nj``x `x hluifq hluifqjui jui~ ~ uci qi`hf qi`hfhgy hgy~ ~ ~gnhj` ~gnhj` ~ujui ~ujui jle nhrh`h~juhglj` j~pinu~ gb `hbi
QI@HFHGL H~`jd h~ j vjx gb `hbi vchnc ilngdpj~~i~ h~~yi~ qi`juie ug ai`hib jle ~gnhj` ~x~uidjuhn H~`jd j~ j qi`hfhgl hln`yei~ j piqbinu iuchnj` jle dgqj` ~x~uid ∑
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^GNHIUX HVR j~ j ~gnhiux h~ dijlu ug ngl~uqynu j aj`jlnie cydjl ~gnhiux vchnc ~ujle~ bgq izyj`hux jle my~uhni jdglf uci ehbbiqilni~ qjni~ `hrhlf uciqihl ∑
^UJUI uci uci pqjn pqjnuh uhni ni~ ~ jle jle eiie eiie~ ~ gb uci uci _qgpci gpciuu Dycj Dycjdd ddje je hln` hln`ye yehl hlf f uci uci ngl~uhuyuhgl gb Djehljc jle ch~ hluiqljuhglj` qi`juhgl~ jnuhrhuhi~ jle uci pqjn pqjnuh uhni~ ni~ gb uci uci 5 fyhe fyheie ie nj`h nj`hpc pc~ ~ ~cgv ~cgv uci uci hdpg hdpgqu qujl jlni ni gb ~uju ~ujui i jle jle fgriqldilu vhuchl uci HVR ngluisu ∑
NHRH@H^JUHGL HVR j`~g h~ ngl~heiqie j~ uci nidiluhlf pgviq aichle uci ngl~uqynuhgl gb uci H~`jdhn nhrh`h~juhgl~ ax= H( ngl~uqynuhlf j fgge Dy~`hd piq~glj`hux hh( ngluqhayuhlf hl ~nhiluhbhn jle hlui```inuyj` eiri`gpdilu ∑
YLF^ 1?>? „ HLUQGEYNUHGL UG H^@JDHN VGQ@ERHIV= ^UYEX GB ^I@INUIE I^^ILUHJ@^
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GAMINUHRI^ GB VGQ@ERHIV ∑
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fhri~ j aj~h~ gq j piq~pinuhri bqgd vchnc vi njl jlj`x}i njuifgqh}i jle ~xluci~h}i ejuj ilja`hlf y~ ug djki ~il~i gb gyq ish~uilni ci`p y~ ug hluifqjui uci bjnu~ hlug j dijlhlfby` vcg`i aj~h~ bgq djkhlf `hbi&~ einh~hgl~ ilja`i djl ug pg~~i~~= j dgei` gb uci vgq`e jah`hux ug isp`jhl jle jl~viq uci zy~uhgl~ jah`hux ug jl~viq uci zyi~uhgl jah`hux ug ~ii ucqgyfc ucqgyfc fgge fgge jle aje rj`yi~ jle jl~viq jl~viq uci zyi~uhgl jah`hux ug klgv cgv ug jnu pqgpiq`x jah`hux ug ngl~uqynu pqgpiq klgv`iefi jagyu ish~uilni jle uqyuc uqyuc jah`hux ug eiri`gp vgq`erhiv
KHLE^ GB VGQ@ERHIV
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eh~uhlnuhgl aiuviil uci qiri`juhgl aj~ie vgq`erhiv vciqihl uci uisu h~ pqi~iqrie jle djl$djei vgq`erhiv~ vchnc cjri jl hln`hljuhgl ugvjqe~ dgqj` jle iuchnj` bgylejuhgl~ uciqi jqi j`~g vgq`erhiv~ vchnc hln`hli ug ~nhiluhbhn aj~h~ pch`g~gpchnj``x gqhiluie bgny~ gl heig`gfhnj` pg`huhnj` `hlfyh~uhn jle guciq bgylejuhgl~ uci uci hlui hluiqp qpqqiuju iujuhg hgl~ l~ jle jle jl~v jl~viq iq~ ~ pqgr pqgrhe heie ie ax uci uci bg``g bg``gvi viq~ q~ gb ijnc ijnc vgq`erhiv ucju eh~uhfyh~c hu bqgd guciq vgq`erhiv~ j fgge vgq`erhiv ~cgy`e pqgrhei `gfhnj` qjuhglj` jle gaminuhri ch~ugqhnj` jle jle nhrh nhrh`h `h~j ~juh uhgl glj` j` irhe irheil ilni ni~ ~ bgq bgq hu~ hu~ jah` jah`hu huhi hi~ ~ ug gbbi gbbiqq djl djl j dgq dgqi dijlhlfby` rh~hgl jle hl~uh`` hl chd j ~il~i gb pyqpg~i
J__QGJNCI^= ^NHILUHBHN, _CH@G^G_CHNJ@ JLE QI@HFHGY^ ∑
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~nhilni jle pch`g~gpcx jqi dgqi `hki diucge~ jle jppqgjnci~ ug ujnk`i pqga`id~ jle h~~yi~; j`~g ucix dgqi `hki ugg`~ jle uinclhzyi~ gb hlzyhqx ucju j~~h~u hl eiri`gphlf vgq`erhiv~ jle jl~viqhlf hu~ zyi~uhgl~ ~gdi guciq ~ncgg`~ gb ucgyfcu pqibiq ug jppqgjnc vgq`erhiv bqgd j dgqi qi`hfhgy~ piq~pinuhri bg``gvhlf uci diucge~ jle ugg`~ gb qi`hfhgy~ jlj`x~h~ H~`jd ainjy~i gb hu~ gqhfhlj` pqi~iqrie jle ngdp`iui vgqe gb Fge ucju gbbiq~ j ng~dhn jle j``$ilngdpj~~hlf vgq`erhiv pqgrhei~ j qij` qi`hfhgy~ vgq`erhiv jle lgu gl`x qi`hfhgy~ jppqgjnc ug vgq`erhiv
^NHILUHBHN J__QGJNC UG VGQ@ERHIV $ qij~gl jle hu~ qjuhglj`h~uhn pjqjehfd h~ uci Fge gb ^nhiluhbhn Hlzyhqx ‡
DJHL _QHLNH_ _QH LNH_J@^ J@^= :, idphqhnh~d idphqhnh~d hl vchnc vchnc j`` h~~yi~ yleiq yleiq eh~ny~~hgl eh~ny~~hgl ~cgy`e ~cgy`e yleiqfg yleiqfg uci uci ui~u gb ispiqhdiluj` jle idphqhnj` qizyhqidilu~ 1, qjuhglj`h~ qjuhglj`h~d d vciqihl vciqihl qij~gl qij~gl jle cydjl hlui``inu hlui``inu j~~ydi~ j~~ydi~ ci pg~huhgl pg~huhgl jle qg`i gb uci ngluqg``iq hluiqpqiujuhgl >, ~k ~kipuhn ipuhnh~d h~d vciqi vciqi gli ~cgy`e j~~ydi j~~ydi ucju jlx klgv`ief klgv`iefi i bjnu gq ai`hib h~ ~yaminu ug ~nhiluhbhn zyi~uhglhlf DIUCGE GB ^NHILUHBHN HLZYHQX :, heiluhbxhl heiluhbxhlf f uci pqga`id pqga`id ucqgyfc ucqgyfc ga~iqrju ga~iqrjuhgl hgl jle y~i gb ~il~i~ ~il~i~ 1, pqgpg pqgpg~hl ~hlf f cxpguc cxpguci~i i~i~ ~ jle j~~ydpu j~~ydpuhgl hgl~ ~ ucju ucju ngy`e ngy`e isp`jh isp`jhl l uci pqga`id pqga`id pg~ie >, ng``inuhlf ng``inuhlf uci ejuj jle hlbgqdjuhg hlbgqdjuhgl l 5, ui~uhlf uci cxpguci~i~ jle heiluhbxhlf uci ngqqinu ngqqinu gli jle uci ahj~ gli gli 9, pqgrhehlf pqgrhehlf hluiqpqi hluiqpqiujuhg ujuhgl l vhuc vhuc irheilni irheilni 2, filiqj filiqjuhl uhlf f hluiqp hluiqpqi qiuju ujuhgl hgl~ ~ 6, eiri`gp eiri`gphlf hlf ~nhil ~nhiluhb uhbin in ucigqx ucigqx 3, i~uja`h~chl i~uja`h~chlf f ~nhiluhb ~nhiluhbhn hn `jv~ `jv~ jle jle bjnu~ bjnu~ - aj~ie gl uci pqhlnhpj` gb ~kipuhnh~d uci bjnu~ jqi zyi~uhglja`i ajnjy~i gb uci jerjlnidilu hl ~nhilni jle uinclg`gfhnj` eh~ngriqhi~ HD_GQUJLU HD_GQUJLU I@IDILU^= :, isjnuhuyei jle pqinh~i ljuyqi gb uci ~nhiluhbhn jppqgjnc 1, nglbhli~ hu ug pcx~hnj` qij`huhi~ ucju njl ai ga~iqrie jle ~yaminuie ug idphqhnj` jle ispiqhdiluj` nglehuhgl~
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EHBBIQILNI^ GB J__QGJNCI^ UG VR ^NHILUHBHN
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ISJNUHUYEI JLE @gv bgq uci riqx iqx qij~ ij~gl gb uci _QINH^ILI^^ diuc diucge ge~~ jle jle ugg ugg`~ y~ie ~ie hl ijnc ijnc ~pciqi gb hlzyhqx
@i~~ ncjlfi~ eyi ug uci ljuyqi gb ~nhiluhbhn hlzyhqx vchnc h~ juujncie dgqi dgqi ug uci uci pcx~h cx~hnj nj`` qij` qij`hu huhi hi~, ~, ~il~i~ ngluqg` jle ngluhlyg~ jerjln jlnidi idilu hl uci ugg`~ jle uinclhzyi~ gb hlzyhqx
^UJAH@HUX
Qirg`r Qirg`ri~ i~ jle nglniql nglniql~~ hu~i`b hu~i`b vhuc vhuc uci pqgfqi~~hri jerjlnidilu vhuchl uci nglbhli~ jle `hdh hdhu~ gb uci pcx~hnj` vgq`e
LJUYQI LJUYQI JLE HLNI_UHGL
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DIJLHLF JLE _YQ_G^I
Dgqi jnnipuja`i
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‡
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Dgqi ~uja`i hl uiqd~ gb ngln`y~hgl jle hluiqpqiujuhgl bgq riqx riqx qij~ qij~gl gl gb hu~ hu~ qi`hj qi`hjln lnii gl gqid gqidh~ h~ii gb `gfh `gfhnn jle jle `jv~ `jv~ gb dhle
HLEHNJUGQ
hu~ uci uci uci uci uci
_iqnihri~ hu hl uiqd gb cjpphli~~, vh~egd, my~uhni, jle rhquyi uiqd~
QI@HFHGY^ J__QGJNC UG VGQ@ERHIV
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Djuiqhj`h~d= Isjdp`i gb jl Isuqidi Vi~uiql Vgq`erhiv ∑
∑ ∑
qibiq ibiqqqie ug j~ ljuy ljuyqj qj`h~ `h~d d gq ~nhi ~nhilu luhb hbhn hn djui djuiqh qhj` j`h~ h~d d ucju ucju eilh eilhi~ i~ uci uci ish~uilni gb jlx ~ypqj$ljuyqj` aihlf gq ~ypqj$hlui``hfilu dhle gq nqijugq uci gl`x qij`hux ucju h~ qij` jle pg~~ha`i h~ uch~ pcx~hnj` qij`hux iluhqi ish~uilni h~ nglbhlie jle qieynie ug vcju gli ~ii~ hl uch~ vgq`eh~
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