Polynomial Algorithms for the Synthesis of Bounded Nets

HAL Id: inria-00074358

https://hal.inria.fr/inria-00074358

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents

Polynomial Algorithms for the Synthesis of Bounded Nets

Eric Badouel, Luca Bernardinello, Philippe Darondeau

To cite this version:

Eric Badouel, Luca Bernardinello, Philippe Darondeau. Polynomial Algorithms for the Synthesis of Bounded Nets. [Research Report] RR-2316, INRIA. 1994. �inria-00074358�

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Polynomial Algorithms for the Synthesis of Bounded Nets

Eric Badouel , Luca Bernardinello and Philippe Darondeau

N˚ 2316

Juillet 1994

PROGRAMME 2

()*,+ $+ - .%

/10&2435687%9;:=<?>#@?ABC:=3D6E5<F0&GH6;0I7J2KGH<F>L>49M@6;GH7ONQP%2K>L2KR%RC<,S6;0T9;G=7%<U6;:@

VJWYXIZIW\[^]]`_badc eH[&fhgjiDf8kml?]noXTfqpsrtiU_vutwDWxXIZTWy[&]]"[^zYpqXT{_z|Z~}_{Upq_bfqXTZIpsgjpq_f

VJWxXI4_zC€psg[Ik

‚C[^wDwoXTWxz„ƒF_bWx_&gy…U_W\g†…D_‡{‰ˆ?aIŠ?‹Œ$c IiUpqfŽfq_z„‹I&c at‘‰w’[&ZI_&k

“”–•j—&˜&™UšI—›‰œ=…U_|k4XILg[^fŽfq_&ƒ‰kml?{FzY…U_&k4phk;wUWYXInUfŽ_]Ÿž XIW–{U_z\kju&¡|…Uphgy…‰gjXI{¢kmphk4zyk8pq{dƒF_&gjpsƒFpq{UZ

¡|…U_zY…U_W„[ZIpŽ£_{"ZIWy[&wU…phk|phkmXT]XIWYwU…Upsg¤zYXzY…U_1g[Ikm_‰ZIW\[^wU…X^žHk4XI]_b{U_zu¥[^{’ƒzY…U_{

gjXI{¢kmzxWYi’gjzYpq{UZzx…U_"{U_zuJ…’[TkQn’__{¦k4XIfq£_§ƒ¨pŽ{©zx…U_"fqpŽzxzY_Wy[&zxiUWY_Qž XTW£T[^WYpqXTi’kQz4l?w’_&k$X^ž

{U_z\kjuªW\[^{UZTpq{UZž WYXI]«_fŽ_]_{?zy[&Wxl{U_zykMzxX¬Vª_zYWxpJ{D_zyk®­œ=…U_`gjXI]`]XI{"wUWYpq{’gjpŽwUfq_$ž XTW

zx…U_‰k4lF{?zx…U_§kmphk=psk=zx…U_bpsƒF_&[$X^ž¯Wx_ZTpqXI{¢k=pq{"ZIW\[^wU…’k®uoWY_wUWY_&km_{?zxpŽ{UZ1w’XkYkmpqnDfq_b_°?zx_{’k4pqXT{’k

X^ž‰wUfs[Igj_&k1pq{¦{U_z\kj­²±³X&¡=_£_Wu%{UX´wUW\[IgjzYphg[&fC[^fqZTXIWYpqzx…D] …¢[Ikn’__{²ƒ?_jµ’{U_&ƒ¦kmX,žL[&W

ž XIWCzx…U_‰k4lF{?zx…U_§kmphk®­ª¶_bZIpq£_„…U_Wx_„_°FwDfqphg®pqzH[^fŽZIXIWYpqzY…U]"k|kmXTfq£?pq{UZ1pŽ{w’XIfŽlF{UXT]ph[&f;zYpq]_

zx…U_dkml?{FzY…U_&k4phk|wUWxXTnUfq_]·ž XTW³n’XIiD{’ƒF_&ƒ{U_zyk=ž WxXI]¸WY_ZIiUfs[^WMfs[^{UZTi’[^ZT_&k³XTWž WYXI]¹µ¢{UpqzY_

[^iUzYXI]"[&zy[?­

º»¼8½x¾‰¿’˜&Àª•I›EÁl?{FzY…U_&k4phk=VJWYXInUfŽ_]ž XIW„ó_z\kjuDVª_zxWYp8ó_zykjuD‚_ZIpqXT{’kju’ÄCfqZIXTWxpŽzx…U]"k

ÅhÆ1Ç

ÈÊÉ4ËÌ

Ç

ÈͪΎÉ4ÏÑÐyÒ

Ó8Ô&Õ×֒Ø;Ù®ÚÑÛ%Ø8Üy֒ÝT܆ڠÞÑßáà=Ö â^Ý&ÝTÙjÚ ÞÑãYä|åà%ÞÑÔ&ã~æ^Ú ã4çIè Ô|éUêë¥êíì’êIî‰ïxðUñ

ÈmòáÈÊÉ~ÈKÎUó¥ôKÈ4ËÏyÈKÉ4õ

åà=Þ Ô&ã8ö¥ê÷ì’êøùê

úûã4ÞhØ¥ÙjÚ Û³ü’ý

ÐTôLÈÊÉKÉ4õ

ÜyçTä=åà%ÞÑÔ&ã–ö¥ê÷ì’êøùê†þŽãmßáß×ÙyØ8ÖÑÔ&Õ×Ý%ÿ®ÚKÜyçÞ ãYä=ÞÑÙâIè4Üoã4Ú çT܆ÚLäÕ×ç&ãmßáß×Ù

õ

Ù®ç=ß×ãYÜ®ã;þŽÚÑÙ

ÞÑÔ&ã8ç^Õ jã4Ú ÖÑÕ×ÞhàCÙyþMÕ×ßÜyç

MÜyÕ×ß

ÚÑÕè;Ü®ä§Ù®â&ã4ß

õ

âIè4Üoã4Ú çT܆ÚLäÕ×ç&ãmßáß×Ù

õ

Ô&Õ×ß×Õ×Ý&ÝIã~܆ڠÙjçTäãY܆âªÕ×Ú Õ×ÖLÜþŽÚ

+ $~ b* $

»?•»› ;_‰wUWxXTnUf_]`_bƒF_1k4lF{?zx…_&km_dƒF_$WD}_&km_&[&iU°¥u’rtiUp~gjXT{’kmpskmzx_[ƒH}_&gjphƒ?_W|w’XIiUW

iU{ZTWy[&wU…U_1ƒ?XI{U{ù}_‰kpqf8_§kmz|phk4XI]XTWxwU…D_[QiD{ ZTWy[&wU…U_1ƒ?_.][^Wyri’[&ZI_‰ƒiD{ WD}_&km_§[^i8uU_&k4z

WD}_&k4XIfŽi w’XTiUWMƒ?pq£_W\km_&kHgjfh[Tkxkm_§k|ƒF_bWU}_&k4_&[^iU°`[^fŽfh[&{FzCƒF_§k=WU}_&k4_&[^iU°¨}_f}_]_{Fz\[^pqWY_&kJ[&iU°WD}_

km_&[&iU° ƒF_V–_zxWYpK­;_wUWxpŽ{’gjpŽwo_1Z~}_{ù}_W\[^f%_&k4z$ƒ?_g[&Wy[TgjzD}_WYphk4_WMfq_§k.k4XIi’kb_{’k4_]nDfq_&kCƒFi

ZIW\[^wU…U_vu’[^wUw’_f}_&k

"!$#&%$')(

uDrtiUp¥Wx_wDWU}_&k4_{FzY_{?zfŽ_&k_°FzY_{’kmpŽXI{’kHƒF_&k%wUfh[Tgj_&k=ƒ?i WD}_&km_§[^i*[

kml?{FzY…|}_zYphkm_W­e%_w’_{’ƒU[&{Fz%fh[„gjXI]wDfq_°?pqzD}_Jzx…ù}_XIWxpsrtiD_CƒF_|fh[Mk4XIfŽiUzxpŽXI{_&kmzJ_°Fw’XI{D_{FzYpq_fŽfq_

_zC[^i¢gjiU{U_‰XIwUzYpq]pskx[^zYpqXT{]_{’[&{Fz+[ƒ?_&k|[^fŽZIXIWYpqzY…U]_&k=iUzYpqfŽphkx[&nUfq_§k{,á[´}_zD}_bwUWD}_&km_{?zD}__

4i’kxri,-[fŽXIWyk®­%óXIi¢kQwUWD}_&km_{FzYXI{’k1phgjpùƒF_&k[^fŽZIXIWYpqzY…U]_&k$_°?wUfŽphgjpŽzx_&kbriUp|WD}_&k4XIfŽ£_{Fz‰_{

zx_]`w’k=w’XIfql?{UXT]ph[&f8fq_$wDWxXInDf._]_¤ƒF_1k4lF{?zx…_§km_1ƒ?_$WD}_§km_&[&iU°"noXTWx{ù}_§k/[1w’[&WxzxpŽWbƒF_‰fh[^{D

Z[&ZI_&k³WD}_ZIiDfqpq_WykXTi0[$w’[&WxzYpqW„ƒ×[&iUzxXT]"[^zY_&k¯µ’{Dphkj­

1O¿¢—§•j½yš$23»,› Ál?{?zx…_&k4_‰ƒF_bWU}_&k4_&[^iU°¥uFWD}_&km_§[^iU°¬ƒF_‰Vª_zYWxpLutWD}_ZIpŽXI{’k®u’[^fŽZIXIWYpqzY…U]_&k

%3' % # !$% # ( % ' ( #( % % ' (

·J $"

! "$#

—&˜&¿8À ªšI—&%Ñ¿

# '

( )

¿¢—§™F—*% ¿

#

•,+4¿’˜.-³»—&˜*%

)

»—&• /

' »102%Ñ¿ # •,% # »10 2 ™U˜3H™ # 0 –™0’»?• 4

Š?­q‹ ‚|_ZTpqXI{¢k=pq{65UXIWx][^f,8[&{UZIi¢[^ZI_§k 787,78797:79787:79787,787,787,78797:7 ;

Š?­×a e%XT]wUiUzYpq{UZd[<|[Tkmpskž XIW=<=XIiU{’ƒ?_&ƒ"‚_ZTpqXT{’kpŽ{"[‚_ZTiUfh[&W 8[^{UZTi’[^ZT_ ‹a

Š?­×Š >C_&gjphƒ?pq{UZ‰iUw’XI{´Á_w¢[^Wy[&zx_&ƒ?{U_&kxk=X&žH[‚_ZTiUfh[&W 8[^{UZTi’[^ZT_ 787,78797:7 ‹j

Š?­ e%XT]wUiUzYpq{UZd[5–pq{UpŽzx_bó_zž WxXT])[1‚_ZTiUfh[&W8[&{UZIi¢[^ZI_?787,787,78797:7 ‹@;

A »102%Ñ¿ # •,% #CB % # %h—&»ED"˜&™FHGª• ! 4

D­q‹ ÁvXI]_,ICW\[^wU… œû_WY]pq{DXIfqXTZIl 787,787,78797:79787:79787,787,787,78797:7 ‹

D­×a ‚|_ZTpqXI{¢k=pq{¬ÄMggj_§kxkmpŽnUfq_8ICWy[&wU…’k³¡|pŽzx…6>³_zY_Wx]pŽ{Uphk4zxpsg 8[^n’_fqpŽ{UZ 797:7 aJ

D­×Š ‚|_ZTpqXI{¢k=pq{65ªpq{Dpqzx_¤ÄMggj_&kYkmpŽnUfq_8ICWy[^wD…’k³¡|pqzY…6>³_zx_Wx]pŽ{Uphk4zxphg 8[&n’_fqpŽ{UZaIŠ

D­ e%XT]wUiUzYpq{UZd[Ávw’[^{U{Dpq{UZ`œûWY__‰[^{’ƒ¬[K<|[Ik4phk|X^žHe%lUgjfŽ_&kž XIWL 78797:7 a^

D­NM >C_&gjphƒ?pq{UZ‰iUw’XI{´Á_w¢[^Wy[&zx_&ƒ?{U_&kxk=X&žH[.5ªpq{UpŽzx_bĄggj_&kYkmpqnDfq_8I³W\[^wU… 797:7 aM

O P ¿ #

š$2–•@% ¿

# (QO

R S

"JH+,*UTC

VJ…UWx_{?ž _i’gy…Fz%[&{’ƒ‚|XW_{Fn’_WYZ$[TƒUƒFWY_&kxk4_&ƒQpŽ{YXZV%‚³[J]\’zx…U_|wDWxXInDfq_] X&ž–gy…’[^W\[IgjzY_Wxp^Wpq{UZ

[^°?pqXT]"[^zYphg[&fqfql¬zx…U_`gjfs[IkxkbX^ž„k4pq]wUfŽ_ƒFpqWY_&gjzY_&ƒZIW\[^wU…’k$fs[^n’_fŽ_&ƒXT{©[^W\gk.¡|…Dphgy…´]"[l

n’_,WY_wUWx_§km_{?zx_&ƒ iD{’[^]nUpqZTiUXIi¢kmfql©n?lE[©km_z X&žk4iUn’km_zykX^žQ[^{²X^£_Wy[^fŽfMg®X?ƒFpq{UZ¦k4_z

zxXTZI_zY…U_WC¡|pqzx… [k4_z|X^ž¯]iUzYi’[^f ƒFp`_¥_WY_{’gj_§k=no_zm¡H__{zY…U_]#­’e%_{?zxWy[&f8zxXzx…’[&z³¡HXIWa

phk8zx…U_HgjXT{’gj_wDz8X^ž

"!$#&%$'

pŽ{$[|ZIW\[^wU… uIƒF_®µ’{U_&ƒb[Ik~[³k4_z8X^ž’£_Wxzxpsgj_&k’¡|…Uphgy…‰[^Wx_H_{?zx_WY_&ƒ;u

_°?pqzx_§ƒ;uFXTWMfq_jž z|pŽ{F£T[&Wxph[&{Fz|n?l"[&fqf–[^W\gk|¡|pqzx… [^{¬phƒF_{?zxpsg[^f¥fh[&no_fK­’œ=…U_‰X^£_Wy[^fŽf8gjX?ƒ?pq{UZ

km_z8ž XIW¯[ZTWy[^wD…1]"[lb[^fŽ¡|[lUk8n’_|gy…UXk4_{1[Tkªpqz\k8km_z–X^ž¥WY_ZIpŽXI{’k®­IÄ´Wx_ZIpqXT{1phk–[wDWxXIw’_WYz4l

X^ž¥zx…D_|£_WxzYphgj_&k’pqz%g®XI{?zy[^pŽ{’kj­e%XI{?£_W\km_fŽlu[³£_Wxzx_°M]"[lMn’_|Wx_wDWx_&k4_{FzY_&ƒ$[Tkªzx…D_|km_zJX^ž

Wx_ZTpqXT{’kª¡|…Upsg†…‰pqz–no_fqXI{DZkJzxXDuI[&{’ƒ$zx…’[&zJWx_wUWx_&k4_{?zy[^zYpqXT{$phk–iU{’[^]nUpŽZIiUXTi’kûpž¥[^{¢ƒ$XI{UfŽl

pž _£_Wxlbw’[&pqW%X^ž–£_Wxzxpsgj_&k8phk

( cb

pŽ{zY…U_³i¢kmi’[&f;k4_{’k4_³n?lkmXT]_|Wx_ZTpqXT{8­FÁpŽ{’gj_C[^fŽf

[^W\gkJ¡|pqzx…d[^{phƒF_{FzYphg[&ffh[^n’_f¢g[^WYWxlbzx…U_CkY[^]_ùg†…¢[^{UZT_|X^ž¥wUWxXTw’_WxzYpq_&k®u[³fh[&n’_fF][§lbn’_

Wx_wDWx_&k4_{FzY_&ƒ"[Ik|zx…U_b]iUzxi¢[^f8ƒ?p`_¥_Wx_{’gj_bn’_z4¡=__{`zx…U_‰Wx_&k4wo_§gjzxpŽ£_Mk4_zyk|X^ž%wDWxXIw’_WYzxpŽ_&k

$% ' $#&' ^% %$'

X^žùzx…U_k4XIiUW\gj_[&{’ƒzy[&WxZT_zb£_WxzYphgj_&k|X^žù[&{Fl[&Wyg1[IkYkmX?gjps[^zY_&ƒ¡|pŽzx…#zY…’[^zbfh[&n’_fJpq{#zY…U_

ZIW\[^wU…8u [^{’ƒzY…’[^zMWY_wUWY_&km_{?zy[&zxpŽXI{"phk|iU{’[&]nUpŽZIiUXTi’kCƒFiU_$zYX"kmpŽ]wUfŽ_{U_&kYkj­Uœ=…D_$ZIW\[^wU…

]"[l"no_‰Wx_&g®XI{’k4zxWxi¢gjzx_&ƒ ž WYXI]¸zx…D_km_zCX^žH]iUzxi’[&f–ƒFp`_¥_WY_{’gj_§kpž%_&[Igy…#£_WYzx_°¡|…Dphgy…

phk1{UXIz`zx…U_¬XIWxpŽZIpŽ{ X^ž.[^{?l [&Wyg"¡|pqzx… [,ZIpŽ£_{©fh[&no_f³psk

( cb

ž WxXT] zY…’[^zfh[&n’_f

nFl kmXT]_WY_ZIpŽXI{8u–¡|…Uphgy…´]_&[&{’kMzx…’[&z1zx…U_`Wx_ZTpqXI{¦gjXT{Fz\[^pŽ{’k1[^fŽfzY…U_"XIWYpqZIpŽ{’k.X&žMzY…U_

[^W\gk³g[^WxWYlFpŽ{UZ1zx…¢[^zCfh[^n’_fLuUnUiUz|{UXTz³zY…U_‰gjXI{¢kmphƒ?_Wx_&ƒ£_WYzx_°¥­?œ=…U_1k4XILg[^fŽfq_&ƒ

"!$#&%$'

#&% (

kmw’_&g®pž l zY…UXk4_´z4¡=X¦ƒFp_;_Wx_{?z"Wx_&riUpqWY_]_{z\kQX&ž`km_w¢[^Wy[&zxpŽXI{8­VJ…UWx_{Fž _i’gy…Fz

[^{’ƒ¬‚X[W_{?n’_WxZ[&wUwUfqpŽ_&ƒzx…U_bWY_ZIpŽXI{’[&f–[^°?pqXI]kzxXk4XIfŽ£_.zY…U_bk4lF{?zx…U_§kmphk=wDWxXInDfq_]ž XTW

_fq_]_{?zy[^WYlM{U_z\kJpq{6XV%‚CJ*\K­ICpq£_{[.k4pq]wDfq_HƒFpqWY_&gjzY_&ƒ.ZTWy[^wD…fh[&no_fq_&ƒ$XT{[&Wygk®uIzx…U_l

gjXI{¢kmzxWYi’gjzbž WxXI]«zY…’[^zbZTWy[^wD… [&{,_fq_]_{Fz\[^Wxl"{U_z.¡|pŽzx…XI{U_wUfs[Igj_w’_WbWx_ZTpqXI{ uûXT{U_

zxW\[^{’k4pqzxpŽXI{1w’_WJfs[^n’_fLuI[&{’ƒ$¡|pqzY…’X&¡WY_fh[&zxpŽXI{’kªn’_z4¡H__{bwUfh[Tgj_&kJ[&{’ƒ$zxW\[^{’k4pqzYpqXI{¢kªfh[&phƒ

ƒFX&¡|{1[TggjXIW\ƒFpq{DZ|zxX|zx…D_]iUzYi’[^fTƒFp_;_Wx_{’g®_&kon’_z4¡=__{M£_WYzxphg®_&k’km__{¤[Ik–km_z\k;X^žDwUfh[Tgj_&kju

XIW|]"[&Wla?pq{UZvkj­?œ=…U_bg[Ikm_„ZIWy[&wU…"X^ž~zx…U_„{U_z|[Tkxk4_]nDfq_&ƒ$pŽ{zx…Upsk¡ù[§lphk%phk4XI]XTWxwU…UpsgzYX

zx…U_1ZTpq£_{#ZTWy[&wU…,pžH[^{¢ƒXT{Ufql¬pžHzx…’[&zMZIW\[^wU…phk„[^{

/ '1c

$')( ##&%$' ($ ( u

¡|…Uphgy…pq]wUfŽpq_&k8_&kYkm_{?zxps[^fqfŽlbzx…’[&z=zx…D_³z4¡=XbWY_ZIpŽXI{’[&f8[^°?pqXT]"kJ[&Wx_„kx[^zYphkKµ’_&ƒ;­Êz%psk¯¡HXIWYzx…

{UXIzYpq{UZ‰zx…’[&z=pŽ{"g[Ik4_³zY…U_CZIpq£_{ZTWy[^wD…phk%zx…U_„g[Ik4_MZIW\[^wU…`X^ž~[^{`_fq_]`_{Fz\[^WYlM{U_zutzY…U_

gjXI{¢kmzxWYi’gjzYpqXI{#fŽ_&[IƒDkzYX"[

($

£_Wyk4pqXT{X^ž¯zx…’[&zM{U_zuo¡|…U_Wx_$_°FzYWy[1wUfh[Tgj_&k|…’[£_

n’__{[IƒDƒF_&ƒ#¡|pqzx…DXIiUzbƒ?phkmzYiUWxnDpq{UZzY…U_$n’_…¢[§£?pqXTiUWMnUiDzMXI{UfŽl#gjXTwUpq_§k³X^žHzx…DXkm_1wDfh[Ig®_&k

g[^{kmzxpŽfqf?n’_b[IƒUƒ?_&ƒ;­1>³_&k4_f’[^{¢ƒ‚_phkmpŽZMXIn¢km_WY£_&ƒQpŽ{6X>M‚CIa\Dzx…’[&z=XI{D_³]"[lbXIwDzxpq]`pW_

zx…U_¤kmXIfŽiUzxpŽXI{X&žJzY…U_bk4lF{?zx…U_§kmphkJwUWYXInUfŽ_] nFlgjXT]wUiUzYpq{UZ‰[&{FlWx_&ƒ?i’gj_&ƒkm_zHX^ž~Wx_ZTpqXT{’k

kmigjpŽ_{Fz„zxX"_{’k4iUWx_`kx[&zxphkKžL[IgjzYpqXT{´X^žùzx…U_Wx_ZTpqXT{’[^fH[^°?pqXT]"k³pŽ{#zx…U_ZIW\[^wU…8­~ijfqXT{UZ¬[

kmpŽ]pqfs[^WMfŽpq{U_uH<=_WY{’[^W\ƒFpq{D_fqfŽXwUWxX&£_&ƒpq{ X<=_W\IŠ]\Hzx…’[&z$zY…U_"km_z$X^žC]`pq{UpŽ]"[^f–Wx_ZTpqXT{’k

¡b­W­z­–km_zbpq{¢gjfqi’k4pqXT{Cphkb[IƒF_§rti’[&zx_ž XTW$zY…’[^z‰wUiUWxw’Xvkm_­³{Fž XIWYzxiU{¢[^zx_fqlu;zY…UphkMWY_&kmiUfŽz

ƒFX_&k|{UXIz„km__]·zxX1fŽ_&[Iƒ"k4wo_§gjph[&fqfqlzxXwUW\[IgjzYphg[&f8[^fŽZIXTWxpqzY…U]"k=¡|pŽzx…"fqX&¡ gjXI]wDfq_°?pqz4l­

¶_"¡|pqfqfùkm…UX&¡·zY…’[^zk4zy[&{’ƒU[^W\ƒ zx_&gy…U{UpsrtiD_&kMX^žbfŽpq{U_&[&W[^fŽZI_nUW\[fq_&[Tƒ´zxX km]XXTzx…

[^fŽZIXIWYpqzY…U]"k.ž XIW`zx…U_¬kml?{?zx…U_&k4phk$X&ž$n’XTiU{’ƒF_&ƒ©{U_z\kQpŽ{ zx…D_ _°FzY_{’ƒF_&ƒ,ž W\[^]_¡HXIWa´X^ž

! '

"!$#&%$'$(

u¡|…Upsg†…E¡H_Wx_#pŽ{FzYWxX?ƒFi¢gj_&ƒ iU{’ƒ?_W£T[^WYph[^{?zž XIWY]"kQn?lC>CWxXk4zx_ [^{’ƒ

Á…UXTWxzxz X>bÁ?IŠ\Lu’€iaFiD{’ƒUX€iaDIŠ*\Ku’[^{¢ƒE<=_WY{’[^W\ƒFpq{U_fqfqXDu>³_‰€psg†…U_fqphkH[^{’ƒ¬Vª_zYWxiU{Up

X< >MV%TŠ\K­eIC_{U_Wy[^f%WY_ZIpŽXI{’kb[^WY_]iUfŽzxphk4_zyk|¡|…U_WY_WY_ZIpŽXI{’kb[&Wx_"k4_zyk®­8Ä ZT_{U_W\[^f%Wx_

ZIpŽXI{#pq{ [fh[&n’_fq_&ƒ"ZIW\[^wU…#pskM[Q]iUfŽzxphk4_z=X&žH£_WxzYphgj_&k=¡|…DXkm_1W\[^{a"X&ž=]`_]n’_W\km…UpŽwpsk

]X?ƒFpµ’_&ƒnFl`[1iU{Upž XTWx]·zYWy[&{’kmfs[^zxpŽXI{ [^fqXT{UZ`[^fqf–[&Wygk=¡|pŽzx…¬[^{¬phƒF_{FzYphg[&fofs[^n’_fL­;Ápq{’g®_

Wy[&{aUk1X^ž„]_]n’_Wyk4…Upqw[&Wx_¬¡|…UXIfŽ_ {?iU]n’_Wyk®uûiD{Upž XTWx] zYWy[^{¢kmfh[&zxpŽXI{’k1XI{©Wy[&{aDk[&Wx_

ƒF_jµ’{D_&ƒ n?lWx_fh[^zYpq£_M{?iU]n’_Wyk®­UÄ ZI_{D_Wy[&fªWY_ZIpŽXI{psk|[QwDWxXIw’_WYz4l ¡|…Dphgy… ][§ln’_1kY[^

zxpskʵ’_&ƒ"[&zCƒFp`_¥_WY_{FzùƒF_ZTWx__&k®uU]_&[TkmiUWY_&ƒQn?lW\[^{aDk=X^ž~]_]n’_Wyk4…Upqw1X&žJ£_WYzxpsgj_&kj­K{¬[

ƒFi’[&f¡ù[lu;[£_WYzx_°"]"[l"n’_1Wx_wDWx_&k4_{FzY_&ƒ#[IkMzY…U_1]iDfqzxpskm_z|X&žHwUWxXTwo_WxzxpŽ_&kM¡|…Uphgy…pŽz

%3' % # !$% # ( % ' ( #( % % ' (

kx[&zxphkKµ’_&kC[^zCk4XI]_Cw’XkmpŽzxpŽ£_MWy[&{a;­ICpŽ£_{"[1kmpŽ]wUfŽ_CƒFpqWY_&gjzx_§ƒZIW\[^wU…¬fh[^n’_fŽ_&ƒXT{[&Wygk®u

XI{U_g[^{gjXT{’kmzYWxi’gjz¤[^{#pq{¢ƒFi’gj_&ƒ"wUfh[Tgj_$zYWy[&{’kmpŽzxpqXT{#{U_zM¡|pŽzx…¬XI{U_1wUfs[Igj_‰w’_WMZI_{U_Wy[&f

Wx_ZTpqXT{8uoXT{U_$zYWy[&{’kmpŽzxpqXT{w’_WCfh[&no_fKu’[^{¢ƒ ¡|pqzY…#[&Wygk|n’_z4¡=__{"wUfs[Igj_§k|[^{’ƒ"zxWy[&{’kmpŽzxpŽXI{’k

¡=_pŽZI…?zx_&ƒ1n?l1{UXIWY]"kJX^ž–iU{Upž XIWY]ÂzYWy[^{¢kmfh[&zxpŽXI{’kH[^{’ƒ"ƒFpŽWx_&gjzY_&ƒ1[IggjXIW\ƒFpq{UZ‰zxX‰zx…U_„kmpŽZI{’k

X^ž„zx…U_pqW‰ƒF_jµ’{Dpq{UZ¬{FiU]n’_Wyk®­–±³_Wx_`[^Zv[^pŽ{8uªzY…U_wUfs[Igj_zYWy[&{’kmpŽzxpqXT{´{U_zd[IkYkm_]nUfq_§ƒpq{

zx…Upsk¡ù[§l1psk=[‰kx[^zYiUWy[&zx_&ƒ{U_zH[^{’ƒpŽzyk%g[Ik4_MZIW\[^wU…`phkpskmXT]XIWYwU…Uphg=zYX$zY…U_³ZTpq£_{ZIW\[^wU…

pž~[&{’ƒXI{Dfqlpž8zY…’[^z|ZTWy[&wU…¬kx[^zYphkKµ’_&kzY…U_Mz4¡=XbWY_ZIpŽXI{’[&f8[^°?pqXT]"kjuWY_&kmz\[^zx_§ƒpq{zx_WY]"kJX^ž

Wy[&{a_&ƒ]_]n’_Wyk4…Upqw8­

œ=…U_¬XInU4_&g®zX&ž$zY…Uphkw’[^w’_WpskQzYX´wUWYX^£?phƒ?_wUW\[IgjzYphg[&fM[&fqZIXTWxpŽzx…U]"k$ž XIWƒF_&gjpsƒFpq{UZ

kx[&zxphkKžL[IgjzYpqXT{ X^žzY…U_,WY_ZIpŽXI{’[&f‰[^°?pqXI]kpŽ{ [

' #

ZIW\[^wU… [^{’ƒ ž XTW#gjXT]wUiUzYpq{UZ pq{

zx…’[&z"g[Tkm_14i’kmz_{UXTiUZI…EZT_{U_W\[^f|WY_ZIpŽXI{’k1zxXpq{’ƒ?i’gj_¬[wDfh[Ig®_zxW\[^{’k4pqzYpqXI{¦{U_z1¡|pŽzx…

[^{©phk4XI]XTWxwU…Dphgg[Ik4_ZIW\[^wU…8­J¶_fŽ_&[£_Qž XTW$ž iUWxzY…U_W1k4zxi’ƒ?l,w’XkYkmpŽnUfq_"_°?zx_{¢kmpqXT{’k.zYX

w’[^WYzxpsgjiUfh[&Wbgjfs[Ikxk4_&k³X&ž|pq{?µ’{UpqzY_$ZTWy[^wD…’kj­H5UXIWbk4iUWx_vu;[µ’{UpŽzx_‰ZIWy[&wU…phk³{U_£_W³zY…U_g[Tkm_

ZIW\[^wU…¬X^ž~[^{"iU{?n’XIiU{¢ƒF_&ƒ"ó_z­t¶_bk4…’[^fŽf;zx…D_Wx_jž XTWx_bƒ?_&[^f¥_°Ug®fqi’k4pq£_fŽl.¡|pŽzx…n’XTiU{’ƒF_&ƒ

{U_z\kjuU¡|…UXvkm_$wDWx_&gjpskm_bƒ?_jµ’{UpŽzxpqXT{"phk=ZIpŽ£_{pŽ{k4_&gjzYpqXI{¬a?­

¶_1zy[Tg a?fq_‰pq{[µ’Wyk4z‰kmzy[&ZI_`[Wx_fs[^°D[^zxpŽXI{#X&ž|zx…D_kml?{FzY…U_&kmpsk³wUWYXInUfŽ_]¹ž XTW.n’XTiU{U

ƒF_&ƒE{U_z\kju=¡|…Upsg†…²phk`[IƒUƒFWY_&kxk4_&ƒŸpŽ{²km_&gjzYpqXT{ Š,ž XIW"fs[^{UZTi’[^ZT_&kƒF_®µ’{U_&ƒEnFl¦Wx_ZTiUfh[&W

_°?wUWx_&kYkmpŽXI{’k®­’Ä fs[^{UZTi’[^ZT_gjfqXvkm_&ƒiU{¢ƒF_W|fq_®ž z=žL[IgjzYXIWyk|]"[l1n’_$psƒF_{?zxpµ¢_&ƒ¡|pqzY…¬[ƒF_

zx_WY]pq{DphkmzYphg1fh[&no_fq_&ƒ´zxWY__­%‚|_ZIpŽXI{’k1pq{¦[#fh[&{UZIi’[&ZI_#]"[lzx…U_Wx_jž XTWx_"n’_#ƒF_jµ¢{U_&ƒ©[Ik

ZI_{D_Wy[&fWY_ZIpŽXI{’kbpq{#zY…U_iD{’ƒF_WYfql?pq{UZzYWx__v­|žCkmw’_&g®ph[^f%pŽ{FzY_Wx_&k4zMk4pq{’g®_¡H_ƒF_&[^f%¡|pŽzx…

n’XIiU{’ƒ?_&ƒ{U_z\k%[^Wx_CZI_{U_Wy[&f’Wx_ZTpqXI{¢k¯¡|pŽzx…n’XIiU{’ƒ?_&ƒWy[&{a1X^ž–]`_]1n’_Wyk4…Upqw8u¡|…Dphgy…1¡=_

g[^fŽf

% '

"!$#&%$')(

­Tœ=…U_|k4lF{?zx…U_§kmphk–wUWxXTnUfq_] ž XTWJfh[&{UZIi’[&ZI_&kJpskû{UXTzHrtiUpŽzx_%zx…D_Ckx[^]`_

[Ik.ž XTW$fh[&n’_fq_&ƒ#ZIW\[^wU…¢kJzx…D_"kmXTfq_`gjXI{’k4zxW\[^pq{?z$XT{´zx…D_{U_zd[Ikxk4_]nUfq_&ƒ ž WYXI]Wx_ZTpqXT{’k

pq{ [ fs[^{UZTi’[^ZT_phkMzxX¬n’_…’[£_[TggjXTWyƒFpŽ{UZ"zxXzY…’[^zbfs[^{UZTi’[^ZT_uª¡|…Upsg†…phkbk4pqZI{Dp µ¥g[&{FzYfql

¡=_&[*a_W=zY…’[^{`…’[£FpŽ{UZ1[1g[Tkm_MZTWy[&wU…"phkmXT]XIWYwU…UpsgzYX1zx…U_MiD{’ƒF_WYfql?pq{UZbzxWY__­?œ=…Upsk=¡=_&[&

a_W1Wx_§rtiUpŽWx_]`_{Fzbpsk$]_z$pžb[&{’ƒ XI{Dfql´pžMzY…’[^zzxWY__¬kx[^zYphkKµ’_&kzY…U_¬km_&gjXT{’ƒWY_ZIpŽXI{’[&f

[^°?pqXT]#uI¡|…Upsg†…1¡ù[IkXTn’km_Wx£_&ƒ1nFld±³XXIZT_Wyk®u Mfq_p4{[^{¢ƒœ=…Ups[^Zv[^Wy[&Y[^{"pq{zx…U_„gjXT{FzY_°Fz

X^žùzxWy[Tgj_1fh[&{UZIi¢[^ZI_§k X±.œ|Ta]\L­8ÄWx_ZTpqXT{#pq{ [fs[^{UZTi’[^ZT_psk³zxXTzy[&fqfql ƒF_zY_Wx]pŽ{U_&ƒn?l

[^{X*_ km_zuF¡|…Upsg†…phkJzx…D_³W\[^{aX^ž–]_]1no_Wykm…Dpqw$X&ž8zY…U_M_]wDzmlb¡HXIWyƒ¥uF[&{’ƒn?l[.£_&g®zxXIW

X^ž~ƒFpskmwUfs[Igj_]_{?zykju¡|…Dphgy…[&Wx_CWx_fs[^zxpŽ£_={?iU]no_WykJƒF_®µ’{Upq{DZ.zY…U_CiU{Upž XTWx] zYWy[^{¢kmfh[&zxpŽXI{’k

[^zYzy[Igy…U_&ƒzxX$fs[^n’_fskj­UÄCn’kmzYWy[Ig®zxpq{DZ$[$fŽpqzYzxfq_|]`XIWx_vuIXI{U_„]"[l.ž XIWYZI_zù[^n’XIiDz³X*_8k4_zykH[^{’ƒ

gjXI{¢kmphƒ?_W

( i

"!$#&%$')(

ƒF_®µ’{U_&ƒ"[Ik=£_§gjzxXTWykX&žJWY_fh[&zxpŽ£_|{FiU]n’_Wyk®uXIW|l_z%_&riUpq£T[&

fq_{?zxfŽl1[Tk]XTWxwU…Upskm]"k;ž WxXT] zx…U_Cž Wx__|]XT{UXIpsƒQX&£_W~zx…U_„km_zHX^ž fh[^n’_fskJzxX$zY…U_„[IƒUƒFpŽzxpŽ£_

]XI{DXIphƒX^ž~Wx_fs[^zxpŽ£_|{FiD]n’_W\kj­œ=…U_‰[&n’kmzYWy[Ig®z|Wx_ZTpqXI{¢k¡|…Upsg†…"[&Wx_bzx…D_MwUWxXT4_&gjzxpŽXI{’k%X^ž

zx…U_1n’XTiU{’ƒF_&ƒWY_ZIpŽXI{’kCpq{#[Wx_ZTiUfh[&WMfh[&{UZIi’[&ZI_1ž XIWY] []X?ƒFiUfŽ_$X^ž%µ’{Dpqzx_dƒFpq]`_{’kmpŽXI{

$% ' $#&' ^% %$'

X&£_W–­I¶_|¡|pqfqf¢km…UX&¡ zY…’[^zHƒF_§gjphƒFpŽ{UZC¡|…U_zx…D_WH[¤WY_ZIiDfh[^W~fh[^{DZIi’[&ZI_bkY[^zxpskʵ’_§k¯zY…U_Ckm_

gjXI{¢ƒ$Wx_ZTpqXI{¢[^f’[&°FpŽXI] [^{’ƒ1g®XI]wUiDzxpq{DZ³pŽ{$zx…¢[^z%g[Tkm_ù[³n’XIiU{’ƒ?_&ƒQ{D_zª¡|pŽzx…1_&riUpŽ£I[&fq_{?z

n’_…’[£FpŽXIiUW1][§l¬n’_Wx_&ƒ?i’gj_&ƒ,zYX#k4XIfq£?pq{DZ µ’{UpŽzx_fŽpq{U_§[^W‰kmlDkmzY_]"kMX&£_Wbzx…U_pŽ{FzY_ZI_Wykju

iU{Upž XIWx] pq{`zx…U_CWx_ZTiUfh[&W=_°?wUWY_&kxk4pqXI{ ­t¶_M_£XTfq£_|zY…U_Wx_®ž WxXI] [bwUWy[Tgjzxpsg[^f¥]_zY…UX?ƒdž XTW

zx…U_`kml?{?zx…U_&k4phkMX^žùn’XIiU{’ƒ?_&ƒ,{U_z\kju;n¢[Ikm_§ƒ,XI{

b %3' % #

[^fŽZIXTWxpqzY…U]"kMƒ?phkxg®X^£_Wx_&ƒ"pq{

zx…U_`fh[^zY_k4_£_{?zxpŽ_&kùž XTW$fŽpq{U_&[&WbwUWxXTZIWy[&]]pŽ{UZX&£_Wbzx…U_Wy[&zxpŽXI{’[&fµ’_fsƒ;­8ijfŽzxXTZI_zY…U_Wu

¡=_XTnUzy[&pq{¦[ w’XTfql?{UXI]ps[^fH[^fŽZIXTWxpqzY…U]«ž XIW1zx…D_"kml?{FzY…U_&k4phkMX^ž„{U_z\k¤ž WxXT] WY_ZIiDfh[^W‰_°?

wUWx_§kxkmpŽXI{’k$pŽ{´zx…D_"kmXTKg[&fqfŽ_&ƒžL[^pŽfqiUWY_&kMzxWY__Qž XTWx]

¡|…Upsg†… pq{´w’[&WxzYphgjiUfs[^Wb]_&[&{’kMzx…U_l

[^WY_MWx_wDWx_&k4_{FzY_&ƒ1nFlzxWY__&kJfh[&no_fq_&ƒ¡|pŽzx…"[TgjzxpŽXI{"k4lF]n’XIfsk[&{’ƒk4zy[^WYWx_&ƒ_°FwDWx_&kYkmpqXT{’k \­

¶_z\[Ig aFfŽ_ pŽ{E[´k4_&gjXT{’ƒEkmz\[^ZI_#zY…U_#ZI_{U_Wy[&fMk4lF{?zx…D_&kmpskQwUWYXInUfŽ_] ž XIWn’XTiU{’ƒF_&ƒ

{U_z\kjuª¡|…Dphgy…´phk‰[IƒUƒFWY_&kxk4_&ƒ´pq{©k4_&gjzYpqXI{©"ž XIW$µ’{UpŽzx_"[&iUzxXT]"[^z\[F­%Ápq{’g®_¡=_"[&Wx_n¢[Ig a

pq{#zY…U_.ž W\[^]_¡HXIWa X&žHfh[^n’_fŽ_&ƒ ZTWy[&wU…’kju8zY…U_.µ’W\kmzMWY_ZIpŽXI{’[&f%[^°?pqXT]¸phk³WY_ÑpŽ]w’Xk4_&ƒ;­’Ä

ZI_{D_Wy[&fWY_ZIpŽXI{pq{[µ’{UpŽzx_[&iUzxXT]"[^zYXI{phkbƒF_zY_Wx]pŽ{U_&ƒn?l#[^{ X]_ km_zu8¡|…Uphgy…#phk³zY…U_

Wy[&{a,X&ž|]_]n’_W\km…UpŽw X&žCzx…U_pq{Dpqzxps[^f%k4zy[&zx_u–[^{¢ƒ,nFl [ £_&g®zxXIW„X^žCWx_fh[^zYpq£_‰{FiU]n’_Wyk

¡|…Uphgy…¬[IkYkmX?gjps[^zx_‰iU{Upž XIWx] zxW\[^{’k4fh[&zxpqXT{’k|zxXfh[^n’_fskj­DÄ WY_ZIpŽXI{"pq{¬[.µ’{Dpqzx_‰[&iUzxXT]"[^zYXI{

phkb[^fŽ¡|[lDkM[Wx_ZTpqXI{#pŽ{#zx…U_fh[&{UZIi¢[^ZI_X^žùzx…U_[&iUzxXT]"[^zYXI{8u¥nUiUzbzx…U_g®XI{?£_Wyk4_$phkC{UXIz

zxWYiU_­¥œ=…U_km_z„X^žù[^n’k4zxW\[IgjzbWx_ZIpqXT{’k³pŽ{#[µ’{UpŽzx_1[&iUzxXT]"[^zYXI{#pskM[kmiDnU]X?ƒFiUfŽ_$X&ž=zY…U_

]X?ƒFiUfŽ_X^ž.[^n’k4zxWy[Tgjz1Wx_ZIpqXT{’k1pq{´zY…U_"fh[^{DZIi’[&ZI_X&žMzY…U_¬[^iUzYXI]"[&zxXT{8­%œ=…U_¬[^n’k4zxW\[Igjz

Wx_ZTpqXT{’k$¡|…Uphgy…©[&Wx_wUWYXI4_&gjzYpqXT{’k.X&žMn’XIiD{’ƒF_&ƒ©Wx_ZTpqXI{¢k$[^WY_"zx…U_"k4XIfŽiUzxpŽXI{’k$X&žb[¬kmlDkm

zx_]«X&žCfqpŽ{U_&[^Wb_&ri’[&zxpqXT{’k.¡|…Dphgy…,_°?wUWY_&kxkM_&ri’[^fŽpqz4l#g®XI{’k4zxWy[&pq{?zykbWx_fs[^zxpŽ£_1zxX kmzy[&zx_&k®u

kmzYWxXI{DZI_WMpŽ{"ZI_{U_Wy[^f8zY…’[^{¬zx…U_bn’XIiD{’ƒF_&ƒF{D_&kxkMg®XI{’k4zxWy[&pq{?zyk=WY_fh[&zxpq£_„zxXzx…U_bfh[&{UZIi¢[^ZI_

X^žHzx…D_1[^iDzxXI][^zxXT{8­¥Ä³fqzYXIZI_zx…U_WuUXI{U_1WY_zxWYpq_£_§kzx…D_1gjXT{’kmzYWy[^pŽ{Fz\kMkm_z³XT{

($3'

%$' #

$#( c$' (

pq{ XZ< >MV%IŠ]\LuU¡|…Uphgy…"k4…UX&¡CkzY…’[^z„[^n’k4zxW\[IgjzCWx_ZTpqXT{’k|[^WY_.pŽ{¬[QXT{U_ XI{U_dgjXIWY

Wx_&k4w’XI{’ƒF_{’gj_¡|pqzx… kml?{’gy…UWxXT{Uphg‰ƒFphk4zy[&{’gj_&k®­8œ=…U_`[IƒF£T[^{?zy[&ZI_X&ž|zY…U_1]XIWY_1[&fqZI_nUWy[&phg

£FpŽ_¡ z\[]a_{#…U_Wx_$psk³zxX`fq_&[TƒƒFpŽWx_&gjzYfqlzYX"[^fŽZIXTWxpqzY…U]"k®­o¶_$¡|pŽfqf~km…UX&¡zY…’[^z¤ƒF_&gjpsƒFpq{UZ

¡|…U_zY…U_W„[dµ’{Dpqzx_‰[&iUzxXT]"[^zYXI{kx[&zxpskʵ’_&k|zx…D_.z4¡HXWY_ZIpŽXI{’[&fJ[&°FpŽXI])[^{’ƒ"zx…U_{#gjXT]wUiU

zxpŽ{UZ¬[ n’XIiU{¢ƒF_&ƒ,{U_zM¡|pqzY…,_&riUpŽ£I[&fq_{?zMn’_…’[£?pqXTiUWu;WY_&ƒFi’g®_[^Z[&pq{´zYX#k4XIfq£?pq{DZµ¢{UpqzY_

fqpŽ{U_&[^W~kmlDkmzY_]"k’X^£_W8zx…U_HWy[^zYpqXT{’[^fµ’_fsƒ;uiU{Upž XIWx]OpŽ{.zY…U_|[&iUzxXT]"[^zYXI{8­TijfŽzxXIZT_zx…D_Wu®¡=_

XInUz\[^pŽ{#[1woXTfql?{UXI]`ph[^f [^fŽZIXIWYpqzY…U]ž XIW|zY…U_‰kml?{FzY…U_&k4phk=X^ž¯{U_zykž WYXI]µ¢{UpqzY_$[&iUzxXT]"[^z\[F­

- J1,) bJ|¦- b

¶,_d[IƒFXTwUzMpŽ{zx…Dphk|w’[^w’_W„[{UXTzy[^zYpqXT{ ž XIW¤V¯fs[Igj_&œ8Wy[^{¢kmpqzYpqXT{{U_z\k³k4fqpŽZI…?zxfqlƒFp`_¥_WY_{Fz

ž WxXT]¹zY…U_bi’kmi¢[^f8XI{D_Uzx…Upsk|km…UXTiUfhƒ"{UXIz„g[&i’km_‰gjXT{Fž i’kmpŽXI{8­

%3' % # !$% # ( % ' ( #( % % ' (

"»

#

%h—*% ¿

# ( !l)

»t—&• {U_z

#( ( i

$'

$#( %$#&' ( &( %

wUfs[Igj_§k

$'

zxW\[^{’k4pqzYpqXI{¢k ( b .# $'

#(8

¡=_pŽZI…?z

$ ' .#&%$' ( %

pŽ{UwUiUz"!

( b

FXTiUzxwUiDz$#

b2 ( %:

$')( ##&%$'&%

#(8 ( (')%

!

( b

%*'

#

% b2 (,+($

+ %

.- J/!

( b + %

,0CJ1#

]"[^WaFpŽ{UZ

% #(9 Kib32

4 5

6879*:,;1<=7>?:>?;A@B@DCE7GF>IHDJKJ?7GL3MNHD9=OP;RQ?STMU<=7)@V;T9HDSW"XZYU[]\_^a`bdca[e`U^f\gb

;TW?L;8Mh7)HDiOI9kj>KW?l)9HDSWnm oXqpsruthvxwy"7.l;TWn;LISJK9kOK7<=7.;.znS{<=7hl)Sz|J?;l)9

WKS9*;19HDSWf}?7Gl;T>?:7~MN7nl)SW?:HVLI7<7)€l$@D>?:HD7)@DCƒ‚…„‡†ˆWK79):‰ŠHewu7wŠWK79*:g:>?l$O"9=O?;T9

‹…ŒŽ)n \/cn` [ ŒŽ* b  X’‘“[ ”*Œ bh• Xw

œ=…U_MX&£_W\[^fqfDno_…’[£FpŽXIiUW%X^ž~[‰VJfh[Ig®_ &œ8Wy[&{’kmpŽzxpqXT{{U_z%pskƒ?_zx_WY]pq{D_&ƒ.n?l1zx…U_„kmXTKg[^fqfŽ_&ƒ

#&'3!

¡|…Upsg†…zx_fqfhk–zx…’[&z=[bzxW\[^{’k4pqzxpŽXI{phkJ_{’[&nUfq_§ƒ1[^z|[M]"[&Wla?pq{UZ„pž8zY…’[^z%]"[&Wla?pq{UZ

kmiUwDwUfqpŽ_&k=_{UXTiUZI…¬Wx_&k4XIiUW\gj_&k=pq{"_&[Tg†…"X&ž%pqz\k=pq{UwUiDz|wUfh[Tgj_&kj­

"»

#

%h—*% ¿

# ((/lB

% ˜*%

#

0,˜ 2Ñ»Š

x –

]

8 ' $'~— K

)˜

#&'3!

%n š™

$')( ##&%$'3%›

#(

_{¢[^nUfŽ_&ƒ

.2 #œŽ+ž›

— +

NŸ

+ %

  J 5

$')( ##&%$'&% #( '

E K

)˜

#&'3!¡— '# $'

)™ #&'6$%$#&'3!/( % # b

%* (

' ¢ K

)˜

#&'3!a—Z£ '

|œŽ+¤›

—Z£

+

¥—

+

(Ÿ

+ % #(

#&'3!

( b #( ' % f—

X% 0 — £

( *¦@ ' %.

$')( ##&%$')(¨§©%*ª)%*«k¬T¬T¬%=­*#( '

8EK )˜

#&'3!"—® #°¯…—©ª

­­­

—­ ($ U—±³²?ª

X

%=±

0

—± %

(´

‹

­­­

µ

#(

#&'3! ( *¦@ ' #(: ' % &—®

X§ 0

—­

¶E…UpqfŽ_Mzx…D_.X&£_W\[^fŽf;n’_…’[£?pqXIiDW|X^ž¯[VJfh[Tgj_ §œûW\[^{’k4pqzxpŽXI{"{U_z|WY_ ’_&g®zykpŽzyk=¡|…UXTfq_‰kmzYWxi’g®

zxiUWY_u8XI{U_`phk.]`XkmzbX&ž zx_{´pŽ{FzY_Wx_§kmzx_§ƒpq{Wx_&k4zxWxpsgjzx_§ƒn’_…’[£?pqXTiUWykbpq{’ƒFi¢gj_&ƒ#nFl#pŽ{UpqzYph[^f

]"[^WaFpŽ{UZk®­

"»

#

%h—*% ¿

# ('¶

1O™U˜·’»FÀ

#

»—I ]"[&Wla_&ƒ

' ,#( ( i ¸ –

,

—®

¹ºG

#( ' =$'f—®

» 5 #(K

pq{Dpqzxps[^f–]"[^WaFpŽ{UZ

( %

Wx_&[Tg†…¢[^nUfŽ_.][^Wla?pq{DZk

%¼ #(9 ($K^ ( ( N½

%9K

¹˜

#&'3! ( ($ E

¾ — ® ›š½

¿ #¼— ›À½

$'¡—

X% 0

—Á£e 'f—Z£›š½

]"[^WaFpŽ{UZZTWy[&wU…

%a #(

$')( ##&%$' ($(

µÃÂ

#0( %

( c (a½

#&' ##( c ¡— ® ( +%

(

=$'( %.

$')( ##&%$')(

gÄ

,Å

½

šÁ

½ '

— % — £ ›

Ä

Æ

— X% 0 — £

fh[&{UZIi’[&ZI_

%' %

*¦$ #@ ' E

$'3!1! % 8K

)˜

#&'3! ! ib

µÃ #( ( % ( *¦$ ' ( %

$')( ##&%$')(

'

EN— ® !

3(9 #( $'3!1! #( b i% (

#

$% ' $#&' ^% %$'

|ž|k4w’_&gjph[&fªpŽ{FzY_Wx_§kmz|pq{#zY…Uphk|w’[&wo_Wb[^WY_1]"[^Wa_&ƒ{U_zykC¡|pqzx…"µ’{UpŽzx_1k4_zykCX^žHWx_&[Tg†…¢[^nUfŽ_

]"[^WaFpŽ{UZk®­UÄ Wx_fh[^°?_&ƒQž XTWx]¸X^ž–µ’{UpŽzx_{D_&kxk=]"[ln’_$ƒ?_jµ’{U_&ƒ"[Tkùž XTfqfqX&¡Ck®­

"»

#

%h—*% ¿

# (A¶

¿ # À–»FÀ

#

»—I

b2 Ž+% 8K

¹˜

' Š –

]

— ®

#(

n’XIiU{’ƒ?_&ƒ

# ( —

+

— ›š½

#( ' #

K )˜

' .#

% '

b2 ( #(

n’XTiU{’ƒF_&ƒ

'

>³WxXvkmzY_[^{’ƒ,Á…DXIWxzYzMXIn¢km_WY£_&ƒpq{ X>.Á?Ta]\–zx…’[&zb[n’XIiD{’ƒF_&ƒ#{U_zC¡|pqzY… µ’{UpŽzx_fŽl]"[&{Fl

zxW\[^{’k4pqzxpŽXI{’kM]i’kmzC…’[£_1[µ’{Dpqzx_k4_zMX&ž|Wx_§[Igy…’[^nUfŽ_$]"[&Wla?pq{UZvkj­¥±³_{’g®_1[^{?ln’XTiU{’ƒF_&ƒ

{U_z|¡|pŽzx…µ’{UpŽzx_‰ƒFpq]`_{’kmpŽXI{][§l1n’_‰zxWy[&{’kʞ XTWx]_§ƒpq{?zxX[$µ’{UpŽzx_b_&riUpq£T[^fŽ_{?z{D_z­

b«& .*1E#*#1 $

œ=…U_$ZTX[&fªX&žJzY…U_‰km_&gjzYpqXT{ psk=zxX`kmXTfq£_MzY…U_Mž XIfqfŽX&¡|pq{UZ1wUWYXInUfŽ_]

-b˜^¿’” 2Ñ»

'¸ !

# 'C b

i% ( $'3! !

Å

9 # ž

#( &(. K )˜

' #6$'3!1! $' # ( % %$'$( ($ 6 '

¶,_|¡|pŽfqf?wUWx_§km_{?zJ[Mw’XIfŽlF{DXI]ps[^fD[^fqZTXIWYpqzx…D]¡|…Upsg†…d[^{’k4¡=_W\kªzx…UpskªwUWYXInUfŽ_]‡ž XTWJWx_ZTiUfh[&W

fh[&{UZIi’[&ZI_&k®­%œ=…U_n’[Ik4phggjXT{’kmzYpqzYiU_{?z.X&žCzx…U_wUWYXIw’Xk4_&ƒ©kmXIfŽiUzxpŽXI{´pskMzx…U_wDWxpq{¢gjpqwUfŽ_1X^ž

[^n’k4zxW\[IgjzHWx_ZTpqXI{¢k¡|…Upsg†…]"[l$pŽ{QžL[Tgjz%no_¤[^wUwUfŽpq_&ƒ1zxX‰[&WxnUpŽzxWy[&Wxlfh[&{UZIi’[&ZI_&k®­F¶_Mk4…’[^fŽf

zx…U_Wx_jž XTWx_1g[IkmzCzx…D_$ƒ?_jµ’{UpŽzxpqXT{X&ž%Wx_ZTpqXT{’kpŽ{¬[ZI_{D_Wy[&f–gjXI{?zx_°?zu’[&{’ƒk4iUn’k4_&rtiD_{FzYfql

ž X?gji’k|XI{¬Wx_ZTiUfh[&W|fh[^{DZIi’[&ZI_&k®­

œ=…UWYXIiUZT…UXIiDzMzx…U_‰k4_&gjzxpŽXI{8u?fq_z

ƒF_{UXTzx_d[

b

i% (

fh[&{UZIi¢[^ZI_‰X&£_WC[dµ¢{UpqzY_

[^fŽwU…’[^n’_z

ӻ

­­­

­

u8Wy[&{UZI_§ƒ,X&£_WbnFl

u [^{’ƒ,ž XIWd[^{?l,][^w

–u

fq_z

¦ƒF_{UXTzx_zx…U_`]XI{UXTphƒ]XTWxwU…Dphkm]

§

§

hŸ!

y­8œ=…?i’kbpq{

w’[^WYzxpsgjiUfh[&WJ

›

yuU¡|…U_WY_"

#

§

$

§"›%

­

&('*) +!,.-$/*021435/1762098;:<9=?>@<91-$A4<B-C,.3

ij{¦[^n’k4zxW\[Igjz1WY_ZIpŽXI{©pq{©[wDWx_jµ’°?LgjfqXvkm_&ƒ,fs[^{UZTi’[^ZT_

X^£_W1[^fŽwU…’[&no_zÂphk1[]XTWx

wU…Upskm]·ž WxXT] zxX –u;kY[^zxpskʞ l?pq{UZzx…D_$Wx_§rtiUpŽWx_]`_{Fz%zY…’[^z

k4…UXIiDfhƒn’_$]"[&wUw’_&ƒ zYX

[^{¬pq{?zx_WY£I[&f;X&ž¬noXTiU{’ƒF_§ƒž WxXT]Ân’_fŽX&¡b­ Lž–XT{U_bpq]"[&ZIpŽ{U_&kzY…U_M]XTWxwU…Dphg³pŽ]"[^ZT_³X&žH[

¡=XTWyƒpq{

[IkzY…U_M]_§[IkmiDWx_CX^ž–£T[^WYph[^zYpqXT{X^ž~[&{"[^n’k4zxW\[Igjz|WY_&kmXTiUWygj_Czx…DWxXIiDZI…¬[$ƒF_zx_WY

]pq{DphkmzYphgMwUWYX?gj_&kxk®u8zx…U_1WY_&rtiDpqWx_]_{?z=ZIi¢[^Wy[&{FzY__&kMzx…¢[^z‰kmz\[^Wx£T[&zxpqXT{,][§l"n’_`[§£XTphƒF_§ƒ

%3' % # !$% # ( % ' ( #( % % ' (

ZIfŽXIn’[&fqfqlbn?lMž __&ƒFpŽ{UZ³pŽ{b_£_Wxl„wUWxX?gj_§kxkªpŽ{

¡|pqzY…1[µ¢°F_&ƒ‰[^]XTiU{?z8X^ž¥pq{UpŽzxps[^fWx_§kmXIiDWygj_­

<=XIiU{¢ƒF_&ƒ"[^n’k4zxW\[IgjzCWx_ZTpqXT{’kju?¡|…Uphgy…"¡|pqfqf’wUfs[l"[^{"_&kYkm_{?zxps[^f;WYXIfŽ_Mpq{"XIiDWCkmzxi¢ƒFlX^ž~Wx_

ZIiUfs[^W|fs[^{UZTi’[^ZT_&kju’kY[^zxpskʞ lzY…U_bk4zxWxXT{UZI_W|Wx_&riUpqWY_]_{?z–zx…’[&z

k4…UXIiDfhƒn’_.][^wUw’_&ƒzYX

[Qµ’{UpŽzx_‰pq{?zx_WY£I[&fªX&ž Ju’Wx_ ’_&gjzYpq{UZ1zY…U_1pq{?zxiUpŽzxpŽXI{"zx…’[&zb[fs[^{UZTi’[^ZT_gjXI{’k4phƒF_Wx_&ƒ¬[Ikb[

{UXI{DKƒF_zx_WY]pq{UpskmzYphg|wUWxX?gj_§kxkCg[^{"XI{Dfql"wUWxX?ƒ?i’gj_‰[Qn’XTiU{’ƒF_&ƒ¬[^]XTiU{?z=X^ž¯Wx_&k4XIiUW\gj_­

"»

#

%h—*% ¿

# '¸(/

»102%Ñ¿

#

•1¿+M™ 2љ

# 0 –™0’»Ã Wx_ZTpqXT{

% #( EKib

;

($ ( $

›

(.$' #&' K1

noXTiU{’ƒF_§ƒ

"!$#&%$' %

#(

"!$#&%$'

%4 ($ 6 ( C

¥›

( ( % /($@b

K1

( b

' % 9 ( %

"!$#&%$')( ( b

% '

"! #&%$')( %(

œ=…U_C[^fŽZI_nDWy[^psg=wUWxXTw’_WxzYpq_&kªX&ž [^n’k4zxWy[TgjzJWY_ZIpŽXI{’kª¡|…Dphgy…$ž XIfqfŽX&¡´pq]]`_&ƒFpŽ[^zY_fql=ž WYXI]zY…U_

ƒF_jµ’{DpqzxpŽXI{¬[^WY_bZ[^zY…U_WY_&ƒ n’_fŽX^¡b­

B

™UšI—

'¸^'

( (

$'

i% ( '

b %$#&' #( ($1 %8Kib ( $'

'

"!$#&%$'

® # %$')( $'.@

® J #( '

, / ' %

($

%

%K

(

#( i% ( '

#&'Š

( (

¡

3(

#( %$' %$# $'

#(:$'Y

#$' !

%&b

ÄMkJ[&fqWx_§[IƒFlbXIn¢km_WY£_&ƒ.pŽ{ X< >„VTŠ\KuzY…U_|n’XIiU{’ƒ?_&ƒ$Wx_ZTpqXT{’kªX^ž [³fs[^{UZTi’[^ZT_³X&£_W–[&fqwU…¢[^

n’_z [^Wx_["k4iUnUZIWYXIiUw X^žHzx…U_1ž Wx__1[^n’_fŽph[&{,ZTWxXIiDw,X&ž|]"[&w’kž WxXT]7zYX –u;¡|…Dphgy…

phk$µ’{UpŽzx_fŽl,ZT_{U_W\[^zx_§ƒk4pq{’g®_ ·psk.µ’{UpqzY_­%ÄMk1[gjXI{¢km_&riU_{’g®_u phk[^fhk4X´[ž Wx__

ZIWYXIiUw¡|pŽzx…`[³µ’{UpqzY_Mk4_zJX&ž–ZI_{U_Wy[^zYXIW\kju¡|…Uphgy…1phkJz\[^{?zy[^]`XIiU{?zJzxX‰[b]X?ƒFiUfŽ_=X^ž8µ¢{UpqzY_

ƒFpq]`_{’kmpŽXI{"X&£_W –­ Ê{¬XIW\ƒF_WMzYXWx_&g®X^£_W

%$'

Wx_ZTpqXT{’kž WxXT]

( i

WY_ZIpŽXI{’k®u

pqz„kmigj_&k|zxX[^zxz\[Igy…#zxX_§[Igy…[&n’kmzYWy[TgjzbWx_ZTpqXI{ › zY…U_$]`pq{UpŽ][&f

% ( h—

kmi’gy…©zx…’[&z1[&{Fl´w’XvkxkmpŽnUfq_ƒFphk4wUfh[Tgj_]_{?z §

¤[IkYkmX?gjps[^zx_§ƒ¡|pqzY…©kmXT]_¡=XIW\ƒ

§Z›#

fq_&[TƒUkzY…U_WY_jž WxXT] zxX1[b{UXI{`{U_Z[&zxpŽ£_|£I[&fqiU_

—

ŠŸ# §

\­Fœ=…D_Mzx_WY]

"!$#&%$'

pski’k4_&ƒ

pq{¬[^fŽf8zx…U_‰k4_&rtiD_f8[Tk³[&{#[^nDnUWx_£?ph[&zxpŽXI{ž XIW

( i

"! #&%$'

­

¶_#[&Wx_{DX^¡¸pŽ{E[#woXvkmpŽzxpqXT{EzxX©ƒ?_WxpŽ£_ ][^Wla_§ƒ,{U_z\kQž WxXT] wDWx_jµ’°?LgjfqXvkm_&ƒ©fh[^{D

ZIi’[&ZI_&k FzY…U_MzxW\[^{’k4pqzYpqXI{¢k[&Wx_MzY…U_„kml?]n’XIfskªpq{zx…D_M[&fqwU…’[&n’_zu?zx…U_CwUfh[Tgj_&k%[^WY_³WY_ZIpŽXI{’k®u

[^{’ƒ"zx…U_b¡H_pqZT…Fz=ž iU{¢gjzxpŽXI{’k|[&Wx_‰km_z|pŽ{¬[^ZIWY__]_{FzH¡|pqzx…"zY…U_b£I[&fqiU_§k=X^ž%WY_ZIpŽXI{’k®­

"»

#

%h—*% ¿

# '¸A¶l)

»t—&•1À–»?˜]%¥»FÀ +4˜&¿ 2љ

# 0 ª™0o»?•{

¾

f

kY[^zxiDWy[^zY_&ƒ1{U_z

#

% #( '



—

h

%

$

›

$'¡—

pq{Fž

§

$

§"›%