An Improved Method for the Computation of Affine Lower Bound

"!$#%'&)( * &,+-.#/( 01#2!3+-4&657#2 98:+<;=+>?#@ A# 0CB .&
D #EF&)!HGI#28JK( L98J.M,+<>N#2/OF0P#@!RQ#2SUTK.#2 >V;WXS O
YZ[ \]^`_ abdc
e =fhg ikj3 ml
n"o$pqsrPt
pdumvw4xyPzdw|{~}br|vmp{€p‚ƒt^r„zdv†…t‡r1{~ˆŠ‰p‹ƒŒ?pd}oŽw|…t^r„{€ˆ
4wm)‘m’Ž’d“,‚tŽ{”
•Ž•$–
Œ—xx˜ ‘™š–$•h›–šœ$œ
’
Konstanzer Online-Publikations-System (KOPS)
URL: http://www.ub.uni-konstanz.de/kops/volltexte/2007/2215/
URN: http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-22156
ž  Ÿ„¡ £¢s¤„¥U¦€¥U§¨£¢© ¡Nª ¢«¥¬ ¡?ª §¨­)®«¯|°²± ª£¡Nª §¨³ ª §¨­
ž  Ÿ„¡ £¢s¤„¥U¦€¥U§¨£¢´µ¯·¶¹¸º¦¬ ¡Nª §»­k®|¯|°´µ¯·¶¹¸º¦¬ ¡Nª §¨¸º¯„³~¼½§¾³€³€¥¯„³€£¢ ¡ ¶ ª
¿ ¯«§»ÀV¥¦£³~§ ªÂ¡?Á ªšÃ ¸º¯|³ ª¡ ¯«Ä
Ÿ„¡ £¢=ÅÆUÇVǫȄÉNÇºÊ—Ë—É Ã ¸º¯„³ ª£¡ ¯«ÄVȷ̘¥U¦€¬ ¡ ¯—Í
Î ¬ ¡ §»ÏÑзҫ¦¥Ò«¦§¨¯ ª ³£Ó§¨¯·¶¹¸V¦€¬ ¡Nª §»­PÔ ®«¯«§Ö՗­V¸º¯|³ ª¡ ¯«ÄºÔ °·¥
×/×/× Ð„¢ ª€ª ÒÐÙØºØN¼½¼½¼Ô §¨¯·¶¹¸V¦€¬ ¡Nª §»­PÔ ®«¯«§Ö՗­V¸º¯|³ ª¡ ¯«ÄºÔ °·¥Xغ±·£¢«¦§Ö¶ ª ¥¯1Ø
"!#$%'&(*)+,-,.0/1
3246578
9 ,$;:%$<
=)+,<>??@A,BDCE
)F&GBH>
IKJ L+MONQPARSLUTWVXYZ[\P]^L+N`_bac*d^egfih+jlk
m n opqr%sgt
u8pv+rwo
x fWP]fyP^MzS|{}V~P€ON}‚TiV_ƒN`L…„†V~KP]ˆ‡‰KPl{}h+fiV~Pˆ‡‰VOL…S.M~fiONQPЇ‰KPl{}h+fiV~P‹fyŒEVO‡wlSLUSOe…V~KPŽh
fWe…†VOL+h+SOP{}N
fWPzM~TiVO„lSOTVOlh+fWegfiQSh+fiV~Pz_‘j^NQPASg„LUSOPl{Uj.SOP]’„†V~KP]zSL+V~SO{“jAfWŒwKŒHNQ]cw”‡(ŒH†NQ{`fWSOTfWPŽhHN`L+NQŒHhSL+N
{}V~PŽO¢ N}’NQP€ONQTiVO†NQŒ`Z*f•c–NOciZKPfi‡‰VOLUegTW—g„†NQŒHhKP]^N`LUNQŒHh+fWegSh+fWPM{}V~PŽON}’‡‰KlP{}h+fiV~PŒ`Z^{}‡Dcw˜–™šZ*›œZQž Ÿ¡c
NQ{`SOKŒHN£VO‡¤h+j^NQfiLŒ+fWe…lTyfW{`fih¥—.SOP]¦NQSOŒHN£VO‡,{}V~e…lK^h+Sh+fWV~PZ8{}V~PlŒHh+SOP€h
SOP]‹S§¨P^N¨TiV _GN`L„†V~KP]
‡©KP{}h+fiV~PŒ8SL+N¤NQŒH†NQ{`fWSOTWTW—%KŒHN`‡©KT•c8ªƒV~PlŒHh+SOP€h6„†V~KPl]%‡©KP{}h+fiV~PŒ8SL+N¤h+j^VOL+V~KM~jTi—EKŒ+NQ]E_‘jNQPfyP€hHN`L+SOT
{}V~e…lKh+Sh+fiV~P¦hHNQ{UjlPfW«œK^NQŒ%SL+NgS*TWfiNQ].hHV’M~TiVO„lSOT(VOh+fWegfiQSh+fWV~PZ{}‡¬cz˜®­šZ'¯šZ(O}Ÿ¡cg°wV_ƒN`ON`LQZ_‘j^NQP
KŒ+fyP^Mz{}V~PŒHh+SOPŽh„V~KlP]±‡©KP{}h+fiV~PlŒ`Z8SOTyT²fWP^‡‰VOLUegSh+fWV~P±S„†V~K^hEh+j^N4Œ+jS†N³VO‡,h+j^N³M~fWONQPˆ‡©KP{}h+fiV~P‹fWŒ
TiV~ŒHh`cb[{}V~e…L+V~egfyŒHNz„†N`h¥_ƒN`NQP#{}V~P€ON}#NQP€ONQTiVO†NQŒ`Z‘_‘jfW{“j´L+NQ«œKfiL+N’fyP´h+j^N.MONQP^N`LUSOT\{`SOŒHN|e<K{“j
µ{}PŠV~e…˜–¶·lŸ8K_Gh+SN…h+fi{}V~V~PPSO{}TNQPŽN}XhHLUVOSLUhHh`N
ZSOV~PP|]4Œ+K{}V~{“jzPŒH„†h+SOV~PŽKhPTi]zV_ƒ‡‰KlN`PL,{}„†h+V~fiV~KPPŒ‘]³‡¸VO‡‰KLPle<{}h+KlfiTiV~h+PfiŒƒSSLUL+fWSNhHSNE§¨†P^V~NTi—šTiP^VV~_ƒegN`L,fySO„†TWŒ`V~cK¹P]¨j^NQ‡‰KŒ+NEPl{}„†h+V~fiV~KPPŒ`] c
‡©KP{}h+¢ fiV~PŒ
SL+NA{}V~PŒHhHLUK{}hHNQ]´‡¸L+V~x eh+j^N’{}VŽN`§³{`fiNQP€h+¢ŒgVO‡wh+j^NzN}œlSOPlŒ+fiV~PŠVO‡h+j^NºM~fiONQP †V~Ti—šP^V~egfWSOT
fWPŽhHV N`LUPŒ+hHNQfWPz†V~Ti—šµP^V~egfySOTWŒ`c VOLL+VO†N`L+h+fiNQŒVO‡ N`LUPŒHhHNQfWPz†V~Ti—œPV~egfWSOTWŒ,h+jNEL+NQSO]^N`LfWŒwL+N`‡‰N`L+L+NQ]
hHV?˜–žšZ,»^Z%`¼^Z%Q™Ÿ¡c P7h+j^N±KPlfi·SL“fWShHN.{`SOŒ+N±h+j^N¦{}V~e…lK^h+Sh+fWV~PSOT_ƒVOL+½¾‡‰VOL’{}V~PŒHhHL“K{}h+fWP^M Œ+K{“j
„†V~KP].‡©KP{}h+fiV~PŒfyµ Œ%P^N`M~TWfiM~fW„lTiNOZ†„lK^h%fWP|h+jN¨e<KlTih+fiSLUfWShHN…{`SOŒHN³SzTWfWP^NQSLL+VOMOL“SOegegfWP^MºlL+VO„lTiNQe
jSOŒ¤hHV…„†NŒHV~TiONQ]c P£h+j^N„LUSOPl{Uj4SOP]4„†V~KP]³‡¸L“SOe…N`_GVOLU½³fih,egS—£jSlNQP³h+jSh,V~P^N%jlSOŒ¤hHVgŒHV~TiON
Œ+K^„lL+VO„lTiNQe¨ŒV~P‹PœKe…N`LUV~KŒ<ŒUK^„„†VQšNQŒEVO‡,h+jN£ŒHh+SLUh+fWP^M.L+N`M~fiV~PZ6ŒHV.h+jSh‡¸VOL
jfiM~j^N`L
]fWegNQPŒ+fiV~PŒ
ŒHV~Tišµ fWP^M
h+j^N<TWfWP^NQSL¤L+VOMOL“SOegegfWP^M…lL+VO„lTiNQegŒƒ„†NQ{}V~e…NQŒwSg{}V~e…lK^h+Sh+fWV~PSOT„lK^L“]^NQPc
P¦h+jfWŒ%lS†N`L_GNglL+NQŒHNQPŽhES’e…N`h+j^Vš]¦‡‰VOL<{}V~PŒ+hHLUK{}h+fWP^M’ŒUK{Uj±S§³P^N¨TiV _GN`L<„V~KlP].‡‰KPl{}h+fiV~PŒ
‡‰VOLƒ†V~Ti—šP^V~egfySOTWŒ6_‘jfy{UjgLUNQ«ŽKfWL+NQŒ(h+j^N{}V~e…lKh+Sh+fiV~P£VO‡'Œ+TiVO†NQŒ`ZŽh+j^N\Œ+V~TWK^h+fiV~P³VO‡'SŒH—œŒ+hHNQe¿VO‡TWfWP^NQSL
NQ«œKSh+fiV~PŒ`ZƒSOP]´S¦ŒHNQ«œK^NQP{}NzVO‡w„lSO{U½ Œ+K^„lŒHh+fWh+K^h+fiV~PŒ`cйjfWŒ…egN`h+j^Vœ] fyP‚MONQP^N`LUSOT,L+NQ«œKfiLUNQŒ
‡¸N`_ƒN`L
SLUfih+jle…N`h+fW{VO†N`LUSh+fiV~PŒ,SOPl]’jSOŒTiV _GN`L\{}V~e…lTiN}^fih¬—³h+jµ SOP’V~K^LL+N`šfiV~KŒ,SlL+V~SO{UjzfWPˆ˜–¶ Ÿ¡c
¹jN³VOL+M~SOPlfWŒ+Sh+fiV~P‹VO‡‘h+j^N£l¢ S†N`L
fWŒ<SOŒ‡‰V~TWTiV _‘Œ`À Pˆh+jN£P^N}šh…ŒHNQ{}h+fiV~PŠ_ƒN£LUNQ{`SOTWTGŒ+V~e…N4„lSOŒ+fW{
]^¢ N`ÁlPlfih+fiV~PŒGSOP]£L+VO†N`L+h+fiNQŒ²VO‡ N`LUPŒHhHNQfyP¨†V~Ti—šP^V~egfWSOTyŒ`c[w§¨P^NTiV_ƒN`L,„†V~KP]¨‡‰KPl{}h+fiV~PŒG„lSOŒHNQ]£V~P
N`LUPŒHhHNQfyPzN}šlSOPŒ+fWV~P’hHVOMON`h+j^N`L_‘fWh+jASOPAN`L+L+VOL\„†V~KP]zSLUN<LUNQŒHNQP€hHNQ]|fWP|dœNQ{}h+fiV~P|™œc\¹‘j^NEL+NQŒUKTih+Œ
SL+NEfyTWTWKŒHhHL“ShHNQ]³„œ—4PŽKegN`LUfW{`SOT†N}^SOe…lTiNQŒfyPzdœNQ{}h+fiV~Pº»^c x fWPlSOTWTi—OZ^ŒHV~e…NE{}V~Pl{`TWKŒ+fiV~PlŒ,SL+N%M~fiONQPc
Þ6Û}ɓÉF×·× ÂHÌ©ÃÌ©Ï¥Ï¥ÄÆ“Æ“× Å× ßF߯UÄ ê ǡƓÑȮɓ׷Ê.ê
ΏËÍÌwˮϡΏÐgˮϡϡкзÑwϡРÒÑ<ÆUÓ¬Ò·ÐQƓÔOÓ¥ÑDÐÇ¡ÔOÑÕѬˮӥǡÐ4ÑÕˮӬëкÆ+Ö¸Ï¡× Ð·ØÙÑÕÉUÚÇ¡ÚÆ+Ï¡ÆUˮϡÛ
Ë®ÛOÝ·Ü×·Òê³Æ“Ó¥ì`зϥРÆUÏ¡É`ˮӬ̩Рϡˮ̕ÛOÓ¬ÜÐQÝ·íÈ®ÑE×·Ë®î}Þ6ÑDÉFÇ¡× Ì•Ë–Ì©Ï+Ï¥ÆUï Æ“σ׷Þ6ߓÜÉF× àšÌ©É“ϥ̩Ɠϕ׷ØiƓߓӥðЦÑÕÚáHâ“Æ“â}Ë®ÈiãUñwäFåò}Ü(ÆUÇ¡æ8È®ÉUç‰ÊŽèUé“óä}ØÙâFÐ ã ç
ô¬õ
õ
æ8ç‰è“éUä}ÄâFà^ãƒÄ·Þ6ìQÚ,ÉF׷ˮϡ̩ÐÏ¥ÆUˮ׷̆ßFΏð ÑÕ˖ϡÚБÆUÏ¡ËÍÐ ÈiñlÑ8ָ̕Ú,׷̩˖ϡϡ˖ÐOÏ¡óÝ Ï†ØöÐ Ø¡çyÝ ï Û}Ç ÉF× Ì©×·Ï¥òFÆ“Ñ¬× ÎßFÄÆ“ê ×·Ñ êÏ¡Ñ8ҷɓǡ̕ӥÐQÝ·×·òÜ ÒÆ“ӥзРÉ`ӬР̕ӬÐQÝ·È®ÑÞ6ÉF׷̩ϥÆU×·ßFÜ àšÉ“̩ϕØiƓӥÐ<áÕâFâFãUä}åQÜ

(qop²vUo£r
<o
r
vo
s;o
r,pƒpv+r\o
N‘]^N`Á*P^NƒeKTih+fyfWP]fW{}NQŒ !#"%$'&zSOŒ6ONQ{}hHVOLUŒ`ZŽ_‘j^N`L+N¤h+j^N)(º{}V~e…†V~P^NQPŽh+Œ6SL+NP^V~PPN`M~Sh+fiON
fWPŽhHN`MON`LUŒ`cº¹j^N¨ONQ{}hHVOLUŒ
¼zSOP]¾¨]^NQP^VOhHN³h+j^N³eKTih+fyfWP]fW{}NQŒ\_‘fWh+jˆSOTWT({}V~egV~PNQP€h+Œ<NQ«ŽKlSOT(hHVA¼zVOL
ZL+NQŒ+NQ{}h+fWONQTi—OZ_‘jfW{“j¦Œ+j^V~KTy]AP^VOh%{`SOKlŒHN…SOeE„lfWM~Kfih¥—OcgªƒV~e…*SLUfWŒHV~PŒSL+N…KŒ+NQ]|NQP€hHL+—œ_‘fWŒ+NOc<[\TWŒHV
h+j^N¦SLUfih+jle…N`h+fW{.VO†N`LUShHVOLUŒ4V~P eKTih+fWfWPl]fW{}NQŒ¨SLUN|]N`ÁlP^NQ]7{}V~e…†x V~P^NQPŽh¥_‘fWŒ+N|" ŒUK{Uj7h+jSh*,+.-zÀ/
+0- 1 " +0- " $ & Z‡‰VOL2+3345687)SOP]:9*‰_wfih+j;-=<´¼>$“c VOL@?BA;C fWh+Œ,e<KTWh+fi†V_ƒN`LUŒ,SL+N
"
?EDÀ/ F ?EDKG J ՝!$
GIH
L KTih+fi†V_ƒN`LUŒVO‡weKTih+fyfWP]fW{}NQŒESL+N’P^VOh
L+NQ«œKfiL+NQ]Šj^N`L+NNM,fWPŒ+hHNQSO]‹_ƒNºŒ+jSOTWTƒ_L“fihHNOQPI " ‡‰VOLgS
ŒHNQ«œK^NQP{}N%VO‡(O47%eKTih+fyfWP]fW{}NQŒQc x VOLwh+j^NEŒ+Ke _ƒNEKŒ+Nh+j^NEP^VOh+Sh+fiV~P
S R À/ S RUT S RWV •ž8$
HD P D T H P D V H P
[0e<KTWh+fi·SL“fWShHN†V~Ti—œPV~egfWSOTYXzVO‡]^N`MOL+N`NZ-[\-# !-]"%$'&‹{`SOP’„†NL+N`LUNQŒHNQP€hHNQ]ASOŒ
R
X?^$_ S D ?aD _‘fih+j D AbCb+¼Ocdecf-g‘SOP] R_ h ¼i
•™8$
HD Pa`
`
`
¹j^N6¥h+j ¢ N`LUPŒHhHNQfWP’V~TW—œP^V~e¨fWSOTVO‡8]^N`MOLUN`NZ-fWŒ
j D ?$ƒÀ/lk #- m ?ED՝5n?^$ RKo Dg
‰»Y$
_‘j^N`LUNh+j^N‘MONQPN`LUSOTWfi`NQ]¨„lfWP^V~egfySOT^{}VŽN`§¨{`fWNQP€h¤fWŒ(]^N`Á*P^NQ]g„œ—np D]R q À/ Gsr H" p DKR JJ!q ZœSOPl]t?ºfWŒ({}V~PŽh+SOfWP^NQ]£fWP
h+j^N‘KlPfih6„†VQtuv ˜ ¼iQFŸ " c µ h²fWŒ6_ƒNQTWTUw¡½šP^V _‘P…h+jShGh+j^N ¢ N`LUPŒHhHNQfyPg†V~Ti—šP^V~egfWSOTWŒ8‡‰VOLUe S%„lSOŒ+fWŒ(fyP…h+j^N
ŒHlSO{}N¢ VO‡6eKTih+fiSLUfWShHN\†V~Ti—šP^V~egfWSOTWŒQZœSOP]4NQSO{“j’†V~Ti—šP^V~egfWSOTfWP4h+j^N‡‰VOLUex•™8$,{`SOPº„†N\LUN`L+NQŒHNQPŽhHNQ]
fWPºfih+Œ N`L“PŒHhHNQfWP4‡‰VOLUe"V ON`L
u
R j
S
X=?$y D D ?^${
•¶8$
HD Pz
_‘j^N`LUNh+j^N}|~€ƒ‚%„ƒ…'~ †‡‚‰ˆŠ1~\‹Œˆ †#~‚a…„ D SL+N%M~fiONQP’„Ž—
z S D p D
Ž8$
Dz  H P p  R qq `  ‡¸VOL ¼tcdecf-g
[b‡‰KPl]SOe…NQPŽh+SOTL+VO†N`L+h¬—¨‡‰VOL‘V~K^LSlL+V~SO{UjAfWŒ,h+j^Nˆ{ŠI‚’‘I~“O”>•i–‡–%—a€˜Šƒ—%~€…\™
š ?
š g9sk X?$˜m ÀN?BA;uœ›0ŒžƒŸs(^ k m À޼¡cd¢cf-ƒ›O
¡­N$
Dz
_‘j^N`LUN…h+j^N¨{}V~PŽON}ˆjŽKTyT6fWŒ]^NQP^VOhHNQ]ˆ„Ž—£žŸ1(^ *c³¹jN…V~fyP€h+Œ p D]¥¤ ¦ R q SL+N¨{`SOTyTiNQ]fˆŠI‚a…\€˜ŠI–œ—iŠI†‚E…„VO‡X'c
¹j^NNQPl{`TiV~Œ+K^L+N¡­N$¤—œfiNQTy]Œ¤h+j^N%fWP^NQ«œKSOTWfWh+fiNQŒ
e¨fWP§ D À~¼cdecf-Q¨}c£X=?$©c´e¨S·a§ D À~¼tcdecŒ-'¨
•¯8$
z
z
ž
‡‰VOL³SOTWT)? Aulc x VOL£NQSOŒHNAVO‡\lL+NQŒHNQPŽ¢h+Sh+fiV~P´_ƒNAŒ+jlSOTWT,ŒHV~e…N`h+fWegNQŒ¨Œ+fWeglTi—‹KlŒHN D hHV‹]^NQP^VOhHNAh+j^N
{}V~PŽhHL+V~T(†V~fWPŽh%SOŒ+ŒHVš{`fWShHNQ]±_wfih+j¦h+j^N N`LUPlŒHhHNQfWP±{}VœN`§¨{`fiNQPŽh Z'_‘j^N`LUN…h+j^N¨{}V~PŽhHN}œh
Œ+j^V~KTy]¦egS½ON
h+jfWŒ<KPSOe<„lfiM~K^V~KlŒ`c š†V~P^NQP€h+fySh+fiV~P±V~P‚{}" V~PŽhHL+V~TƒV~fyP€h+Œ`Z ¢ z D N`LUPŒHhHNQfyPˆ{}VœN`§¨{`fiNQPŽz h+Œ`Z(VOL¢ONQ{}hHVOLUŒ…fWŒ
SOTWŒHVP^VOh²LUNQ«ŽKfWL+NQ]gj^N`L+NNMšh+j^N`LUN`‡¸VOL+N P " fWŒ²S<ŒHNQ«ŽKNQP{}N‘VO‡[(Z4Š,{}V~PŽhHL+V~T†V~fWP€h+Œ²VOL N`LUPlŒHhHNQfWP
{}VœN`§¨{`fiNQPŽh+Œ}‰_‘fih+j D $“ZlSOP] z ! z fWŒSgŒ+NQ«ŽK^NQPl{}NVO‡(¦ONQ{}hHVOL“Œ`c
z z
o Ur (q £r\t…o
s t…o
u8pv+r\o
µ P
h+jfWŒ6ŒHNQ{}h+fiV~Pg_GNŒ+jV_´j^V _ S§¨P^NTiV _GN`L²„V~KlP]‡‰KPl{}h+fiV~PŒ8‡¸VOLGe<KTWh+fi·SL“fWShHNG†V~Ti—šP^V~egfySOTWŒ'„*SOŒHNQ]
V~P ¢ N`LUPŒHhHNQfyP‚N}œlSOPlŒ+fiV~P {`SOP „†Nº{}V~PŒHhHLUKl{}hHNQ]‚„Ž—ŠV~PTi—ŠŒHV~TišfWP^M|S¦ŒH—œŒ+hHNQe VO‡wTWfyP^NQSL
NQ«ŽKSh+fWV~PŒ
hHVOMON`h+j^N`L…_‘fWh+jˆS.ŒHNQ«ŽKNQP{}N4VO‡,„lSO{+½ŠŒ+K^„lŒHh+fWh+K^h+fiV~PŒ`c’¹‘j^N³Œ+fye…lTiNQŒHhEh¥—œN£VO‡S§¨P^N4TiV _GN`L
„†V~KP]
‡©KP{}h+fiV~P‚fWŒ…S¦{}V~PŒ+h+SOP€hgV~PNO¢c‚¹‘j^NºTiN`‡¸h˜w¥jlSOP]‚Œ+fW]^N4VO‡¡•¯8$fWe…lTWfWNQŒEh+jSh¨h+j^Nº{}V~PŒHh+SOPŽhg‡‰KlP{}h+fiV~P
L+V œfy]^NQ]4„Ž—£h+j^NEe¨fWPfWeKe N`L“PŒHhHNQfWP’{}VœN`§¨{`fiNQPŽh
ž P ?$_ D 7egfyP§ D À€¼tcfecf-Q¨
•›8$
fWŒSOP‹S§³P^N£TWV_ƒN`L„†V~KPl]±‡©KP{}h+fiV~Pˆ‡¸VOL
z h+j^N³V~TW—œP^z V~e¨fWSOTX M~fiONQPЄޗŒ•™8$EV ON`L…h+j^N£KlPfih%„†VQ0uc
¹j^N…‡‰V~TWTiV _‘fWP^M4{}V~PŒHhHL“K{}h+fiV~P±SOfWe¨¢ ŒhHV’ÁlP]|jŽ—Ž†N`L+*TWSOP^NQŒlSOŒ+ŒUfWP^M4h+j^L+V~K^M~j|h+jN¨{}V~P€hHLUV~T6†V~fWP€h P
©SOŒ+ŒHVš{`fWShHNQ]4_‘fWh+j¨h+j^NegfyPfWeKe N`LUPŒHhHNQfyP£{}VœN`§¨{`fiNQPŽh D $²_‘jfW{“j³SlL+VQ^fWµ egShHN\‡‰L+V~e „NQTWV_7h+j^z N
TiV _GN`LlSL+h\VO‡²h+jN{}V~PŽON}|jœKTWT'VO‡(h+j^N
{}V~P€hHLUV~TV~fyP€h+Œ\fWP{}L+NQSOŒUfWP^M~Ti—4_ƒNQTWT•c P.SO]]fih+fWV~P’hHV P Z†_ƒN
_‘fWTyTG]^NQŒUfiM~PShHN;( SO]]fih+fWV~PSOT¤{}V~P€hHL+V~TV~fyP€h+Œ ! " z c dœh+SLUh+fWP^M|_‘fih+j ž P Z²_ƒNº_‘fWTWT¤ {}V~Pz Œ+hHLUK{}h
‡‰L+V~e"h+j^NQŒHN<{}V~P€hHL+V~T'†V~fWP€h+Œ,S¨ŒHNQ«ŽKNQP{}N%VO‡6S§¨P^z NETWV_ƒN`Lz „†V~KP]4‡©KP{}h+fiV~PŒ)ž1 žƒ"c NENQPl]’K^
_‘fih+jOžƒ"lZ^SEjŽ—Ž†N`L+*TWSOP^N_‘" jlfWµ {Uj¨lSOŒ+ŒHNQŒGh+j^L+V~K^M~j£STiV_ƒN`LG‡©SO{}N`h¤VO‡h+j^N\{}V~P€ON}4jŽKTyTŒHlSOPPNQ]g„œ—gh+j^N
{}V~PŽhHL+V~T†V~fWPŽh+Œ P1 1 c Pgh+j^N" {}V~K^LUŒHN,VO‡†h+jfyŒ6{}V~PŒHhHLUK{}h+fWV~PZ~_ƒN,_‘fWTWTœMONQP^N`LUShHN\SŒHN`h(VO‡†TWfWP^NQSL“Ti —
fWP]N`NQPl ]^NQP€h¤ONQz {}hHVOLUŒZ§ z ! ¨<SOP]º_ƒN%_‘fWTyT{}V~eglK^ hHN<ŒUTiVO†NQŒ¤‡¸L+V~e P hHV fWP’]lfiL+NQ{}h+fiV~P c
[\TWŒHV^Z _‘fWTyT*]^NQPVOhHN%h+j^N%ONQ{}hHVOL{}V~PP^NQ{}h+fWPM PSOPl] c
z z
z z
!#"%$'&)(+*-,
.0/2143658795;:<1>=?5>/2@BAC
D

FG
`N h E
IKJ
¼c c
G
G
G
J
J
J
¼
Dz hHV z P fWP’]fiLUNQ{}h+fiV~P À
‡‰VOL‘SOTWTi'_wfih+j h P H
L
ªƒV~e…*K^hHN%Œ+TiVO†NQŒ D ‰‡ L+V~e"h+j^N<{}V~P€hHL+V~T'†V~fWP€h
5 P
D z DR TT D 5 z DR T T
N`h6 „†NgSºeKTih+fWfyP]^N}ºT _‘fih+j¦Œ+e¨SOTWTiNQŒHhS„lŒHV~TWKhHN…·SOTWKNVO‡¤SOŒ+ŒHVš{`fWShHNQ]±ŒUTiVO†N
{}V~PŽhHL+V~TƒV~fyP€h D R D T & Zh+j^N³Œ+TWVON yt D T Z6SOP]ˆh+j^N³ONQ{}hHVOL TiV _GN`Lw„V~KlP]£‡‰Kz Pl{}h+fiV~P z
ž11?$y P 4 _ kY?*5 -=P m z
™
NM
M
D
OM
R
TS
VU
WM
X
E[
ZU
T
c \NQŒ+fiM~PlShHNgh+j^N
D D T o R D c \N`ÁlP^N£h+j^N
QP
YP
ž 1(
5
795;:<14=5>/2@BA
C
FG
G
G
cc

I J
J
J
 N`h    o
¼c
c
¼
Œ+Kl{Uj’h+jlSh  67¼iI 1 5 I
՝`¼>$
VOLUegSOTWfi`Nh+jlfWŒ¤ONQ{}hHVOLwh+jœKŒ+TW—*À
  ՝O!$
ªƒV~e…*K^hHN%Œ+TiVO†NQŒ D ‡¸LUV~e h+j^NE{}V~PŽhHL+V~T†V~fWPŽh D hHV PfWPº]lfiL+NQ{}h+fiV~P  À
 D 5‰o ž  o  DR $ ‡‰VOL‘SOTWT’z (N}^{}z N`h_‘j^N`LUN œ5n P  7¼i
՝Qž8$
D z D RD
N`hZ  „†NgSºe<KlTih+fWfWP]N}’_‘fih+j¦Œ+egSOTyTiNQŒHhS„lŒHV~TWKhHN…·SOTWKNVO‡,SOŒ+Œ+Vœ{`fWShHNQ]ˆŒ+TiVO†N D c \NQŒ+fiM~PlShHNgh+j^N
{}V~PŽhHL+V~TƒV~fyP€h  D R D & Z6h+j^N4Œ+TiVO†N  D Z(SOPl]‹h+jN³ONQ{}hHVOL  D o R D c \N`ÁlP^N£h+j^N
TiV _GN`Lw„V~KlP]£‡‰Kz Pl{}h+fiV~P z
ž  ?$_ ž  o !?$[4   k ? 5 '- P m ՝Q™8$
C ÀƒdœV~TišfWP^M ՝`¼>$¤‡‰VOLh+j^N<{}VŽN`§¨{`fWNQP€h+Œ  1  o LUNQ«ŽKfWL+NQŒ¤h+j^NEŒHV~TyK^h+fiV~P4VO‡6SgŒH—šŒHhHNQe VO‡
5 ³TWfWP^NQSL<NQ«ŽKlSh+fiV~PŒEfyP 5 ³KP^½šP^V_wPŒ`c4¹jfWŒ%Œ+—œŒHhHNQe jSOŒSzKPlfW«ŽKNgŒHV~TWK^h+fiV~Pˆ]K^NghHV.h+j^N
TWfWPNQSLfWP]^N`†NQP]^NQPl{}N\SOe…V~PM~ŒHhh+j^N%ONQ{}hHVOL“Œ 1 " Z^M~fiONQPzfyP4h+j^N‡¸V~TyTiV_‘fyP^M
h+j^N`VOL+NQeºc
 ! †‘I~ ‚ ™*$… #%1†‚ ! …”i'~ &_€{„ƒ… ˆ{)Š (2—iŠI‚~ ‚E…„t+Š * -,
~ …  ~…”%~‘I~ˆ…#ŠI€{„}†‚ C "
* ŠI€I 1 /."0 ”i~ ‚n…”i~}‘I~ˆ…#ŠI€{„  !   #N€~}– †‡‚~1#I€ƒ–/™ †‚32>~Q—’~‚32>~ ‚E… , * ŠI€
I 1( .
4
/5 ‰„Ž—ºfWPl]K{}h+fiV~Pa$“À
\N`ÁlP^N³ONQ{}hHVOLUŒ  SOPSOTiVOMO V~o K ŒU Ti —|„Ž—¦h+S ½šo fWP^ MA o h+ j^N³ÁlLUŒHh {}V~e…†V~P^NQPŽh+Œ<VO‡ ¢ cz¹j^NgLUNQŒ+KTihEjV~TW]Œ
‡‰VOL ¿c\[wŒ+ŒUKe…NEh+jlSh  !   o SL+N
TWfWP^NQSL“Ti—£fyP]^N`†NQP]^NQPŽh`c ¢ —’SO]l]fWP^M¨SOPAN}šhHLUS
{}V~e…†V~P^NQPŽh`Z6_GNºjSON4h+jSh  SL+N4TWfWP^NQSL“Ti—¦fWP]^N`†NQP]^ NQ PŽh`c  — ՝`¼> $“ZƒP^VOh+fWP^MAh+jSh
V~PTi—.h+j^NgÁlLUŒHh {}V~e…†V~1P^  NQPŽh+Œ%VO‡ SL+N¨P^V~P`N`L+V^Z_ƒN¨jSON¨h+jSh    o ¼šZ‡‰VOL
* I 1 5 Z†f•c–NOc
fWŒw  fWP’h+j^ N<VOL+ h+j^VOMOV~PSOT{}V~ e…  *TiNQe…NQPŽh‘VO‡ ! 1  c\dšfyegfWTWSLUTW—g„Ž — 



՝Qž8$“Z_ƒN\jlSQONh+jSh
7h ¼šZf•c–NOc fWŒ¤P^VOhƒVOL+h+j^VOMOV~PSOT†hHV c(¹j^N`L+N`‡‰VOL+N
fWŒ,P^VOhwfWP4h+j^NEŒ+K„lŒHlSO{}NŒHlSOPlP^NQ]4„Ž— 1   o c 6
x VOLh+j^NZ(‹fihHN`LUSh+fWV~PŒVO‡6h+j^N<S„V ONSOTWMOVOLUfih+j eºZ*h+j^NEŒHV~TyK^h+fiV~P’VO‡(ŒUK{UjAS¨ŒHNQ«œK^NQP{}N<VO‡(ŒH—œŒ+hHNQegŒ
VO‡wTyfWP^NQSLNQ«ŽKSh+fWV~PŒ_GV~KTy]ŠPVOLUegSOTWTi—¦LUNQ«ŽKfWL+N 7 (824:9t(<;$<SLUfih+je…N`h+fy{¨VO†N`LUSh+fiV~PlŒ`c±°‘ V o _G N`ON`L
_ƒN¨{`SOP¦h+S½ON³SO]·SOPŽh+SMON¨VO‡¤h+j^N…‡©SO{}h%h+jSh`ZfWP|h+j^N h+jˆfihHN`LUSh+fWV~PZh+j^N…ONQ{}hHVOLUŒ 1 SL+N
»
G
G
G
G
J
J
J
J
G
D
J
G
J
G
J
G
J
G
J
H
L
[
NM
[
M
[
D
QM
S
R
U
M
X
P
P
[
U
:
=?1
#:<@
14:
P
0
14@
@
0
[
E
[
[
W
[
E
K P{“jSOP^MONQ]‡‰L+V~e h+jN(L+N`šfiV~KŒfihHN`L“Sh+fiV~Pc¹‘j^N(ŒHV~TWK^h+fWV~PVO‡œh+jNQŒHN²ŒH—šŒHhHNQegŒ{`SOPEh+j^NQP%„†N‡‰VOLUe<KlTWShHNQ]
SOŒARSOKlŒ+Œ+fWSOP7NQTWfyegfWPSh+fiV~P7S*TWfiNQ]¾L+V__wfWŒHN¦hHV h+j^N±Œ+fyP^M~TiNf(f5 !$7(f5 !$4e¨ShHLUfف¾_wj^V~ŒHN
L+V _‘Œ‘{}V~PŒUfWŒHh,VO‡8h+j^N%ONQ{}hHVOLUŒ " o " o " o SOP]ºLUfiM~jŽh˜w¥jSOP]zŒ+fW]^N¡5Z " ! "" o $ & c µ P
SO]]fWh+fiV~PZSgŒHNQ«œK^NQP{}N<VO‡„lSO{+½Yw¥Œ+K^„lŒ+h+fih+K^h+fiV~P’Œ+hHN`lŒ‘jSOŒ‘hHV¨„†N†N`L+‡‰VOLUe…NQ]c²¹‘j^NQPzSOTihHVOMON`h+jN`LwV~PTW—
(<;_4 9t( $¤SL“fih+je…N`h+fW{VO†N`LUSh+fWV~PŒ,SL+N%L+NQ«œKfiLUNQ]c
N`h
"
V
F
\- D 47!$
DH
"
¹j^N`LUNSL+Nh+j^NQP ¢ N`LUPlŒHhHNQfWP.{}VŽN`§¨{`" fWNQP€h+Œ`"ZŒ+V£h+jlShwh+j^N…{}V~e…*K^h+Sh+fiV~P.VO‡(h+j^N
Œ+TiVO†NQŒ D ՝Qž8$wfWP
SOTWT6fihHN`L“Sh+fiV~PŒL+NQ«œKfiLUNQŒ%ShEe…V~ŒHhZ( 4 9t($\SLUfih+jle…N`h+fW{
VO†N`LUSh+fiV~PŒQc¨¹jfWŒPN`_ SL+V~SO{“j
h+j^N`L+N`‡‰VOL+N,L+NQ«œKfiLUNQŒ8TWNQŒ+Œ{}V~e…lK^h+Sh+fiV~PlSOTšN}XVOL+h(fyP<MONQPN`LUSOT^h+jSOP
h+j^N," e…N`h+jVœ]…fWPº˜–¶·Ÿ¡Z€_‘jfW{“ jfyŒ„*SOŒHNQ]
V~Pºh+j^N<ŒHV~TWK^h+fiV~P4VO‡SgTWfyP^NQSL,L+VOMOLUSOe¨egfWP^M
L+VO„*TiNQe _‘fih+jºK^lhHV 5 %{}V~PŒHhHLUSOfyP€h+Œ`c
†…” …”i~}‚ŠN$… #N…\†ŠI‚ +Š *Z…”i~ # ŠI‘N~ #I– ! ŠI€ƒ†…” ( , †…e” ŠI– 2s„ * ŠI€ #N–‡– 7¼i 1( …” #8…
ž  k -_
m * ŠI€ 7¼i 1 z
4
/5 ‰„Ž—ºfWPl]K{}h+fiV~Pa$“À
¢ —‰•›8$“Z_GN<SOTiL+NQSO]^—4jSQON<h+jSh@ž P D R P cG[wŒ+ŒUKe…Nh+jSh
z
ž  o k - m 8 ‡‰VOL t7¼i 1 5 I
z
¹j^NQP4_ƒNEjSONE‡‰VOL t7¼…„œ—n՝Q™8$,SOP]ºh+jNEfWP]Kl{}h+fiV~P4j€—œ†VOh+j^NQŒ+fWŒ¤h+jSh
ž  k -=P m ž  o 2k -P m 4   k - P 5 -=P m
P
µ ‡ tI 1 5´Z_ƒN%{`SOPz{}V~P{`TWKl]^N%Kz Œ+fWPM;՝`¼>$
ž  k - m ž  o 2k - m 4   k - 5 '- P m
4   z
x fWPSOTWTW—OZšfW‡  Z_ƒNESlTi—£ÕQž8$¤hHVgVO„lh+z SOfWP

 

ž  k - m ž  o k - m 4 z D 5‰o ž D  o  D R $  k - 5 - P m
  R 
ž  o k -œm 4 5‰ž  o k -m
 6 z
T Ö¸×\É“Ý Ç'ÓÕÉFÚ Ý Ï¥Æ+Ï¡ËÍɓ׷ÌÕÜ ÓD؉ÄìQÑÕÓDÏHÄä ÜΆz Ñ6зÆHî}ÑӥзÉF̕ÑD×Ñ Æ“ÓDÏ¡È V á6ÓDÉF׷̩ϕǥÆUË®×QÏ¡ÌÕÄ
¶
2
D
0M
#:<@
14@
14:
@
R
S
[
U
[
ZU
[
ZU
[
[
µ PºlSL+h+fy{`KTWSLQZš_ƒNEjSQONEh+jSh
ž " k -y
m 7¼i !(y
՝}»Y$
z
_‘jfy{Uj’e…NQSOPlŒh+jSh@žƒ"4lSOŒ+Œ+NQŒh+j^L+V~KM~j’SOTWT^(O" 4 %{}V~P€hHLUV~T'†V~fWPŽh+Œ Ps ! " cdšfWP{}N žƒ"4fWŒ,„œ—º{}V~Piw
ŒHhHLUKl{}h+fiV~P³STiV _GN`L¤„†V~KP]¨‡‰KPl{}h+fiV~PZ Ps ! eKŒHhGh+j^N`L+N`‡‰VOL+NŒHlzSOP£S<TiV _Gz N`L¤‡©SO{}N`h¤VO‡h+j^N\{}V~PŽON}
jœKTWTVO‡6SOTWT{}V~P€hHLUV~T†V~fWPŽh+Œ`c
z z
[\ŒfWPˆ˜–¶ Ÿ¡Zl_GN%VO„lh+SOfWP’S
†V~fWPŽh¥_‘fWŒ+NN`L+L+VOL,„†V~KP]4‡‰VOLh+j^N%KPl]^N`L+NQŒHh+fWe¨Sh+fWP^M
‡‰KlP{}h+fiV~P;žƒ"lc
~ …)§ ¨ R
2>~ ‚aŠN…'~…”i~}|~ €{‚%„…'~†‚0ˆ{Š!~\‹Œˆ†~ ‚E…„¡Š * #N‚b
( g‘#I€ƒ† #8…'~2—iŠI– ™I‚a)Š († #I–,+Š *
H
D
P
D
!
.
0
2>~ €~~”i~‚n…”i~ #‹dz ‚~}–UŠ¢~€ ŠI•i‚32 *ƒ• ‚ˆ…\†ŠI‚ žƒ"£„ #N…\† „ &,~ƒ„v…”i~ # —iŠs„ƒ…'~ €{†ŠI€ƒ†)~ €{€ŠI€ ŠI•i‚32
¼tc£X=?$=5‰žƒ"?$©c´e¨S· D 5‰žƒ" - À<¼tcdecf-
v_?:A uE
µ Pºh+j^NKPfiSLUfWShHN{`SOŒHNOZh+jfWŒ,N`LUL+VOL„†V~KPz]ºŒH†NQ{`fiÁlNQŒ,hHV¨h+j^NE‡¸V~TWTWV_‘fWPM„†V~KPl]4_‘jfW{“jºN}šjlfi„lfih+Œ
«œKSO]^LUSh+fW{{}V~PŽON`L+MONQP{}N_‘fih+j4LUNQŒH†NQ{}h,hHVgh+j^N%_‘fy]^h+j£VO‡8h+jN%fWP€hHN`LU·SOTWŒQZŒHN`N³˜–¶·Ÿ¡c
•1—8—iŠs„~ (  #I3‚ 20…” #N……”i~ #I„„{• (2—…\†ŠI‚%„BŠ * 0 ”i~ŠN€~ ( . ” ŠI– 2 , …”i~ ‚ …”%~
#˜‹d‚~}–K
Š ¢~ € ŠN• ‚ 2 *ƒ•i‚aˆ…\†ŠI‚;ž " „ #N…\†‡„ &©~ƒ„Z…”i~t~ €{€ŠI€ ŠI•i3‚ 2
š 5 P 5 P P
¼tc£X?^$=5‰ž " ?^$©c´egS· k z D D 5 Dz 5 z D T 5 z D m k - 5 -m À%¼tcd,cf-gy h P ›O_?:Abu’
R R R R
x LUV~e ˜–¶·Ÿ_GN\SOTiL+NQSO]^—…½šP^V _¾h+jShƒS§¨P^NwV~TW—œP^V~e¨fWSOTWŒ6{}V~fWP{`fy]^N_‘fih+jgh+j^NQfiLGS§³P^NwTiV _GN`Lƒ„†V~KP]
‡©KP{}h+fiV~PŒ{}V~PŒHhHL“K{}hHNQ]Šh+j^N`L+NQfWPc NºL+NQŒ+NQP€h
j^N`L+N£‡¸VOL
h+j^N£„†V~KP]ˆ‡‰KPl{}h+fiV~PŒ<L+VšfW]^NQ]‹„œ—±h+j^N
S„†VONESOTWMOVOLUfih+je"S…lL+VŽVO‡_‘jfW{“jºfWŒ,Œ+j^VOLUhHN`Lh+jSOP4h+jSh‡‰VOLh+j^N%egVOL+NMONQP^N`LUSOT{`SOŒ+NE{}V~PŒ+fW]N`L+NQ]ºfWP
˜–¶·Ÿ¡c
~ …sX=?$y
4 ?œ 4t K4 ">?E" . 0 ”i~ ‚…”i~)–UŠ ¢~ € ŠI•i3‚ 2 *ƒ•i‚aˆ…\†ŠI‚Zžƒ"Oˆ{ŠI†‚aˆ † 2>~ƒ„
P
.
y†\…”
XŒŠI‚;u
` `
`
4
/5
µ ‡EXAfyŒ,ÀS§¨P^NOZh+j^NQPb-^ %SOP] D Xg$“Zl¼cd¢c Z*SOP]4_GN<{`SOPz{}V~P{`TWKl]^N‡¸LUV~ex՝}»Y$
z žƒ" $y X ${ ¼i !(y
dšfWPl{}N\h+jN%ONQ{}hHVOLUŒ " SLUN%TWfWP^NQSLUz TW—¨fWP]^N`†NQP]NQP€h`Zšh+j^N%ŒHh+ShHNQegNQP€h\‡¸V~TyTiV_‘ŒQc 6
¹jN`VOL+NQe ™œc–»ˆŒUK^MOMONQŒHh+Œ³h+jSh¨SOTWe…V~Œ+h¨S§¨P^N’†V~Ti—šP^V~egfySOTWŒ
Œ+j^V~KTW]‚„†N’SlL+VQ^fWegShHNQ] L“Sh+j^N`L
_ƒNQTWTl„œ—…h+j^NS§¨P^NTiV_ƒN`L¤„†V~KP]g‡©KP{}h+fWV~Pž " c(¹‘jfWŒ²fyŒ²{}V~P^ÁL“e…NQ]¨„œ—gV~K^L¤PœKe…N`LUfW{`SOTlN}œ†N`LUfWNQP{}NQŒ`c
¢ N`LUPŒHK^hHN¦NQfyPˆhHV´{}VœLUN`V~§¨KP{`]fiNQfWPŽPh+MˆŒN`SOL+PlL+]±VOL“Œ`h+j^ZN£fWPTiSOV{`_ƒ{`N`K^L<LUSO„†{`V~fWKNQŒºPl]|eg‡‰SQK—#Pl{}„†h+N±fiV~PfWP€Œ`hHc LUVœ]Œ+Kl{}NQNQ{`]#fySOTWfyTiP€—AhHV fWh<h+egj^N±S—±{`SOjTy{`SKTW†SNQh+P¦fiV~P7h+jVOSh‡h+h+j^j^NN
{}V~e…lKhHNQ]ˆTiV _GN`L„†V~KP]|‡©KP{}h+fiV~P¦SOTWK^NgfyŒ%MOL+NQShHN`Lh+jSOP±h+jN³{}VOL+L+NQŒ+V~Pl]fWP^M4VOLUfiM~fyPSOT‡‰KlP{}h+fiV~P
Ž
#:<@
@B1>@
14:
2=?1
#:<@
14@
14:
@
P
SOTWK^NOc‹¹‘jfWŒ
egSQ—‚TiNQSO]‚hHV¦N`L+LUV~P^N`V~KŒ
L+NQŒ+KlTih+Œ…fWP‚SlTWfy{`Sh+fiV~PŒ`c x KP{}h+fiV~PŒ
_wjfW{Uj‚SL+NºM~KlSLUSOPiw
hHN`NQ]ŠTiV_ƒN`L<„†V~KPl]¦‡‰KlP{}h+fiV~PŒ%fyP¦h+j^N¨lL+NQŒHNQP{}NgVO‡,LUV~KP]fWPM£N`LUL+VOLUŒE{`SOP‹„†NgVO„h+SOfWPNQ]ˆSOTiV~P^MAh+j^N
Œ+K^MOMOµ NQŒ+h+fiV~PŒegSO]NEfWP±˜–¶ Ÿ¡c
P’˜ Ž Ÿ_GNfyP€hHL+Vš]K{}N¤STiV _GN`L6„†V~KP]<‡©KP{}h+fiV~P‡‰VOL(KPfiSLUfWShHNƒ†V~Ti—œPV~egfWSOTWŒ_‘jfW{“j
fWŒ{}V~e…†V~ŒHNQµ ]
VO‡h¥_ƒV…S§¨P^N\TiV_ƒN`L¤„V~KlP]…‡©KP{}h+fiV~PŒQc¹‘j^NN}šhHNQPŒ+fiV~o P³hHV<h+jN\eKTih+fiSLUfWShHNw{`SOŒHN\fy ŒGSOŒG‡¸V~TyTiV_‘ŒQÀ P
NQSO{Uj£ŒHhHN`Zœ{}V~e…lK^hHN\Œ+TiVO†NQŒ6 SOŒ(„†N`‡‰VOL+NOZ€„*K^h(ŒHNQTiNQ{}h  SOŒ²h+j^N‘MOL+NQShHNQŒ+hGP^N`M~Sh+fiON D ·SOTyK^NOZ€SOP] 
SOŒwh+j^NŒUegSOTWTiNQŒHh‘V~ŒUfih+fiON D SOTWK^NOc x L+V~e NQo SO{Uj.L+N`šfiV~Kµ ŒwTiV_ƒN`L„V~KlP]º‡©KP{}h+fiV~P:ž  o ZlMONQP^N`L“ShHN
h¥_ƒV’P^N`_ TiV _GN`L„†V~KP]A‡©KP{}h+fiV~PŒQZKŒU" fWP^M  SOP]  c PŒHhHNQSO]|VO‡ƒS4ŒHNQ«ŽKNQP{}N
VO‡²‡©KP{}h+fiV~PŒQZ*_ƒN
P^V _ŠVO„lh+SOfWP<S‡‰hHN`L=(£fWhHN`LUSh+fiV~PŒ8K^hHVž TiV_ƒN`L„†V~KP]%‡©KP{}h+fWV~PŒ']KN²hHVh+j^Nƒ„lfWPSL+—hHL+N`N¤ŒHhHLUKl{}h+K^L+NOc
¡_
fih+j¨h+jlfWŒ²e…N`h+jVœ]Zœ_ƒN\{}V~e…*K^hHNwTiV _GN`L¤„†V~KP]g‡‰KPl{}h+fiV~PŒ(‡‰VOL¤S<PœKe<„N`LGVO‡'eKTih+fiSLUfWShHN†V~Ti—šP^VIw
egfWSOTyŒv•™8$wfWP:(‹SLUfWS„*TiNQŒ‘_wfih+jA]N`MOL+N`N¡-y b ;$'&´SOP] zPV~Piw¡`N`L+V4hHN`LUegŒ`c%¹‘j^N<P^V~P%w¡`N`L+V
{}VœN`§¨{`fiNQPŽh+Œ,SL+NLUSOP]^V~egTW—…MONQP^N`LUShHNQ]º_‘fWh+j A±˜U5%IQFŸ¡cG¹jNQŒHNw„†V~KPl]¨‡©KP{}h+fiV~PlŒGSL+N{}V~e…*SL+NQ]
hHV4h+j^N
„†V~KP]’‡©KP{}h+fWV~PŒ‘VO‡GV~K^LL+N`šfiV~KŒ\e…` N`D h+j^Vš] ˜–¶·Ÿ¡Z_‘jfW{“jAKh+fWTWfi`NQŒwh+j^N
TWfWP^NQSL\L+VOMO¢ LUSOe¨egfWP^M
ŒHV~TiON`
L ˜ÙFŸ¡Z^SOP]£hHV…{}V~PŒHh+SOPŽh,„†V~KP]¨‡‰KPl{}h+fiV~PŒƒ]^N`ÁlP^NQ]³„Ž—¨h+j^N\e¨fWPfWeKe N`LUPlŒHhH" NQfWP
{}VœN`§¨{`fiNQPŽh PZŽ{}‡Dc@•›8$“c²¹8S„lTiNEwTWfWŒHh+Œ6h+jN‘L+NQŒ+KlTih+Œ6‡‰VOLG]fÙX†N`L+NQPŽh(SOTWK^NQŒ(VO‡^(6Z zZœSOP] M[ Œ4‹!$ fWŒ
h+j^N%PœKe<„N`L,z VO‡ ¢ N`LUPŒHhHNQfyPº{}VŽN`§¨{`fWNQP€h+Œ`c µ P4NQSO{“jz{`SOŒHN¨`¼O¼gLUSOP]^V~e †V~Ti—šP^V~egfWSOTyŒG_ƒN`L+NMONQP^N`L“ShHNQ]
SOP]h+j^N¢ e…NQSOP…{}V~eglK^h+Sh+fiV~P
h+fWegN¤SOPl]<N`LUL+VOL(SL+N¤M~fiONQPc6¹j^N¤h+fWegNƒLUNQ«ŽKfWL+NQ]E‡‰VOL6h+j^N,{}V~e…lKh+Sh+fiV~P
VO‡,h+j^N N`LUPlŒHhHNQfWPˆ{}VœN`§¨{`fiNQPŽh+ŒfWŒEfWPl{`TWK]^NQ]^Mh+jfWŒ%fyŒ%NQ«œKSOT(hHVAh+j^N¨h+fWegNg‡¸VOL<h+j^N³{}V~PlŒHh+SOP€h„†V~KP]
‡©KP{}h+fiV~PŒQc8[\PgK^†N`L„†V~KP]V~Pgh+jN]fWŒ+{}L+N`*SOP{}—E„†N`h¥_ƒN`NQPgh+jN†V~Ti—œPV~egfWSOTšSOP]gfih+Œ6TWV_ƒN`L²„†V~KP]
‡©KP{}h+fiV~P4V ON`L
u³fWŒ{}V~e…lKhHNQ]’SO{`{}VOLU]fWPM…hHV¨¹j^N`VOL+NQe1™œc͙gSOŒ
7egS· 5‰žƒ" -
D zD
¹j^NzL+NQŒ+KTih+Œg_GN`L+NzL+Vš]K{}NQ] _‘fWh+j ‹V~P S‹žœc–» R°wAaƒªc²¹j^NzegNQSOP SOTWK^NQŒ…‡‰VOL¨h+j^NAh¥_ƒV
P^V~Piw¥{}V~PlŒHh+SOP€h…„†V~KPl]ˆ‡©KP{}h+fiV~PlŒ<SL+NºON`LU—‹Œ+fWe¨fWTWSLQZ_‘fih+j‹V~K^LgP^N`_"e…N`h+jVœ]ŠN}^jfi„lfih+fyP^MAS|Œ+TWfWM~j€h
fWe…lL+VONQe…NQPŽh%fWP|SOTWT8„lK^hh+j^N…ÁlLUŒHh{`SOŒHNOc…°‘V _GN`ON`L<‡¸VOL%SOPˆfWP]fišfW]KlSOT†V~Ti—œPV~egfWSOT•ZV~P^N…e…N`h+j^Vš]
egS—#]^NQTyfiON`LºS Œ+fiM~PfiÁ*{`SOP€h+Ti—¾Œ+K^†N`LUfiVOL£„†xV~KP]#‡‰KlP{}h+fiV~P#hHV h+j^N¦VOh+j^N`LQZ_‘fWh+j¾h+jN¦L+NQŒ+KTih+Œ£V~PTW—
‡‰L+NQ«ŽKNQP€h+Ti—4fW]^NQPŽh+fW{`SOTfyPºh+j^N (B?žg{`SOŒHNOc VOL2( c¾»gh+j^NE{}V~e…*K^h+Sh+fiV~P’h+fye…N%‡‰VOL‘V~K^L‘PN`_?„†V~KP]
‡©KP{}h+fiV~PŒ8fWŒVO‡h+j^N,Œ+SOe…NƒVOLU]^N`LVO‡le¨SM~Pfih+¢ K]^NƒSOŒ‡¸VOLh+j^N¤{}V~PŒHh+SOPŽh6„†V~KP]E‡‰KPl{}h+fiV~PŒ`ZSOP]
fWŒ8e<K{“j
fWe…lL+VONQ]4V ON`Lh+j^NL+N`šfiV~KŒ¤SLUV~SO{Ujc N`‡‰VOL+NV~P^N{}V~KTW]4h¬—Ž*fW{`SOTWTi—¨{}V~eglK^hHN„†V~KP]³‡‰KPl{}h+fiV~PŒ
fWPºTiNQŒUŒ,h+jSOP’SgŒ+NQ{}V~P]ºV~PTi—£‡‰VOL(‰c‚»%M‡‰VOL‘h+j^N%P^N`_be…N`h+j^Vš]ºh+jfWŒ,{`SOPA]^V~P^N‡‰VOL(‰c ¯œc
7rwo
u_“tvUrwo
NgjSONlL+NQŒHNQPŽhHNQ]¦S³P^N`_ e…N`h+jVœ].‡‰VOL\h+jN
{}V~eglK^h+Sh+fiV~P.VO‡GS§³P^NTWV_ƒN`L„V~KlP]’‡©KP{}h+fiV~PlŒ‘‡‰VOL
eKTih+fiSLUfWShHNg†V~Ti—šP^V~egfySOTWŒ„lSOŒHNQ]ˆV~P ¢ N`LUPlŒHhHNQfWP‹N}œlSOPlŒ+fiV~PZ8‡¸VOL_‘jfy{UjˆSzMONQP^N`LUSOTƒ{}¢ V~PŒHhHLUKl{}h+fiV~P
L+NQ«œKfiLUfyP^Mˆh+j^N±Œ+V~TWK^h+fiV~P#VO‡<S TyfWP^NQSL4L+VOMOLUSOe¨egfWP^MŠL+VO„lTWNQe _¤SOŒºM~fiONQP fyP˜–¶Ÿ¡c —#V~K^LºP^N`_
e…N`h+j^Vš]zS§³P^N%„†V~KP]4‡©KP{}h+fiV~PlŒ{`SOPz„†NE{}V~eglK^hHNQ]zeK{“jze…VOL+N{Uj^NQS*Ti—OZ*SOP]Afih‘egS—4h+j^N`L+N`‡‰VOL+N
„†NwVO‡'MOL+NQShHN`LLUSO{}h+fy{`SOT*KŒ+NOc µ P]N`NQ]³V~PN\egS—³{}V~e…*K^hHNK^hHV…ž " VO‡'h+j^NQŒHNP^N`_7„†V~KP]¨‡‰KPl{}h+fiV~PŒ
‡‰VOL(SŒ+fWP^M~TiN¤M~fiONQP
†V~Ti—šP^V~egfySOT€_‘jlfW{Uj HV~fWPŽh+Ti—%„†V~KP]h+j^N{}V~PŽON}gjŽKTyTŽVO‡*h+j^N{}V~PŽhHL+V~T^†V~fWPŽh+Œ6e<K{“j
e…VOL+N<{`TiV~ŒHNQTi—³h+jSOPzS…Œ+fyP^M~TiN„†V~KP]4‡©KP{}h+fiV~P4‡‰L+V~e"V~K^L,lL+N`œfWV~KŒ,SL+V~SO{“jZlfWPºTWNQŒ+Œ,h+fWe…NOc
­
U
M
U
U
M
8U
R
!"#$&%(')#$+*,!,
- /.10243
5627981.17:.+;<2=973
>?/@A;<2B=793
J =97K!.IL27
J =97K!.IL27
[
P
*
+
$
[
P
*
+
$
UY
S
T ULSNVXWYZ
U Y
\
\
^
_
` ab aHaaHa!cHa
ab aHaaHad` a#b `e W
W bc W c
d Wa
cH` ab aHaa W1g
ab aHaa g#W
W b `He`
W b d/fHf
^#b eHd/f
ab aHaa)fhc
^bi_ WHW
W a ^a
W ^ W ab aHaa g `
^ ^a
e W ab aHaa g f
ab aHa W ^
^bjfF`)f
g b c)_!`
c _a
dH^_ ab aHaH^!c
_#b d)fFe
ab aHa` g
_b a!c)_
^ ^a
f!^!` ab aHa WHW
cBb ac g
ab a W d
g bg _ g
^ _a
d/_!d W ab aHa` g
db `c W
ab ^!c
d#bi^!` W
^ _a
_!`Ha!c/` ab aH` W
bg c g
d#bi_!a g
fb W c g
^
^
^
c
c
d
e
Wa
CEDFHG4I2B=8+;62=793
J =7K!.1I2B7NMPO)Q
]*($+ U Y
\
a#b aaHaH^!a
ab `)fFd
a#b aa/^_
W b dH`H_
a#b aH^ g
^#b _!c g
a#b aaHeH^
^#b ec)f
^b eH^
_#b a/_!d
cb cHe
g b c/a g
k [1!]1l[m!
W $<*()]
µ hEfWŒ_ƒ VOL+h+j‹P^VOh+fWP^Mºh+jShfWP|h+j^N¨{`KL+L+NQPŽh%ON`LUŒ+fiV~P±VO‡ƒV~KL<SOTiMOVOLUfWh+je h+j^N³{“j^V~fW{}NgVO‡,]fWL+NQ{}h+fiV~P
ONQ{}hHVOLUŒ ՝O!$fWŒ<LUSh+j^N`L…SL+„lfihHL“SL+—Oc¦°‘V _GN`ON`L³V~K^LPœKe…N`L“fW{`SOT²N}š†N`LUfiNQP{}N4Œ+K^MOMONQŒ+h+Œ
h+jSh
h+jfWŒ
egS—³fWPon*K^NQP{}N‘h+jN\LUNQŒ+KTih+SOPŽhG„†V~KPl]g‡©KP{}h+fiV~P£©f•c–NOc(_‘jlfW{Uj£TiV_ƒN`L,‡©SO{}N`hƒVO‡h+j^N{}V~P€ON}ºjœKTWTVO‡h+j^N
{}V~PŽhHL+V~TƒV~fyP€h+ŒfWŒ<NQe<KTyShHNQ]a$“c¦[ ‡‰K^h+KL+N³e…Vš]fiÁ*{`Sh+fiV~PˆhHV.h+j^N4SOTiMOVOLUfih+jle egS—ˆh+j^N`LUN`‡¸VOL+N4KŒHN4S
Œ+fWeglTiNGjNQK^LUfWŒHh+fy{(‡©KP{}h+fiV~P<hHV%{Uj^VœV~ŒHN,h+j^NQŒ+NƒONQ{}hHVOL“Œ(fWP
SOP…SO TihHN`LUPSh+fWON¤]lfiL+NQ{}h+fiV~P
Œ+K{“jh+jSh(Se…VOL+N
Œ+KfWh+S„lTiN‡‰SO{}N`h%VO‡ƒh+j^NgTiV _GN`L<{}V~P€ON}ˆjœKTWTfWŒ]^NQŒ+fWM~PShHNQ]c fWh+j|h+j^N…VOL+h+j^VOMOV~PSOTyfih¥—|L+NQ«œKfiL+NQegNQP€h
՝`¼>$“Zlh+jN`L+NESL+N (;5 ]^N`MOL+N`NQŒ‘VO‡‡¸L+N`NQ]V~e fWP4h+jfWŒ,Œ+NQTiNQ{}h+fiV~Pc
qu pEo
r (?
s r2elGo\p
¹j^N%SOKxh+j^VOLUŒMOL“ShHN`‡‰KTyTi—£SO{U½œPV_‘TiNQ]MON<Œ+K^lVOLUhƒ‡‰L+V~e3h+j^N L fWPfWŒHhHLU—¨VO‡ ]Kl{`Sh+fiV~P’SOPt] s‘NQŒHNQSLU{“j
VO‡h+j^N NQ]I N`LUSOuT s‘N`lK^„lTWfy{¨VO‡ER\N`LUe¨SOP€— KP]N`Lg{}V~P€hHLUSO{}h4P^V^c?­·¼€­·¼O¼^c ¹‘j^N`—ŠSOTyŒHV¦h+jSOP^½ \LQc
ª¤j^L“fWŒHh+fWSOP SOPlŒ+ŒHV~P4‡‰VOLwjfWŒ¤{`SL+N`‡©KTLUNQSO]fWP^M…VO‡8h+j^NEegSOPœKŒ+{}L“fih,SOP]’jfyŒƒjNQTi‡©KT†{}V~ege…NQPŽh+Œ`c
v ²q^²o
uy_
˜ÙFŸ ¢ N`L+½ONQTySOSL L ciZ *À fWPNQSL‘a(L+VOMOL“SOegegfWP^M¨ªƒVš]^NOc
‡‰hHPÀ ww ‡‰hHc®fW{`Œ`c–NQTWNOc–h+K^NOc®PT w lK„ w·Ti Œ+V~TiOHN w
˜–ž Ÿ…ª,SL+MO. V
Rc޹cŽSOP]£dšj.fWŒ+€Hjl‚ SE”ca՝Q›NŽNŽ8$“ZyxH¹j^N ¢ N`L“PŒHhHNQfWP…‡‰VOLUe VO‡†SE†V~Ti—œPV~egfWSOT•Zjz|{ .9} ~„ .~ #N… .
|@•i€ $… #I3‚ 2-#N+€ 2sX„ ’ŠI– |Z†­› ƒœ¯šc
˜–™ Ÿ x TiV~Kl]SOŒ’ª\cƒ[<c •ž¼O¼O¼>$“tZ ~ x \N`hHN`LUegfWPfyŒHh+fW{¦RTiVO„lSOT%”\h+fyegfiQSh+fiV~PÀ±¹‘j^N`VOL+—OZ L . N`h+j^€ Vš]Œ`ZSOP]
[wlTyfW{`Sh+fiV~PŒ`jZ z ~€ƒ†~„ ŠI¢ ‚ˆŠI‚’‘N~…“ „—…\† (‡† † #N…\†ŠI‚ #I3‚ 2 †…‰„ ˆ©—8—a– †\ˆ #N…\†ŠI‚%Š„ ’ŠN– EZ ‹ETWK€_ƒN`L
[\{`SO]claGK^„lT•ciZ \VOLU]^LUNQ{UjŽh`Z V~ŒHhHV~PZ V~P]^V~Pc
˜ »Ÿ…R SLUTiVX I cZ՝Q›O¯NŽ8$“ŒZ xUª¤V~P€ON`L+MONQPŽhz „†V~KPl]Œ£‡¸VOL’h+j N¦LUSOP^MON±~ VO‡
e<KlTih+fiSLUfWShHN|†V~ Ti—œPV~egfWSOTWŒ`jZ z .
‚a…'~€ƒ‘ #I9– Ž #N…”i~ ("#N…\†ˆ„ ‘’“ , ‹…c fy{+½ONQT•Z^NQ]fWhHVOLQZ ~ˆ!…\•i€~ ŠN…'~ƒ„6†•‚ ”y)Š (2—a•%…'~€ ˆ †#~‚aˆƒ–~ EŠI–
—  — Z†dšLUfWP^MON`LZ ¢ N`LUTWfyPZ™~!­ ƒœ¶NŽœc
˜–¶ Ÿ…RSLUTiVX . I ciZ I SOPŒ+ŒHV~P.ª\clSOP]Ad^egfih+jº[<cla8c•ž¼O¼~™8$“EZ x V_ƒN`L\„V~KlP]4‡‰KlP{}h+fiV~PŒ¤‡‰VOL‘†V~Ti—šP^V~egfUw
SOTyŒ`jZ z˜{ ”y)Š (2—a•%$… #N…\†\ŠN3‚ #I– #I3‚ 2™ˆ©—8—a– †~ 2™Ž #N…”i~ ("#N…\†\ˆ „“ZhHV£S†NQSLQc
¯
X
ZP
D
P
P
D
D
˜ Ž Ÿ…RSLUTiVX I ciZ I SOPŒ+Œ+V~P£ª\c€SOPl]£dšegfWh+j…[Ecœa¢ c•ž¼O¼~™8$“Zyx µ P{`TyKŒ+fiV~P…fWŒ+VOhHV~PfW{`fih¬—VO!‡{}V~PŽON}Yw¥{}V~Pl{`SQON
N}šhHNQPŒ+fWV~PŒ,‡‰VOL†V~Ti—œPV~egfWSOTWŒG„lSOŒHNQ]ºV~P N`LUPŒHhHNQfWP4N}šlSOPŒUfiV~PZjzX”yŠ)(2—a•%…\†‚ Z*hHV¨S†NQSLQc
˜®­Ÿµ°\SOPŒHNQ PZ oc s%cœÕQ›O›Ož8$“Z xURTiVO„lSOT'”\lh+fWegfiQSh+fiV~P Œ+fWP^M µ P€hHN`LU·SOT[\PSOTi—šŒ+fWŒ`jZ z L SLU{}NQT \N`½Ž½ON`LZ
P{ciZ N`_(VOL+½c
˜–¯ Ÿ ‹%NQSL+‡¸VOhHh sEc ¢ c_՝Q›O›NŽ8$“uZ x s‘fWMOVOL+V~KŒ%RTiVO„lSOT6dœNQSLU{“j. À\ªƒV~PŽh+fWPœK^V~KŒ\a(L+VO„*TiNQegŒ`jZ z ~€ƒ†#~ƒ„ ~ ŠI‚
¢ˆ{ŠIV~‚’ŒH‘NhHV~~“PZ „—V~…\P† (]V~† P† #Nc …\†ŠI‚ #I3‚ 2Œ†…–„ ˆ©—8—a– †\ˆ #N…\†\ŠN‚%„ ’ŠI–  OZ ‹%TWKŽ_GN`L’[\{`SO]ca²K„lT•ciZ \VOLU]L+NQ{UjŽh`Z
˜–› Ÿ .fi„† N`L+h+f c SOP]aSOP€hHNQTWfy]^NQŒªc.ª\— ci•ž¼O¼~ž8$“lZ xUªƒV~PŽON}<NQPŽONQTiVO†NQŒ'VO‡*e…V~P^V~egfWSOTyŒVO‡^Vš]]<]N`MOL+N`NOjZ z
{
–KŠ #I– „—…\† (v†† #8…\†\ŠI‚ ’ŠI– “ZQ¶~­!ƒ*ŽO¯œc
˜Ù`¼·Ÿa²LUSOK^hHQŒ+{“jz¢ °<ciZ ¢ VŽNQjle c*SOP]’aSOTWKŒHQPŽ— L c•ž¼O¼~ž8$“EZ x ¢N` QfiN`LSOP] ¢ wDdœlTWfWPN¹NQ{UjlPfW«œK^NQŒ`jZ z
dšLUfWP^MON`LZ N`LUTWfyPZ^°‘NQfW]NQTi„†N`L+M^c
˜ÙOFŸ swSh+Œ+{UjN`½g°Ec€SOPl]?sVO½šP^N I c՝Q›O¯O¯8$“Zx N`_7ª¤V~e…lK^hHN`L L N`h+j^Vš]Œ6‡‰VOLƒRTiVO„*SOT*”\h+fWe¨fiQSh+fiV~PZjz
TWTWfWŒ¤°wVOL+_ƒVŽVš] h+]ciZ*ª¤jfW{“j^NQŒHhHN`LQc
˜ÙQž Ÿ¹8SQ_¤SLUegSOTySOPf L c'SOP]‹dšSOjlL fWPfW]fyŒ µ cc¢•ž¼O¼~ž8$“Z xUªƒV~P€ON}^fiÁl{`Sh+fWV~PˆSOP]‹RTiVO„lSOTG”\lh+fWegfiQSsw
h+fWV~P±fWP‹ªƒV~PŽh+fWPœK^V~KŒ%SOPl] fiœNQ]i w PŽhHN`MO~ N`L V~PTWfWP^NQSL<a(L+VOMOLUSOe¨egfWP^M^ÀE¹‘j^N`VOL+—OZ[\TiMOVOLUfWh+jegŒ`.Z
dš
VO‡¸h¬_ƒSL+NOZSOPl]³[wlTWfy{`Sh+fiV~PŒ`jZ z ~€ƒ†~„ ¢ ŠI‚aˆ{ŠI‚’‘I~–“ „—…\† († † #N…\†ŠI‚ #I3‚ 2t†…„ ˆ,—8—–/†ˆ #N…\†ŠI‚%Œ„ EŠI–
“Z ‹%TWKŽ_ƒN`L‘[w{`SO]cla²K^„*T•ciZ wVOL“]^L+NQ{UjŽh`Z V~ŒHhHV~PZ V~P]V~Pc
˜ÙQ™ Ÿ†N`hHh+TiN`L L cŽSOPl]£RSLUTWVX I c՝Q›O›O¢ ¯8$“yZ x s‘VO„lKŒHh+PNQŒ+ŒGSOPlSOTi—œŒUfWŒ6VO ‡†0 V~Ti—šP^V~. egfWSOTWŒ_wfih+jg. †V~Ti—šP^V~. egfWSOT.
* SLUSOe…N`hHN`L²]^N`†NQP]NQP{}—EKŒ+fyP^M N`L“PŒHhHNQfWP
N}šlSOPŒ+fWV~PZjz
€ #I‚%„ ˆ
•%…#Š)("#N… ”yŠI‚E…\€ EŠI–
OZ»€žO¶ ƒ€»€™šc
P
P
D
D
D
D
D
P
›