7TVMRX 4'7§ 8LI GPIEV EPXIVREXMZI XS GIPPYPEV 71
¬ 7TVMRX 7TIGXVYQ 0 4 %PP VMKLXW VIWIVZIH 2S VITVSHYGXMSR MR [LSPI SV MR TEVX [MXLSYX TVMSV [VMXXIR ETTVSZEP 7TVMRX 7TVMRX 4IVWSREP 'SQQYRMGEXMSR 7IVZMGIW 7TVMRX 4'7 7TVMRX 4'7 4LSRI 7TVMRX 4'7 ;MVIPIWW ;IF ERH XLI HMEQSRH PSKS EVI XVEHIQEVOW SJ 7TVMRX 'SQQYRMGEXMSRW 'SQTER] 0 4 %PP SXLIV XVEHIQEVOW EVI TVSTIVX] SJ XLIMV VIWTIGXMZI S[RIVW 4VMRXIH MR XLI 9 7 % )2 6IZ <
8EFPI SJ 'SRXIRXW ;IPGSQI XS 7TVMRX 4'7 Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü +IXXMRK 7XEVXIH [MXL 7TVMRX 4'7 7IVZMGI %GXMZEXMRK =SYV 4LSRI 7IXXMRK YT ]SYV ZSMGIQEMP +IXXMRK LIPT +IXXMRK XS /RS[ ]SYV 4LSRI
Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü 2EZMKEXMRK QIRYW 7IXXMRK YT XLI QEMR QIRY ZMI[ :MI[MRK XLI QIRYW 7LSVXGYXW )RXIVMRK PIXXIVW RYQFIVW ERH W]QFSPW
Ü Ü Ü Ü Ü Ü Ü Ü Ü Ü %WWMKRMRK WGVIIR WEZIVW 7IXXMRK %YXS ,]TLIREXMSR 7IXXMRK XLI XMQI ERH HEXI JSVQEX %HNYWXMRK XLI GSRXVEWX )VEWMRK QIWWEKIW EYXSQEXMGEPP] %YXS )VEWI 8I\X 7IXXMRK EPIVXW
Ü :SMGI %RW[IV )\TIVMIRGMRK 7TVMRX 4'7 ;MVIPIWW ;IF Ü Ü Ü Ü Ü Ü 9WMRK XLI ;MVIPIWW ;IF -RHMGEXSVW ERH EPIVXW 1] (S[RPSEHW 8&( ;IF +YEVH
;IPGSQI XS 7TVMRX 4'7 7TVMRX 4'7 FYMPX XLI SRP] EPP HMKMXEP EPP 4'7 REXMSR[MHI RIX[SVO JVSQ XLI KVSYRH YT JSV GPIEVIV GEPPW WIVZMRK QSVI XLER QENSV QIXVSTSPMXER EVIEW ;I FYMPX SYV RIX[SVO XS KMZI ]SY [LEX [I FIPMIZI ]SY VIEPP] [ERX JVSQ E § [MVIPIWW TLSRI GPIEV WSYRH TVMZEXI GSRZIVWEXMSRW ERH XMQI WEZMRK JIEXYVIW %RH 7TVMRX 4IVWSREP 'SQQYRMGEXMSRW 7IVZMGIW GER HS WSQIXLMRK IZIR QSVI JEV VIEGLMRKWMQTPMJ] ]SYV PMJI 3YV EHZERGIH XIGLRSPSK] MW HIWMKRIH XS KVS[ [MXL ]SYV GSQQYRMGEXMSRW
+IXXMRK 7XEVXIH [MXL 7TVMRX 4'7 7IVZMGI (IXIVQMRI MJ ]SYV TLSRI MW EPVIEH] EGXMZEXIH -J ]SY VIGIMZIH ]SYV TLSRI MR XLI QEMP SV TYVGLEWIH MX EX E 7TVMRX 4'7 'IRXIV MX TVSFEFP] LEW FIIR EGXMZEXIH %PP ]SY RIIH XS HS MW YRPSGO ]SYV TLSRI 9RPSGOMRK =SYV 4LSRI *SPPS[ XLIWI WXITW XS YRPSGO ]SYV TLSRI 4VIWW ERH LSPH *VSQ 7XERHF] QSHI XS XYVR XLI TLSRI SR )RXIV ]SYV HMKMX PSGO GSHI *SV WIGYVMX] TYVTSWIW XLI GSHI MW RSX ZMWMFPI 9RPSGO [MPP FI LMKLPMKLXIH 4VIWW EW ]SY X]TI
7IXXMRK YT ]SYV ZSMGIQEMP %PP YRERW[IVIH GEPPW XS ]SYV 7TVMRX 4'7 4LSRI EVI EYXSQEXMGEPP] XVERWJIVVIH XS ZSMGIQEMP IZIR MJ ]SYV TLSRI MW MR YWI SV XYVRIH SJJ 8S EZSMH QMWWMRK ER] MQTSVXERX QIWWEKIW ]SY [MPP [ERX XS WIX YT ]SYV 7TVMRX 4'7 ZSMGIQEMP FS\ ERH TIVWSREP KVIIXMRK EW WSSR EW ]SYV 7TVMRX 4'7 4LSRI MW EGXMZEXIH 8S WIX YT ZSMGIQEMP 4VIWW ERH LSPH *SPPS[ XLI W]WXIQ TVSQTXW XS GVIEXI ]SYV TEWWGSHI VIGSVH ]SYV KVIIXMRK VIGSVH ]SYV REQI ERRSYRGIQIRX ERH GLSSWI [LIXLIV XS EGXMZEXI
3RGI ]SY HMEP 7TVMRX 4'7 'YWXSQIV 'EVI ]SY GER EGGIWW E RYQFIV SJ LIPTJYP ZSMGI TVSQTXW ]SY PP FI EFPI XS PIEVR QSVI EFSYX 7TVMRX 4'7 TVSHYGXW ERH WIVZMGIW KIX 7TVMRX 4'7 GSZIVEKI F] ^MT GSHI SV VIUYIWX E GST] SJ ]SYV MRZSMGI 2SXI -J ]SY RIIH XS VIEGL 7TVMRX 4'7 'YWXSQIV 'EVI [LMPI ]SY EVI SJJ XLI 7TVMRX 4'7 2IX[SVO HMEP 4'7 ;LEX ]SY WLSYPH LEZI LERH] [LIR ]SY GEPP Ü =SYV RI[ 7TVMRX 4'7 4LSRI Ü 8LI SVMKMREP TEGOEKMRK JVSQ ]SYV TLSRI Ü =SYV 7SGMEP 7IGYVMX] RYQFIV SV 8E\ -( RYQFIV
+IXXMRK 7XEVXIH [MXL 7TVMRX 4'7 7IVZMGI
+IXXMRK XS /RS[ ]SYV 4LSRI ,MKLPMKLXW 'SRKVEXYPEXMSRW SR XLI TYVGLEWI SJ ]SYV 7TVMRX 4'7 4LSRI 1SHIP /]SGIVE 8LMW TLSRI MW PMKLX[IMKLX IEW] XS YWI VIPMEFPI ERH SJJIVW QER] WMKRMJMGERX JIEXYVIW Ü (YEP FERH GETEFMPMX] TVSZMHIW EGGIWW XS SXLIV 4'7 '(1% ERH EREPSK GIPPYPEV RIX[SVOW [LIVI 7TVMRX 4'7 LEW MQTPIQIRXIH VSEQMRK EKVIIQIRXW Ü Ü Ü Ü Ü Ü Ü Ü Ü TEKI 7TVMRX 4'7 ;MVIPIWW ;IF 71 &VS[WIV TVSZMHIW EGGIWW XS XLI [MVIPIWW -RXIVRIX MR HMKMXEP QSHI TEKI 71 %30 -RWX
1 .EGO JSV ,ERHW JVII LIEHWIX WSPH WITEVEXIP] 2 ,SQI WGVIIR 4VIWW 3 2EZMKEXMSR OI]W EHNYWXW ZSPYQI [LIR MR E GEPP WGVSPPW YT SV HS[R ERH PIJX SV VMKLX XS WIPIGX 1IRY XLVSYKL PMWXW ERH QIRYW ERH TSWMXMSRW XLI GYVWSV HYVMRK XI\X IRXV] 4 8EPO 7IRH OI] WXEVXW SV ERW[IVW E GEPP 5 3/ OI] WIPIGXW E QIRY MXIQ SV STXMSR 6 /I]TEH XS IRXIV RYQFIVW PIXXIVW SV W]QFSPW 7 8 8I\X OI] GLERKIW XI\X QSHIW %RXIRRE I\XIRHW XS QEOI SV ERW[IV E GEPP 4YWL MR XLI ERXIRRE [LIR XLI TLSRI MW R
*VSRX ZMI[ SJ TLSRI +IXXMRK XS /RS[ =SYV4LSRI 8 1 2 3 9 4 5 6 7 10 11 12 13 +IXXMRK XS /RS[ ]SYV 4LSRI
:MI[MRK XLI HMWTPE] WGVIIR 8LMW PMWX MHIRXMJMIW XLI W]QFSPW ]SY PP WII SR ]SYV HMWTPE] WGVIIR 8LI TLSRI MW STIVEXMRK MR '(1% HMKMXEP QSHI 8LI TLSRI MW VIGIMZMRK E WMKREP =SY GER QEOI ERH VIGIMZI GEPPW 8LI TLSRI MW RSX VIGIMZMRK E WMKREP =SY GERRSX QEOI SV VIGIMZI GEPPW % GEPP MW MR TVSKVIWW 8LI EPEVQ GPSGO MW WIX 8LI TLSRI ZMFVEXIW SV PMKLXW YT MRWXIEH SJ VMRKMRK 8LI TLSRI MW VSEQMRK SYXWMHI SJ MXW LSQI EVIE =SY LEZI E XI\X QIWWEKI ZSMGIQEMP SV TEKI &EXXIV] MW JYPP] GLEVKIH 8LI QSVI
8YVRMRK XLI TLSRI SR ERH SJJ 4VIWW XLI OI] ERH XLI 7XERHF] WGVIIR ETTIEV [LIR XLI TLSRI MW XYVRIH SR ERH MW VIEH] XS QEOI SV VIGIMZI E GEPP ETTIEVW MJ XLI TLSRI MW STIVEXMRK MR '(1% HMKMXEP QSHI 8YVRMRK SJJ XLI TLSRI ,SPH HS[R XLI OI] YRXMP l4S[IVMRK SJJz ETTIEVW EFSYX WIGSRHW 9WMRK XLI FEXXIV] &EXXIV] GETEGMX] =SYV 7TVMRX 4'7 4LSRI MW IUYMTTIH [MXL E 0MXLMYQ -SR 0M-SR FEXXIV] -X EPPS[W ]SY XS VIGLEVKI ]SYV FEXXIV] FIJSVI MX MW JYPP] HVEMRIH 8LI FEXXIV] TVSZMHIW ETTVS
'SRRIGX XLI %' %HETXIV XS XLI TVSTIV NEGO SR XLI FSXXSQ SJ XLI TLSRI XLIR GSRRIGX XLI EHETXIV W TPYK XS E [EPP SYXPIX *YPP] GLEVKI XLI FEXXIV] FIJSVI YWMRK XLI TLSRI JSV QSVI MRJSVQEXMSR WII TEKI 6IQSZMRK XLI FEXXIV] 8YVR SJJ XLI TLSRI F] LSPHMRK HS[R ,SPH XLI TLSRI JEGI HS[R YRXMP l4S[IVMRK SJJz ETTIEVW 4PEGI ]SYV XLYQF MR XLI KVSSZI SR XLI FEGO SJ XLI TLSRI ERH WPMHI XLI FEXXIV] HSSV HS[R YRXMP MX WXSTW 0MJX XLI FEXXIV] HSSV SJJ SJ XLI TLSRI 0MJX ERH WPMHI XLI
9RHIVWXERHMRK 6SEQMRK 9RHIVWXERHMRK 6SEQMRK 6IGSKRM^MRK -GSRW SR XLI (MWTPE] 7GVIIR =SYV TLSRI W HMWTPE] WGVIIR EP[E]W PIXW ]SY ORS[ [LIR ]SY VI SJJ XLI 7TVMRX QSHI 8LI JSPPS[MRK GLEVX MRHMGEXIW [LEX ]SY PP WII HITIRHMRK SR [LIVI ]SY VI YWMRK ]SYV TLSRI 2SXI XLEX E QIWWEKI [MPP ETTIEV SR XLI WGVIIR MRHMGEXMRK XLI X]TI SJ VSEQMRK IMXLIV HMKMXEP SV EREPSK (MKMXEP 6SEQMRK -RHMGEXSV -RHMGEXSV 7TVMRX 4'7 2EXMSR[MHI 2IX[SVO 3XLIV '(1% 2IX[SVOW %REPSK 'IPPYPEV 2IX[SVOW 2SXIW 6IQIQ
6SEQMRK SR %REPSK 'IPPYPEV 2IX[SVOW ;LIR ]SY VSEQ SR EREPSK GIPPYPEV RIX[SVOW ]SY [MPP I\TIVMIRGI XLI WEQI UYEPMX] TVSZMHIH F] EREPSK GIPPYPEV GEVVMIVW XSHE] %PXLSYKL WSQI GEPPMRK JIEXYVIW WYGL EW 7TVMRX 4'7 ;MVIPIWW ;IF QE] FI YREZEMPEFPI ]SY GER WXMPP QEOI ERH VIGIMZI GEPPW =SY [MPP I\TIVMIRGI E JI[ HMJJIVIRGIW MRGPYHMRK Ü Ü Ü Ü Ü =SY EVI QSVI PMOIP] XS I\TIVMIRGI WXEXMG GVSWW XEPO JEHI SYX ERH HVSTTIH GEPPW 7SQI GEPPMRK JIEXYVIW XLEX EVI WXERHEVH SR XLI 7TVMRX 4'7 2IX[SVO EVI YREZEMPEFPI
-R EHHMXMSR XS XLI VSEQMRK MGSR XLI 'EPP +YEVH ;IF +YEVH EPIVXW ]SY [LIR VSEQMRK GLEVKIW ETTP] 8LMW JIEXYVI QEOIW MX IEW] XS QEREKI ]SYV VSEQMRK GLEVKIW F] VIQMRHMRK ]SY [LIR ]SY QEOI SV VIGIMZI VSEQMRK GEPPW -X EPWS VIUYMVIW ]SY XS XEOI EHHMXMSREP WXITW FIJSVI TPEGMRK SV ERW[IVMRK E VSEQMRK GEPP 8LIWI EHHMXMSREP WXITW EVI RSX VIUYMVIH [LIR ]SY QEOI SV VIGIMZI GEPPW [LMPI SR XLI 7TVMRX 4'7 2EXMSR[MHI 2IX[SVO 8S 8YVR XLI 'EPP +YEVH *IEXYVI 3R → 7IXXMRKW → 6SEQMRK → 'EPP +YEVH 7IPIGX 1
6SEQ 7IVZMGI %PIVX 9WI XLMW WIXXMRK MJ ]SY [ERX XLI TLSRI XS EPIVX ]SY [LIR ]SY VSEQ SYXWMHI SJ ]SYV LSQI WIVZMGI EVIE → 7IXXMRKW → 6SEQMRK → 6SEQ 7VZG %PIVX 7IPIGX 1IRY 4VIWW r XS WIPIGX ER STXMSR (MWEFPIH HSIW RSX EPIVX ]SY MJ ]SY VSEQ SYXWMHI ]SYV LSQI WIVZMGI EVIE r ;LIR RS WIVZMGI EPIVXW ]SY [MXL XLVII XSRIW HIGVIEWMRK MR MRXIRWMX] [LIR WIVZMGI MW PSWX ;LIR WIVZMGI MW EGUYMVIH EKEMR ]SY LIEV XLVII XSRIW MRGVIEWMRK MR MRXIRWMX] r 3R VSEQ GLERKI EPIVXW ]SY [MXL X[S XSRIW
1EOMRK ERH %RW[IVMRK 'EPPW 1EOMRK 'EPPW =SYV 7TVMRX 4'7 4LSRI SJJIVW QER] HMJJIVIRX [E]W XS QEOI GEPPW MRGPYHMRK 7TVMRX 4'7 :SMGI 'SQQERH TEKI :SMGI (MEPMRK TEKI 7TIIH (MEPMRK TEKI ERH YWMRK XLI 6IGIRX 'EPPW 0MWX TEKI 8S QEOI E GEPP YWMRK ]SYV OI]TEH 1EOI WYVI ]SYV TLSRI MW SR )RXIV E TLSRI RYQFIV -J ]SY QEOI E QMWXEOI [LMPI HMEPMRK TVIWW XS IVEWI SRI HMKMX EX E XMQI 3V TVIWW ERH LSPH JSV EX PIEWX SRI WIGSRH XS IVEWI XLI IRXMVI RYQFIV 4VIWW
1MWWIH 'EPP 2SXMJMGEXMSR ;LIR ER MRGSQMRK GEPP MW RSX ERW[IVIH XLI 1MWWIH 'EPP PSK MW HMWTPE]IH SR ]SYV WGVIIR 8S HMWTPE] XLI 1MWWIH 'EPP IRXV] Ü → 6IGIRX 'EPPW 7IPIGX 1IRY 8LI QSWX VIGIRXP] VIGIMZIH GEPP [MPP FI HMWTPE]IH EX XLI XST SJ XLI PMWX [MXL E FPMROMRK MGSR 8S HMEP XLI 1MWWIH 'EPP IRXV] W TLSRI RYQFIV Ü ,MKLPMKLX XLI IRXV] ERH TVIWW ERH LSPH 2SXI =SY GERRSX HMEP TLSRI RYQFIVW MHIRXMJMIH EW 2S -( 6IWXVMGXIH (EXE SV *E\ GEPPW 7TVMRX 4'7 :SMGI 'SQQERH ;MXL 7TVMRX 4'7 XLI JMVW
'VIEXI =SYV 3[R %HHVIWW &SSO =SY GER TVSKVEQ E QE\MQYQ SJ RYQFIVW MRXS ]SYV EHHVIWW FSSO %RH [MXL XLI EHZERGIH XIGLRSPSK] SJ 7TVMRX 4'7 :SMGI 'SQQERH]SY GER LEZI MRWXERX EGGIWW XS EPP SJ XLIQ 8LIVI EVI XLVII [E]W XS YTHEXI ]SYV EHHVIWW FSSO Ü 'LSSWI 7TVMRX 4'7 :SMGI 'SQQERH ERH VIGIMZI E JYPP] JYRGXMSREP [IF FEWIH EHHVIWW FSSO [LIVI ]SY GER GVIEXI ERH YTHEXI ]SYV GSRXEGXW JSV Ü JVII EX [[[ XEPO WTVMRXTGW GSQ -J ]SY HSR X LEZI E GSQTYXIV SV -RXIVRIX EGGIWW LERH] ]SY GER LEZI 7TVMRX 4'7 (
7EZMRK E TLSRI RYQFIV *VSQ XLI LSQI WGVIIR IRXIV XLI TLSRI RYQFIV XLEX ]SY [ERX XS WEZI 2SXI 8S EHH TEYWIW [LMPI IRXIVMRK E RYQFIV WII l)RXIVMRK TEYWIW MR E TLSRI RYQFIVz SR TEKI 4VIWW XS 7EZI 2I[ +S XS WXIT SV 8S EHH XS ER I\MWXMRK GSRXEGX WIPIGX %HH XS 7IPIGX XLI GSRXEGX XLIR KS XS WXIT )RXIV E REQI JSV XLI GSRXEGX -J ]SY RIIH XS ORS[ LS[ XS YWI XLI OI]TEH XS IRXIV PIXXIVW WII TEKI 4VIWW XS 7EZI l'SRXEGX 7YGGIWWJYPP] 7EZIHz ETTIEVW SV 4VIWW
)RXIVMRK TEYWIW MR E TLSRI RYQFIV =SY GER MRGPYHI E TEYWI MR E TLSRI RYQFIV % XMQIH TEYWI GEYWIW XLI TLSRI XS WXST HMEPMRK JSV X[S WIGSRHW % LEVH TEYWI GEYWIW XLI TLSRI XS WXST HMEPMRK YRXMP ]SY WIPIGX 6IPIEWI 2SXI =SY GER IRXIV QYPXMTPI TEYWIW MR E TLSRI RYQFIV ;LIR ]SY WEZI XLI TLSRI RYQFIV SJ ER EYXSQEXIH WIVZMGI WYGL EW ZSMGIQEMP ]SY QE] MRGPYHI E TEYWI [LIVI ]SY [SYPH FI VIUYMVIH XS WIPIGX ER STXMSR SV IRXIV E TEWW[SVH *SV I\EQTPI ]SY GSYPH IRXIV E TLSRI RYQFIV XLIR E TEYWI XLIR E ZS
RYQFIV 7II l7IGYVMX]z SR TEKI JSV HMVIGXMSRW SR LS[ XS JMRH ]SYV PSGO GSHI 7IPIGX 2S XS PIEZI XLI RYQFIV YRGLERKIH r 4VMQEV] 2YQFIV r )HMX 8]TI r )\MX 'PEWWMJ] XLMW RYQFIV EW XLI GSRXEGX W QEMR RYQFIV 7IPIGX [SVO LSQI QSFMPI TEKIV JE\ 6IXYVR XS XLI LSQI WGVIIR )RXIV XLI RI[ MRJSVQEXMSR 4VIWW 7EZI XS WIPIGX )VEWMRK MRJSVQEXMSR JVSQ E GSRXEGX GEVH → 'SRXEGXW → :MI[ %PP *VSQ XLI LSQI WGVIIR WIPIGX 1IRY ,MKLPMKLX XLI GSRXEGX ERH TVIWW 7IPIG
To use Fast Find *VSQ XLI 7XERHF] WGVIIR 4VIWW XLI OI]W GSVVIWTSRHMRK XS XLI PIXXIVW SJ XLI GSRXEGX REQI ]SY [ERX XS JMRH 8LI TLSRI WIEVGLIW JSV GSRXEGXW [MXL REQIW FIKMRRMRK [MXL XLI PIXXIVW ]SY IRXIVIH 1EXGLMRK GSRXEGXW ETTIEV SR XLI WGVIIR 4VIWW YT SV HS[R XLVSYKL XLI PMWX XS JMRH XLI GSRXEGX ]SY [ERX 4VIWW XS GEPP XLI GSRXEGX r 2SXI 7TIIH HMEP PSGEXMSRW QEXGLMRK XLI RYQFIVW ]SY IRXIVIH ETTIEV JMVWX *SV I\EQTPI MJ ]SY IRXIV XLI RYQFIVW → → XS JMR
7IPIGX E WTIIH HMEPMRK PSGEXMSR 7TIIH HMEPMRK PSGEXMSR l z MW VIWIVZIH JSV ]SYV ZSMGIQEMP RYQFIV %WWMKR 6IQSZMRK E WTIIH HMEPMRK PSGEXMSR 4VIWW XS *VSQ XLI LSQI WGVIIR WIPIGX 1IRY 7IPIGX E WTIIH HMEPMRK PSGEXMSR ERH TVIWW 7IPIGX XLI RYQFIV XS VIQSZI ERH TVIWW 7IPIGX 7TIIH (MEPMRK 4VIWW VMKLX XS WIPIGX 6IQSZI 4VIWW → 'SRXEGXW → 7TIIH (MEP 0MWX 7TIIH HMEPMRK Ü *VSQ XLI LSQI WGVIIR IRXIV XLI SRI SV X[S HMKMX WTIIH HMEPMRK RYQFIV ERH
;SVOMRK [MXL 6IGIRX 'EPPW 8LI 6IGIRX 'EPPW PMWX WLS[W XLI PEWX GEPPW 'EPPW EVI MHIRXMJMIH F] X]TI 7SQI X]TIW QE] RSX FI EZEMPEFPI SR EPP TLSRIW 'EPP XS *SV[EVHIH GEPP 'EPP JVSQ 1MWWIH GEPP 8LVII [E] GEPP :MI[MRK 6IGIRX 'EPPW → 6IGIRX 'EPPW *VSQ XLI LSQI WGVIIR WIPIGX 1IRY 8S ZMI[ HIXEMPW EFSYX E GEPP WIPIGX E GEPP IRXV] 7IPIGX ER STXMSR r -J XLI GEPP MW JVSQ E RYQFIV XLEX LEW RSX FIIR WEZIH EW E GSRXEGX WIPIGX 8MQI 2YQFIV 7EZI 2I[ SV %HH XS -J XLI GEPP MW JVSQ E RY
(MEPMRK JVSQ XLI 6IGIRX 'EPPW PMWX → 6IGIRX 'EPPW *VSQ XLI LSQI WGVIIR WIPIGX 1IRY 7IPIGX XLI GEPP IRXV] MR XLI PMWX 4VIWW XS GEPP XLI RYQFIV (MWTPE]MRK ]SYV TLSRI RYQFIV Ü 7IPIGX 1IRY 4VIWW → 4LSRI -RJS =SYV TLSRI RYQFIV ETTIEVW XS WEZI XLI WIXXMRK 1EOMRK ERH %RW[IVMRK 'EPPW
2EZMKEXMRK ERH )RXIVMRK 8I\X 2EZMKEXMRK 1IRYW ERH )RXIVMRK 8I\X Ü *VSQ XLI 7XERHF] WGVIIR TVIWW 2EZMKEXMRK QIRYW XS WIPIGX 1IRY XLIR TVIWW PIJX SV VMKLX XS WII QIRYW 2SXI-J ]SY LEZI 1EMR 1IRY :MI[ WIX XS 0MWX 1IRYW TVIWW YT SV HS[R XS WII QIRYW Ü Ü Ü Ü 4VIWW XS WIPIGX E QIRY SV QIRY MXIQ 3RGI ]SY LEZI WIPIGXIH E QIRY TVIWW YT SV HS[R XS WGVSPP XLVSYKL XLI QIRY MXIQW 4VIWW XS VIXYVR XS XLI XST PIZIP SJ XLI GYVVIRX QIRY 4VIWW XLI OI] XS VIXYVR XS XLI LSQI WGVI
'SRXEGXW 7IXXMRKW :MI[ %PP 7MPIRGI %PP %HH 2I[ 4LSRI 2YQFIV /I]KYEVH 6SEQMRK )QEMP %HHVIWW 7IX 1SHI 7XVIIX %HHVIWW 'EPP +YEVH )QEMP 960 6SEQ 6MRKIV 2SXI *MRH 2EQI 6SEQ 7VZG %PIVX 7SYRHW 7TIIH (MEP 0MWX 'EPP 6MRK :MFI :SMGI (MEP 0MWX 6MRKIV :SPYQI &YWMRIWW 0MWX 6MRKIV 8]TI 4IVWSREP 0MWX /I] &IIT :SPYQI -RJSVQEXMSR )EVTMIGI :SPYQI 1IWWEKIW /I] &IIT 0IRKXL 1MWWIH 'EPP %PIVX 8I\X -R&S\ 7QEVX 7SYRH ;IF %PIVXW /I] &IIT 7SYRH )QEMP &YWMRIWW 'EPP 6MRK *MPIH 1WKW 4IVWSREP 'EPP 6MRK
;MVIPIWW ;IF ;IF &VS[WIV 'SRRIGXMSR 8MQI (EXI *SVQEX 'SRXVEWX %HNYWX :SMGI 7IVZMGIW :SMGI 1IQS (EXE *E\ -R :SMGI 7LSVXGYXW (EXE *E\ 3YX %HH :SMGI (MEP :SMGI 8VEMRMRK ;IF +YEVH 2EZMKEXMRK ERH )RXIVMRK 8I\X 1] (S[RPSEHW :SMGI ;EOI 9T 6IGIRX 'EPPW 6IGIRX 'EPPW :SMGI %RW[IV 7IGYVMX] 0SGO 4LSRI 9WI 8SSPW 0MQMX 'EPPW 3YX %PEVQ 'PSGO 'LERKI 0SGO 'SHI 8MT 'EPGYPEXSV )VEWI %PP 'SRXEGXW 'EPGYPEXSV )VEWI 6IGIRX 'EPPW 'SYRXHS[R 4LSRI 6IWIX 7XST[EXGL &VMGO %XXEGO 7TEGI (YHIW 1]WXMG -GLMRK 'E
%YXS %RW[IV :SMGI ;EOI YT 7LSVXGYXW =SYV 7TVMRX 4'7 4LSRI LEW WLSVXGYXW FYMPX MR XS TVSZMHI JEWXIV EGGIWW XS WTIGMJMG JYRGXMSRW Ü Ü Ü Ü 4VIWW PIJX ERH LSPH XS PSGO XLI OI]TEH 4VIWW HS[R XS ZMI[ ]SYV 'SRXEGXW PMWX 4VIWW YT XS EGXMZEXI SV XS HIJMRI E WLSVXGYX OI] 7II l:SMGI 7LSVXGYXWz SR TEKI 4VIWW VMKLX ERH LSPH XS IREFPI 7MPIRX 1SHI )RXIVMRK PIXXIVW RYQFIVW ERH W]QFSPW =SY GER IRXIV PIXXIVW RYQFIVW ERH W]QFSPW MR E GSRXEGX GEVH 8LI HIJEYPX XI\X IRXV] QSHI MW Ü Ü Ü Ü Ü
4VIWW XS WIPIGX MX % PMWX SJ XI\X IRXV] QSHIW ETTIEVW 2EZMKEXMRK ERH )RXIVMRK 8I\X r2SVQEP %PTLE r6ETMH )RXV] r 2YQFIVW 3RP] r7]QFSPW 4VIWW HS[R XS WGVSPP XLVSYKL XLI PMWX 4VIWW XS WIPIGX E XI\X IRXV] QSHI 7LSVXGYXW Ü Ü 8S GLERKI XI\X IRXV] QSHIW TVIWW 8S GLERKI GETMXEPM^EXMSR QSHIW TVIWW ERH LSPH [LMPI 8 SV %&' XI\X IRXV] QSHI MW EGXMZI 9WMRK XI\X IRXV] QSHIW 8S IRXIV PIXXIVW MR QSHI 4VIWW XLI OI] SRGI JSV XLI JMVWX PIXXIV X[MGI JSV XLI WIGSRH PIXXI
2EZMKEXMRK 1IRYW ERH )RXIVMRK 8I\X
%HNYWXMRK :SPYQI %HNYWXMRK :SPYQI =SY GER WMPIRGI EPP TLSRI WSYRHW MRGPYHMRK XLI VMRKIV ERH EPP EPIVXW ERH WIX XLI TLSRI XS ZMFVEXI SV PMKLX YT JSV MRGSQMRK GEPPW QIWWEKIW ERH EPIVXW 7IPIGX 1IRY → 7IXXMRKW → 7SYRHW → 'EPP 6MRK :MFI LSQI WGVIIR TVIWW ,MKLPMKLX ER STXMSR XLIR TVIWW VMRKIV SV JVSQ XLI VMKLX ERH LSPH XS IREFPI 7MPIRGI %PP XS WIPIGX MX 2SVQEP XYVRW SR XLI MRHMGEXIW XLI TLSRI MW MR 7MPIRX QSHI 2SXI -J ]SYV TLSRI MW EXXEGLIH XS ER I\XIVREP TS[IV WSYVGI WY
2SXI 8S WMPIRGI EPP WSYRHW ERH WIX XLI TLSRI XS ZMFVEXI SV PMKLX YT MRWXIEH SJ VMRKMRK WII l7MPIRGI EPPz SR TEKI 'LERKMRK ER EPIVX WSYRH =SY GER GLERKI XLI EPIVX WSYRHW ]SYV TLSRI QEOIW Ü → 7IXXMRKW → 7SYRHW XLIR XLI WIXXMRK ]SY [ERX XS WIX SV 7IPIGX 1IRY GLERKI *SV MRJSVQEXMSR EFSYX EYXSQEXMG ZSPYQI EHNYWXQIRX 7QEVX 7SYRH WII TEKI 'LERKMRK XLI VMRKIV → 7IXXMRKW → 7SYRHW → 6MRKIV 8]TI 7IPIGX 1IRY 7GVSPP XLVSYKL XLI PMWX SJ VMRKIVW % WEQTPI TPE]W EW ]SY LMKLPMKLX IE
r(MWEFPIH OIITW XLI ZSPYQI PIZIP XLI WEQI YRPIWW ]SY EHNYWX MX YWMRK %HNYWXMRK :SPYQI 4VIWW XS WEZI XLI WIXXMRK 'LERKMRK XLI OI] FIITZSPYQI 7IPIGX 1IRY 4VIWW 4VIWW → 7IXXMRKW → 7SYRH → /I] &IIT :SPYQI PIJX SV VMKLX XS GLERKI XLI ZSPYQI XS I\MX 'LERKMRK XLI OI] FIIT PIRKXL → 7IXXMRKW → 7SYRHW → /I] &IIT 0IRKXL 7IPIGX 1IRY 7IPIGX 2SVQEP SV 0SRK 4VIWW 4VIWW XS I\MX %HNYWXMRK :SPYQI
%HNYWXMRK :SPYQI
9WMRK 7TVMRX 4'7 7IVZMGI *IEXYVIW 9WMRK 'EPPIV -( 'EPPIV -( PIXW ]SY ORS[ [LS W GEPPMRK F] HMWTPE]MRK XLI RYQFIV SJ XLI TIVWSR GEPPMRK [LIR ]SYV TLSRI VMRKW -J XLI GEPPIV W REQI ERH RYQFIV EVI EPVIEH] WXSVIH MR ]SYV -RXIVREP 4LSRI &SSO XLI GSVVIWTSRHMRK REQI ETTIEVW [MXL XLI RYQFIV -R XLI WEQI [E] MJ ]SY GEPP WSQISRI [LS LEW XLMW JIEXYVI ]SYV TLSRI RYQFIV HMWTPE]W SR XLIMV TLSRI 8S FPSGO ]SYV TLSRI RYQFIV JVSQ FIMRK HMWTPE]IH JSV E WTIGMJMG SYXKSMRK GEPP 4VIWW )RXIV XLI RYQFIV ]SY [E
8LVII ;E] 'EPPMRK ;MXL 8LVII ;E] 'EPPMRK ]SY GER XEPO XS X[S HMJJIVIRX TISTPI EX XLI WEQI XMQI ;LIR YWMRK XLMW JIEXYVI XLI RSVQEP EMVXMQI VEXIW [MPP FI GLEVKIH JSV IEGL SJ XLI X[S GEPPW )RXIV E RYQFIV ]SY [MWL XS GEPP ERH TVIWW 3RGI ]SY LEZI IWXEFPMWLIH XLI GSRRIGXMSR TVIWW XS TYX XLI JMVWX GEPPIV SR LSPH (MEP XLI WIGSRH RYQFIV ]SY [MWL XS GEPP ERH TVIWW ;LIR ]SY VI GSRRIGXIH XS XLI WIGSRH TEVX] TVIWW SRGI QSVI XS FIKMR ]SYV XLVII [E] GEPP -J SRI SJ XLI TISTPI ]SY
1EREKMRK 1IWWEKMRK =SY GER VIGIMZI ERH IVEWI QIWWEKIW 'LIGO [MXL ]SYV WIVZMGI TVSZMHIV JSV JIEXYVIW EZEMPEFPI MR ]SYV EVIE Ü Ü Ü 2I[ YRVIEH QIWWEKIW EVI WXSVIH MR ]SYV 8I\X -R&S\ ERH EVI FSPH 3RGI ]SY LEZI VIEH E QIWWEKI ]SY GER WEZI MX XS ]SYV *MPIH JSPHIV IVEWI MX SV PIEZI MX MR ]SYV 8I\X -R&S\ %PP SJ XLI JSPPS[MRK TVSGIHYVIW WXEVX EX XLI LSQI WGVIIR YRPIWW SXLIV[MWI MRHMGEXIH )VEWMRK QIWWEKIW → 1IWWEKIW → )VEWI 1WKW 7IPIGX 1IRY ,MKLPMKLX XLI STXMSR ]SY [ERX ERH TVIWW
/RS[MRK ;LIR =SY ,EZI 1IWWEKIW 8LIVI EVI WIZIVEP [E]W ]SYV 7TVMRX 4'7 4LSRI EPIVXW ]SY SJ RI[ QIWWEKIW Ü Ü Ü &] HMWTPE]MRK E QIWWEKI SR XLI WGVIIR &] TPE]MRK ER EWWMKRIH EPIVX X]TI SV ZMFVEXMRK &] HMWTPE]MRK EX XLI XST SJ ]SYV TLSRI W WGVIIR 1IWWEKI 8]TIW 8LIVI EVI JSYV X]TIW SJ QIWWEKMRK JIEXYVIW EZEMPEFPI JVSQ ]SYV 7TVMRX 4'7 4LSRI W QIRY =SY GER VIGIMZI ZSMGIQEMP E RYQIVMG TEKI 7TVMRX 4'7 ;IF 1IWWEKIW ERH 7TVMRX 4'7 ;IF %PIVXW EW PSRK EW ]SYV TLSRI LEW IRSYKL QIQSV] PSGEXMSRW XS WXSVI XLI
2I[ :SMGIQEMP 1IWWEKI %PIVXW ;LIR ]SY VIGIMZI E RI[ ZSMGIQEMP QIWWEKI ]SYV TLSRI EPIVXW ]SY F] 2I[ 1IWWEKIW ERH XLI RYQFIV SJ ZSMGIQEMPW :SMGIQEMP ERH TVIWW XS EGGIWW ]SYV 7TVMRX 4'7 :SMGIQEMP HMWTPE]MRK Ü Ü Ü 7IPIGX QIWWEKIW -KRSVI XS GPIEV XLI EPIVX RSXMJMGEXMSR -KRSVMRK XLI RSXMJMGEXMSR HSIW 7IPIGX RSX IVEWI XLI QIWWEKI MXWIPJ 6IGIRX 'EPPW PMWX 8LI QIWWEKI [MPP FI SR 8LI GEPP [MPP ETTIEV SR ]SYV 1IWWEKIW PMWX XLI 6IXVMIZMRK =SYV :SMGIQEMP 1IWWEKIW =SY GER VIZMI[ ]SYV QIWW
:MI[MRK XI\X QIWWEKIW → 1IWWEKIW → 8I\X -R&S\ 7IPIGX 1IRY 4VIWW 4VIWW 6IEH XLI QIWWEKI ERH WIPIGX ER STXMSR JVSQ XLI FSXXSQ SJ XLI WGVIIR YT SV HS[R XS WGVSPP XLVSYKL XLI PMWX SJ QIWWEKIW XS VIEH E QIWWEKI MRHMGEXIW ER l9VKIRXz QIWWEKI r )VEWI XLI GYVVIRX QIWWEKI r 7EZI XLI QIWWEKI XS ]SYV *MPIH JSPHIV r 7EZI 2I[ WEZIW XLI WIRHIV W MRJSVQEXMSR EW E RI[ GSRXEGX r (SRI VIXYVRW ]SY XS XLI 8I\X -R&S\ r 3/ VIXYVRW ]SY XS XLI QIWWEKI WGVIIR 4VIWW XS WII
2YQIVMG 4EKI 3TXMSRW %JXIV ]SY HMWTPE] E RYQIVMG TEKI WIPIGX ER STXMSR LMKLPMKLX MX ERH TVIWW Ü Ü Ü 7EZI XS WEZI XLI RYQIVMG TEKI XS XLI *MPIH JSPHIV )VEWI XS HIPIXI XLI RYQIVMG TEKI (SRI XS KS FEGO XS XLI 8I\X -R&S\ 0MWX 7IRHMRK 7TVMRX 4'7 ;MVIPIWW ;IF 1IWWEKIW 8LIVI EVI XLVII [E]W XS WIRH E 7TVMRX 4'7 ;MVIPIWW ;IF QIWWEKI XS E 7TVMRX 4'7 4LSRI )QEMP ]SYV TLSRI RYQFIV $ QIWWEKMRK WTVMRXTGW GSQ 8LVSYKL XLI 7TVMRX 4'7 ;IF WMXI[[[ WTVMRXTGW GSQ 7IPIGX XLI [MVIPIWW [IF QIWWEKMRK P
7TVMRX 4'7 ;MVIPIWW ;IF 9THEXI 3TXMSRW 8S LEZI 7TVMRX 4'7 ;MVIPIWW ;IF 9THEXIW EYXSQEXMGEPP] WIRX XS ]SYV TLSRI WII l7MKRMRK YT JSV 7TVMRX 4'7 ;MVIPIWW ;IF 9THEXIWz SR TEKI %JXIV ]SY HMWTPE] E 7TVMRX 4'7 ;MVIPIWW ;IF 9THEXI TVIWW XS HMWTPE] 7TVMRX 4'7 ;MVIPIWW ;IF 9THEXI STXMSRW 8S WIPIGX ER STXMSR LMKLPMKLX MX ERH TVIWW Ü Ü Ü 6IEH XS HMWTPE] XLI QIWWEKI EKEMR )\XVEGX 960 XS I\XVEGX E 960 ERH PMRO XS MX [MXL XLI 1MRM&VS[WIV )VEWI 1IWWEKI XS HIPIXI XLI QIWWEKI )VEWMRK %PP ;IF 1IWW
'LERKMRK =SYV 4LSRI W 7IXXMRKW 'LERKMRK =SYV 4LSRI W 7IXXMRKW /I]KYEVH 8LI /I]KYEVH PSGOW ]SYV OI]TEH XS TVSXIGX ]SYV TLSRI EKEMRWX EGGMHIRXEP OI]TVIWWIW [LIR XLI TLSRI MW XYVRIH SR ERH E GEPP MW RSX MR TVSKVIWW =SY GER WXMPP ERW[IV SV WMPIRGI ER MRGSQMRK GEPP 8YVRMRK OI]KYEVH SR → 7IXXMRKW → /I]KYEVH 7IPIGX 1IRY ,MKLPMKLX XLIR TVIWW XS WIPIGX ER STXMSR r +YEVH 2S[ PSGOW XLI OI]TEH RS[ r W EYXS KYEVH PSGOW XLI OI]TEH MJ RS OI] MW TVIWWIH JSV WIGSRHW r Q EYXS KY
2SXI /IITMRK FEGOPMKLXMRK SR HYVMRK E GEPP HVEMRW XLI FEXXIV] QSVI UYMGOP] ERH VIHYGIW XEPO ERH WXERHF] XMQIW 'LERKMRK XLI FERRIV → 7IXXMRKW → (MWTPE] → 1] &ERRIV 7IPIGX 1IRY 7IPIGX )HMX 4VIWW XS GPIEV XLI WGVIIR ERH IRXIV ]SYV RI[ XI\X 4VIWW X[MGI XS WEZI l7IXXMRK 7EZIHz ETTIEVW SR XLI WGVIIR %WWMKRMRK WGVIIR WEZIVW 8[S WGVIIR WEZIVW EVI TVSZMHIH [MXL ]SYV TLSRI ;LIR IREFPIH XLIWI KVETLMGW HMWTPE] WIGSRHW EJXIV XLI PEWX OI]TVIWW -RGSQMRK EPIVXW GPIEV WGVIIR
'LERKMRK ]SYV ZSMGIQEMP RYQFIV → 1IWWEKIW → 1WK 7IXXMRKW → :SMGIQEMP 2YQFIV 7IPIGX 1IRY 7IPIGX )HMX XS GLERKI XLI RYQFIV XLEX MW GYVVIRXP] EWWMKRIH XS WTIIH HMEP )RXIV XLI RI[ RYQFIV XLIR WIPIGX ER STXMSR PSGEXMSR l z 'LERKMRK =SYV 4LSRI W 7IXXMRKW =SY GER GLERKI XLI TLSRI RYQFIV EWWMKRIH XS WTIIH HMEPMRK PSGEXMSR l z r 7EZI WEZIW XLI RI[ RYQFIV E TLSRI RYQFIVz SR TEKI r ,EVH 4EYWI IRXIVW E LEVH TEYWI MR XLI RYQFIV 7II l)RXIVMRK TEYWIW MR E TLSRI RYQFIVz SR TEKI )VE
r7SJX FIITW WIXW XLI TLSRI XS FIIT WSJXP] IZIV] QMRYXIW 8S WXST XLMW VIQMRHIV TVIWW SV SV TVIWW XS WIPIGX -KRSVI r 0SYH FIIT SRGI WIXW XLI TLSRI XS FIIT SRGI PSYHP] [LIR E QIWWEKI MW VIGIMZIH r 0SYH FIITW WIXW XLI TLSRI XS FIIT PSYHP] IZIV] QMRYXIW 8S WXST XLMW VIQMRHIV TVIWW SV SV TVIWW XS WIPIGX -KRSVI 6IWIXXMRK XLI ZSMGIQEMP GSYRX → 7IXXMRKW → 1WK 7IXXMRKW → 6IWIX :1 'SYRX 7IPIGX 1IRY 7IPIGX =IW XS VIWIX XLI GSYRX SV 2S XS GERGIP [LIR ]SY VIGIMZI XLI
7IPIGX 3YX SJ TLSRI XS LEZI XLI EPIVXW GSQI SYX SJ XLI TLSRI SV 3YX SJ 7IXXMRK %YXS %RW[IV -J ]SYV TLSRI MW EXXEGLIH XS E ,ERHW JVII 'EV /MX WSPH WITEVEXIP] ]SY GER WIX MX XS ERW[IV ER MRGSQMRK GEPP EJXIV WIGSRHW r → 7IXXMRKW → %GGIWWSVMIW → %YXS %RW[IV → 7IPIGX 1IRY %JXIV WIGSRHW 0ERKYEKIW 0ERKYEKIW ERH WTIGMEP GLEVEGXIVW =SYV TLSRI QE] WYTTSVX )RKPMWL ERH 7TERMWL PERKYEKIW -J ]SY WIPIGX )RKPMWL IRXIV XLI PIXXIVW TVMRXIH SR XLI OI]W -J ]SY WIPIGX ERSXLIV PERKYEKI ]SY GER
'LERKMRK =SYV 4LSRI W 7IXXMRKW
7IXXMRK =SYV 4LSRI W 7IGYVMX] 7IXXMRK =SYV 4LSRI W 7IGYVMX] %GGIWWMRK XLI 7IGYVMX] QIRY → 7IXXMRKW → 7IGYVMX] 7IPIGX 1IRY )RXIV ]SYV HMKMX PSGO GSHI X]TMGEPP] SV XLI PEWX HMKMXW SJ ]SYV TLSRI RYQFIV =SY QYWX YWI ]SYV GSHI XS WIX ER] SJ XLI STXMSRW SR XLI 7IGYVMX] QIRY 0SGOMRK ERH YRPSGOMRK XLI TLSRI ;LIR ]SY LEZI PSGOIH ]SYV TLSRI ]SY GER SRP] GEPP E RYQFIV ]SYV WIVZMGI TVSZMHIV LEW WIX YT EW ER IQIVKIRG] RYQFIV E WIVZMGI TVSZMHIV RYQFIV SV E TVMSVMX] RYQFIV
9RPSGOMRK XLI OI]TEH → 4VIWW → MR XLMW SVHIV 9RVIWXVMGXMRK GEPPW Ü Ü → 7IXXMRKW → 7IGYVMX] → 0MQMX 'EPPW 3YX 7IPIGX 1IRY 7IPIGX 2S JSV YRPMQMXIH GEPPW SV WIPIGX =IW XS 'SRXEGXW XS EPPS[ GEPPW XS GSRXEGXW SRP] 'LERKMRK ]SYV PSGO GSHI 1IRY → 7IXXMRKW → 7IGYVMX].
7IPIGX 4LSRI 6IWIX % QIWWEKI ETTIEVW l6IWIX 7IXXMRKW#z 7IPIGX =IW XS VIWIX XLI TLSRI % QIWWEKI ETTIEVW l6IWIX %00 TLSRI 7IPIGX =IW % GSRJMVQEXMSR l4LSRI WIXXMRKW 6)7)8 z ETTIEVW WIXXMRKW#z r 7IPIGX 2S EX ER] XMQI XS GERGIP 2SXI =SYV HMKMX PSGO GSHI 6IGIRX 'EPPW PMWX 'SRXEGXW HMVIGXSV] -R&S\ TLSRI 7IXXMRK =SYV 4LSRI W 7IGYVMX] GSRXIRXW QIQSW ERH WIVZMGI TVSKVEQQMRK EVI RSX VIWIX [LIR ]SY VIWIX ]SYV 7IXXMRK =SYV 4LSRI W 7IGYVMX]
7IXXMRK =SYV 4LSRI W 7IGYVMX]
