HAL Id: inria-00074013
https://hal.inria.fr/inria-00074013
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de
Using Singular Displacements for Uncalibrated Monocular Visual Systems
Thierry Viéville, Diane Lingrand
To cite this version:
Thierry Viéville, Diane Lingrand. Using Singular Displacements for Uncalibrated Monocular Visual
Systems. RR-2678, INRIA. 1995. �inria-00074013�
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
Using Singular Displacements for Uncalibrated Monocular Visual Systems
Thierry Vie´ville and Diane Lingrand
N˚ 2678
Octobre 1995
PROGRAMME 4
0 ##1',32&456 879:
;=<->@?BAA*CEDF>HGJIK>@LHL@?MON P6Q9>RMON:?ST>@N-UVAWMON P
X:Y[Z$\$Y^]W__`/acb d'ZfegZWh[ikjJlm`Wnoip_=]q\f`/`rhsJikt[ikZfu
X-Y[ZWv[`rhwd'ZfegZqh[xyikt
dT]qzmz{Z$YRh|m`Y[`~}m`*Y[}m`u(J$ oqyb }rh^ZfemY[`$f/b $(zO]W\$`*t
=Wf
uh^m`zY[`~t`~u$hz]qz{`*Yn`8Y[`rsJik`]qum| }*Zf_zB¡k`rh^`=h^m``*jJl]¢h[ipZ$umt]Wu|£h^m`¥¤¦ZfY[_=]¢¡§ikt^_¨TBip}
]¢¡§¡kZ©h^Zª]q}oip`rsf`9]_ikuBip_=]¢¡wz]qY^]q_¥`rh^`*YRik«¢]¢h[ikZfu¬Zq¤wh^m`Y[`rh[ipuO]¡T|BiptzB¡®]q}*`*_¥`*u$h¤¦ZfY=]_Z$umZB}*lB¡¯]WY
sJiptl]¡t[°Bt[h^`*_©'i§h^ZflBhT}]¡±ipeY^]h[ikZfuV²
³ Z$umt[ik|m`*YRipum\h^m`5`*_¥`*Y[\$`*um}*`,ZW¤´]W}rh[i±sf`/sJikt^l]¢¡4t[°Bt[h^`*_t¤¦Z$YTBik}µ` $¶·¶¸m }*Z$umt[ik|m`*Yh^]¢h
h^m`+}]¢¡§ikemY^]¢h[ipZ$u(z]qY^]q_¥`rh^`*Y[tK]qY[`+`ri§h^m`*Y¹ouZwu5ZfYºB»m`*|¼n¢`½|m`rsf`r¡pZ$zc]qu(]¢¡§h^`*Y[u]¢h[i±sf`t[h^Y^]¢h^`*\W°,lt[ipu\
h^m`T¤@]q}h+h^O]h}*`*YRh]iku8}r¡¯]Wt^t+Zq¤t^zg`~}ri¯]¡g|Bikt^zB¡¯]W}*`*_`~u$h^t+ikum|ml}~`*t`*umZ$lm\$=`*jolO]h[ikZfut+h^Zc`rsW]¢¡plO]h^`Th^m`
}]¡±ikemY^]h[ikZ$u8z]qY^]W_`rh^`*Y[t~nBtZ(h^]¢h`}]WuY[`~}*Zs$`*Y+h^m`,]¢¾u`/ZfY¿-lm}r¡±ip|m`]qu8t[h^Y[lm}rh^lmY[`ZW¤h^m`/t}~`*um`
w`~uum`*`*|m`*|¼²
À
t[°Bufh^`~tiptZW¤w]¢h1}]quÁeg`Y[`*}~Z~sf`*Y[`*|Á¤¦Z$Yt[ikum\$lB¡¯]WY8|oipt^zo¡®]q}*`~_`*u$h^t8ikuÁh^`*Y[_t9ZW¤5}¢]q_`*Y^]
}]¡±ikemY^]h[ikZ$u¼n+t}~`*um`µ\f`*Z$_`h^YR°Â]qum|¬¹fikum`*_=]h[ik}*tiptzmY[Z$zgZft^`*|¼²£Ãª`µ\Wi±sf`Wn ¤¦ZfY5h^m`|Bi±Ä¼`*Y[`*u$h=¡p`rsf`r¡kt
Zq¤½}]¢¡§ikemY^]¢h[ipZ$u¼n¼]Wu`»]qlmt[h[i±sf`5¡§ikt[h/ZW¤´h^m`\$`~Z$_`rh^YRip}]Wu|¹fikum`*_=]h[ik}5ipuB¤¦Z$Y[_=]h[ikZ$u9wBik}}]que{`
Y[`*}*Zsf`*Y[`*|¼²µÅmZq¡§¡kZ'ipum\9]µt[h^Y^]h^`*\q°e]qt^`*|Zfut^z{`*}ri¯]¡-¹fikum| ZW¤|oipt^zo¡®]q}*`~_`*u$h^t~nt^lm}ª]qtº»`~| ]¢»oikt
Y[Zqh]h[ikZfutZ$YzmlmY[`yh^Y^]Wumt¡®]¢h[ipZ$umt½¤¦ZfY½ipumth]Wum}*`Wno`,|m`*t^}*YRike{`,ZÆh^Z¥|`h^`*}rhTh^BiptTz]qYRh[ip}*lB¡¯]qY}r¡®]qt^t^`*t
Zq¤K|Bikt^zB¡¯]W}*`*_`~u$h~²
Çm`5ip_zB¡k`*_`~u$h]¢h[ipZ$uZq¤´h^m`*t^``~jJl]¢h[ikZfumtikt,]qu]¡±°B«*`~|`~Y[`=]qum|h^m`Y[`]¢¡§ik«]h[ikZfuikt,Y[`*z{Z$YRh^`*|
]qtw]t[ikum\W¡k`/_ZB|mlB¡k`WnBh^Z=eg`/`*_(eg`*|m|m`*|iku9]coip\$BÈ@¡k`rsf`r¡R_]q\$`,Éwu|m`*Y[t[h]Wu|Bipu\¿-u$sJipY[Z$um_`*u$h~²
ÊËfÌVÍ[θÏ$Ð
h^Y[lm}rh^lmY[`]Wu|FÑ9Zqh[ipZ$u¼n
Ð
ikum\$lB¡®]qYÒTikt^zB¡¯]W}*`*_`*ufh^t*n
Ð
`¡±¤¯È
³
]¡±ikemY^]h[ikZ$u
ÓkÔÕ@ÖRר'Õ+ÙKÚÛÖRܦÝÞ
87F¼ / 2& # ©(*)/
J
³
`8z]qzBik`*Y(`*t[hclum`8Y[`rsBlm`Wn´}*Zf_zB¡rh*`8|m`8|rs$`¡kZ$zmz{`*_`*u$h^tcumZ$lBs$`¢]qlo»Vn´|`~t*jJl]h[ikZ$umt(`rh|ml
¤¦Z$Y[_]¢¡±ipt^_`,jJlBi-z{`*Y[_`rh[h^`*ufh/|Z$eBh^`*uBipYTlmum`5z]qY^]W_rh^YRipt]h[ikZfu_ipuoip_=]¢¡p`5|ml9_¥Z$lBs$`~_`*u$h/Yh[ikuBik`*u
zgZflmY'lmut°th~_`/sJikt^lm`r¡4_ZfuZB}~lo¡®]¢ipY[`umZ$u}¢]¢¡±ipemYW²
³ Z$umt[ik|*Y^]Wu$h¡*_`~Y[\$`*um}*`c|`ct[°Bt[h*_`*tsJipt^l`¡kt,]q}h[i±¤¦t/zgZflmYT¡k`*t^jJlm`r¡pt/Z$uum`z{`*lBh,zo¡plmt/}*Z$umt[i±È
|*Y[`*Y+jJlm`¡k`*t+z]qY^]W_rh^Y[`*t+|m`w}]¢¡§ikemY^]¢h[ipZ$u=t^Z$u$h½}*Z$umuJlmt+uBig_*_`}*Zfumth]Wu$h^t~nfZfu|rsf`r¡kZfzz{`Tik}iglmum`
t[h^Y^]¢h*\Wik`/]¡±h^`*Y[u]h[i±sf`e]qt*`t^lmY´¡k`T¤@]i±hjJlm`/|m`*t}r¡®]qt^t^`*t+z]qYRh[ik}~lo¡§i*Y[`~t½|m`/_ZflBs$`*_¥`*u$hzg`*Y[_¥`rh[h^`*u$h
|m`\~u~Y[`*Y]qt^t^`*«T|~jJl]¢h[ikZfumt½z{Z$lmYrsW]¡klm`*Y+¡k`*tz]qY^]W_rh^Y[`*t|m`}]¡±ipeY^]h[ikZfuVnBzg`*Y[_¥`rh[h]qu$hw]ikumt[iV|m`
Y*}*lmz*Y[`*YÈ t[ie{`*t^ZqikuBÈ:¡¯]t[h^Y[lm}rh^lmY[`,`*lm}r¡±ip|oip`*umum`|m`/¡¯]ct}*um`/Z$emt^`*YRs~`W²
Ò/]Wumt-}*`z]qzBik`*YnJlmum`'t[°Bu$h^*t^`w|`}*`jJlBigz{`*lBhrh^Y[`Y*}*lmz ~YWnf¡pZ$Y[t-|m`w_Z$lBsf`*_`*u$h^t+t[ipu\flB¡±ik`~Y[t*n
`*uh^`~Y[_`|m`}¢]¢¡±ipemY^]¢h[ikZfu¼n|Û]¢h[h^YRikemlBh^t/\~Z$_rh^YRipjJlm`*t`rh}riku*_=]h[ikjJlm`*ty|`,¡¯]=t^}!*um`(`*t[hzmY[Z$z{Z$t*`W²
u|*}*YRi±hy¡k`*t/|Bi±Ä*Y[`*u$h^t/uBi§s$`]Wlo» |m`}]¡±ikemY^]h[ikZ$uF`rh/|mZ$umum`lmum`5¡§ikt[h^``»mO]Wlmth[i§s$`c|m`*t/|Bi±Ä"~Y[`*u$h^`*t
ikuB¤¦ZfY[_=]¢h[ipZ$umt'ZfeBh^`*uJlm`*t$#}]WjJlm`uBi§s$`]Wl¼²
¿:ut^loi§sW]qu$hlmum`th^Y^]h*\qip`'e]Wt%~`'t^lmY-}*`~YRh]¢ikumt-h °Bzg`~t+|`w|*zB¡¯]q}~`*_`*u$h^t~n$h^`r¡kt jJlm`'È zO]WY-`»m`*_zB¡k`rÈ
|m`*t+Y[Zqh]h[ikZfut]WlBh^Z$lmY+|]»m`Tº»`Z$l=|m`*t´h^Y^]Wumt¡®]¢h[ipZ$umt+zmlY[`~t*nBZ$u8|*}*YRi§h}*Z$__¥`*u$h|rh^`*}rh^`~Y+|`wh^`r¡kt
_Zflosf`*_`~u$h^t~²
&ik_zB¡~_`*u$h]h[ikZ$uª|m`µ}*`~t*jJl]h[ikZ$umt`~th¥]qu]¡±°Bt*`8|]qumt}~`µz]qzBip`*Y`rhclmum`µY]¡±ipt]h[ikZfu t^Z$lmt
¤¦Z$Y[_¥`|lmu_ZB|mlB¡k`¡pZ$\qip}rik`¡'#=ikufh*\$Y[`*Y(]Wlt`iku|lmu£¿-u$sJipY[Z$umum`*_`*ufh5|À u]¢¡±°t`c|m` Ð *jJlm`*um}*`*t
|_=]q\f`*t'`~thw`»z*YRik_¥`*u$h*`W²
( ¸¢rÍ^)* %Ð h^Y[lm}rh^lmY[`(`rhyÑ9Z$lBs$`~_`*u$h~ngÑ9Zflosf`*_`~u$h^t Ð ikum\flo¡§ik`*Y[t~n Ð `r¡§¤¯È ³ ]¢¡§ikemY^]¢h[ipZ$u
¶g¸VÏ W¯¸g¶
8˯Ë$Î ¦¶4Ë4ËJ¸~Ì ¸ ¸m¯¸g¶ÂÎ4ËB¶ ¶¸f)¯KB¯¸g¶
²§ Ð `h[h[ikum\h^m``~jJl]¢h[ikZfumt¬²,²(²,²²(²,²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
B²§$²§
³
]q_`*Y^]c_ZB|m`r¡4]qum|¤¦Y^]q_`/ZW¤Y[`¤¦`*Y[`*um}*`W²&²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
B²§$² ÉTt[ikum\z{Zqipu$h^tT]Wt'zmYRip_i±h[i§s$`*t~²c²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
B²§$² À t^loi§h]qeB¡k`/_¥ZB|`¡Zq¤4h^m`/iku$h^YRiput[ip}5z]qY^]W_`rh^`*Y[tZq¤4h^m`,}]q_¥`*Y^]B²²,²,²5²,²,²
B²§$²a d'`~zY[`~t`~u$h]¢h[ipZ$uZq¤:YRik\qip|µ|BiptzB¡®]q}*`*_¥`*u$h^t~² ²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
² X]WY^]q_`rh^`~YRik«]h[ikZ$uZq¤:_ZWh[ikZ$u8w`~uumZ}]¡±ikemY^]h[ikZ$u¼²:²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
B²²§ Ç`rÈ Y[`*zmY[`*t^`*ufh]¢h[ikZfu]qum|µh^m`È _=]h^YRi»V²¼²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
B²² Ç`,}]Wt^`Zq¤:]zmlmY[`Y[ZWh]¢h[ipZ$u¼nO]qum|8h^m`zB¡®]qu]qY}]qt^`W²o²5²,²,²,²5²,²,²,²5²,²,²
¦¶ ËJ:9Ï ¯ )¯mfË ËB¶g ¸ ¸!¯¸g¶Â¶)kÌ"¯# $
²§ %w`~u`~Y^]¢¡4YRik\Wik||Bikt^zB¡¯]q}~`*_`*u$h~² ²(²,²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
² %w`~u`~Y^]¢¡4zB¡¯]WuO]WYYRik\qip||Bikt^zB¡¯]W}*`*_`~u$h~²m²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
² ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-umZh^Y^]qumt[¡¯]h[ikZfuV² ²,²,²,²5²,²,²,²5²,²,²
²a ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-zmlmY[`,Y[Zqh]¢h[ipZ$u¼²K²5²,²,²,²5²,²,²,²5²,²,²
² ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-Y[`rh[ipu]¢¡h^Y^]qumt[¡¯]h[ikZfuV²1²,²5²,²,²,²5²,²,²
² ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-zmlmY[`/h^Y^]qumt[¡¯]¢h[ipZ$u¼²Â²,²,²5²,²,²,²5²,²,² *a
² ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-zmlmY[`,zo¡®]qu]qYh^Y^]qumt[¡¯]h[ikZfuV²Á²,²,²5²,²,² *a
² ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-Y[`rh[ipu]¢¡4|Bikt^zB¡¯]W}*`*_`*ufh~²/²5²,²,²,²5²,²,²
² ¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-Y[`rh[ipu]¢¡4zB¡¯]WuO]WY|oipt^zo¡®]q}*`~_`*u$h~²c²5²,²,²
²§!(¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&º»`*|F]»oiptTY[ZWh]¢h[ikZfu¼²²,²5²,²,²,²5²,²,²
²§f£¿¡k`*_¥`*u$h]qYR°1|Bikt^zB¡¯]W}*`*_`*ufh^t'ZW¤h^m`,}]W_`*Y^]'&-«*ZBZf_©|Bikt^zB¡¯]q}~`*_`*u$h~² ²5²,²,²,²5²,²,²
)Ë ¶*¦¶+¯ËJm,¯$) ¸m¯¸{¶ ª¸VÏ' )¯Ë
-
aO²§ ³ Zf_5eBikuBipu\=|Bi§ÄV`*Y[`*ufhT_ZB|m`r¡pt'ZW¤K|oipt^zo¡®]q}*`~_`*u$h^t ²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,²
aO² ÉTt[ikum\=]t[h]¢h[ipt[h[ik}]¡V¤¦Y^]q_`Z$Y[¹² ²,²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
am²²§ Ç`(¿´]WYR¡±°JÈ@sJiptipZ$u_ZB|mlB¡k`W²²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
am²² ¿¡§ik_ipuO]h[ikum\=Z$lBh[¡§ik`*Y[t~²²(²,²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² qa
am²² d'`ºOuBipu\ch^`,`*t[h[ip_=]¢h[ipZ$u¼²©²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² qa
am²²a ³
Z$_zmlBh[ikum\=}*ZsW]qYRi®]qum}*`*tw]qum|}*Z$_¥zO]WYRikum\|Bi±Ä¼`*Y[`*u$hw_ZB|m`r¡pt*²o²5²,²,²,²5²,²,² qa
am²² R_¥zo¡p`*_`*ufh[ikum\]_Zqh[ipZ$u_ZB|mlB¡k` ²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
aO² ¿4»zg`~YRik_`*ufh]¢¡KY[`*t^lB¡±h^t%²,²(²,²²(²,²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
am²²§ ÉTt[ikum\t[°Bufh^`h[ik},|]¢h] ²(²,²,²²(²,²,²²(²,²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
am²² À u1`»O]q_¥zo¡p`'i§h^Y[`]¡4|]¢h]&´\$YRip|t^}*`*um`W²²,²²(²,²,²5²,²,²,²5²,²,²,²5²,²,² $
am²² À u1`»O]q_¥zo¡p`'i§h^Y[`]¡4|]¢h]&´`»oh^`*Y[u]¡4t}~`*um`W² ²,²,²5²,²,²,²5²,²,²,²5²,²,² $
am²²a À
u1`»O]q_¥zo¡p`'i§h^Y[`]¡4|]¢h]&´\$`*um`*Y^]¡|Bikt^zB¡¯]W}*`*_`*ufh~²O²,²,²,²5²,²,²,²5²,²,² (
. /
¸g¶4) 4¯¸{¶
Ç`y]qu]¢¡§°Bt[ikt´ZW¤V_ZWh[ikZfuikuh^m`T}]Wt^`'ZW¤]qu=lmum}]¡±ikemY^]h^`*|_ZfuZB}~lo¡®]qYKik_=]W\$`t`~jJlm`*um}*`T]qt½]¢¡kY[`¢]q|B°
eg`~`*uµ|m`rsf`r¡pZ$zg`~|µe$°8t^`rsf`*Y^]¡4]qlBh^mZ$Y[t~no}~Z$umt[ik|m`*YRikum\z{Zqipu$hw]qum|¢Z$Y´¡§ikum`/}*ZfY[Y[`*t^zgZ$um|m`*um}*`*t+ZfY}*Z$Y[Y[`*t[È
zgZfum|`~u}~`*t´eg`h `*`*u=zB¡®]qu]qY:zO]h^}m`*t]Wum|lmtipum\`i±h^m`*Y]/|Bikt^}*Y[`rh^`wZ$Y´]/}*Zfu$h[ikuolZflmt+Y[`*zmY[`*t^`*u$h]¢h[ipZ$u
Zq¤4h^m`,YRik\Wik||BiptzB¡®]q}*`*_¥`*u$heg`rh `*`*uhZ=Z$Y_ZfY[`¤¦Y^]q_`*t~²
Çm`*t^`t[h^l|Bip`*t9]WY[` _¥Zqh[i±sW]h^`*|Æe$°Áh^m` ¤@]W}rhh^O]h !#"$%"!# &'
()*+#,'-/.0/132§(!4@²65TZ`rsf`*Yngi±h]Wteg`*`~u9|m`*_Z$umt[h^Y^]¢h^`~|h^]¢h~nOiku9h^m`(\$`*um`*Y^]¡4}]qt^`WnOi±hwikt
umZqh+z{Z$t^t[ikeB¡k`+h^Z,t^`r¡±¤¯È }]¡±ikemY^]h^`½h^m`T}¢]q_`*Y^]wm`*u«*ZBZf_ikum\,Z$Y:_ZB|Bi±¤¯°Jipu\/h^m`'ipu$h^YRikumt[ik}y}]¢¡§ikemY^]¢h[ipZ$u
z]qY^]W_`rh^`*Y[t~²
³ Z$umt[ik|m`*YRipum\yh^Bipt´¤@]q}rh~n$h^m`T¹W`r°ik|m`]/ZW¤Vh^m`TzmY[`*t^`*u$h+t[h^lm|B°ikt:h^O]h *ËËJ)-¦¶ )¯mÏ ¯ )¯BÍ
$Ë ËB¶g¦¶Ï 4$Ë9ËB¶4¸ *-ÂË87 4o!¯¸g¶4¸ Ë B) 4BË94Ë9$)¯Ko!¯¸g¶ m Ë$ËJ#
ÅmZ$Y+iput[h]Wu}~`Wnoº»`*|F]»oipt'Y[ZWh]¢h[ikZfumt½ZW¤K¹JumZ~wu9]Wum\q¡k`~t½ZfYzlmY[`,Y[Zqh]h[ikZfut92:44]¡±¡kZ·h^Z`*t[h[ik_=]h^`
h^m`=}]¢¡§ikemY^]¢h[ipZ$uz]qY^]W_`rh^`*Y[t~n¼h^m`ripYlmum}*`*YRh]iku$h °ª]qum|¼n¼¤¦Z$Y,]\qi±sf`*u£¹$ikum|£Zq¤|Bikt^zB¡¯]W}*`*_`~u$h~nTBip}
z]qY^]W_`rh^`*Y[t,]WY[`Z$zBh[ik_]¢¡±¡§°`*t[h[ik_]¢h^`*|¼n¼t^Z8h^]¢h(]q}h[i±sf`sJikt^l]¢¡:t[h^Y^]¢h^`*\Wik`*t/}¢]queg`c|`s$`r¡pZ$z{`*|¼²¥u
h^m`=Zqh^m`*Y/]qum|¼nzmlmY[`h^Y^]qumt[¡¯]h[ikZ$umt,|mZumZqh(]¡±¡pZ~ h^Z}¢]¢¡±ipemY^]¢h^`h^m`8¿-lm}r¡§ik|m`]qu£\$`~Z$_`rh^YR° Zq¤+h^m`
t^}*`*um`32±f14 nOemlohi±h^ty]¢¾=um`/\f`*Z$_`h^YR°%2§*a$4@²
³ Zq¡§¡k`*}h[ikum\=]¢¡§¡h^Bikt'ipuB¤¦Z$Y[_=]h[ikZ$u1]qum|1}*Z$umt[ik|m`*YRipu\]tlBi§h]qeB¡k`,t[h]¢h[ipth[ip}]¢¡¼¤¦Y^]q_`rZfY[¹]qtiku2§4 n
i±hikth^m`*uz{Z$t^t[ikeB¡k`h^ZipuB¤¦`*Y½wBik}9¹$ipu|1Zq¤K|Bikt^zB¡¯]W}*`*_`*ufh'i±¡§¡ikum}*Y[`]Wt`,]hT_¥Z$t[hh^`/ipuo¤¦ZfY[_=]¢h[ipZ$u
;
lmt^lO]¡±¡§°Y[`~zY[`~t`~u$h^`*| ef° h^m`=ikufs$`*Y[t^`Zq¤w]}*ZsW]WYRi¯]qum}*`=_]¢h^YRi»<Z$uh^m`8t}~`*um`=\$`*Zf_`rh^YR°fn-Z$eBv[`~}rh
¹$ipu`~_=]¢h[ip}*t]Wu|}]¡±ikemY^]h[ikZ$uz]qY^]W_`rh^`*Y[t~²
ÇBiktikth^m`\fZJ]¡Zq¤4h^Biktz]qzg`~Y²
uZfY[|`~Y½h^Z8]h[h]¢ikuh^BiktTZfeBv[`*}rh[i§s$`Wn`(]WY[`yºY[t[hw\$Zqipum\h^Z=Y[`rsJip`rÆh^m`/h^`~Z$YR°1Zq¤K_Zqh[ipZ$uTm`*u
umZ}]¡±ikemY^]h[ikZ$u&´`*jJl]¢h[ipZ$umt~nz]qY^]W_`rh^`*YRip«]¢h[ipZ$uZq¤K_Zqh[ipZ$u¼n`rh^}$²±²±²
ê`h^`~uµ]WY[`T\fZqikum\,h^Z5zmY[ZfzgZ$t^`w]t[°Bufh^`~tiptZq¤Vw]¢h+}]Wu=eg`wY[`*}*Zs$`~Y[`*|=iku=h^`*Y[_tZq¤¼t^}*`*um`T\f`*ZqÈ
_`rh^YR°µ]qum|=¹$ikum`*_]¢h[ik}~t wm`*u=}]¡±ikemY^]h[ikZ$uipt+umZqh+\Wi±sf`*u]qt+]Wuikumzmloh"&´|m`*t^}*YRike{`'h^m`T|Bi§ÄV`*Y[`*ufh½¤¦ZfY[_t
Zq¤½}]¢¡§ikemY^]¢h[ipZ$u¼n{h^m`|Bi±Ä¼`*Y[`*u$h/¡p`rsf`r¡kt,Zq¤½}]¢¡§ikemY^]¢h[ipZ$u]qum|\Wi±sf`=]qu`»mO]Wlmth[i§s$`c¡±ikt[h/ZW¤´h^m`|Bi±Ä¼`*Y[`*u$h
\$`~Z$_`rh^YRip},]qum|¹fikum`*_=]h[ik}/ikuB¤¦Z$Y[_]¢h[ikZfuh^Z¥eg`,Y[`*}*Zsf`*Y[`*|¼nO|m`*zg`*um|Bikum\h^m`,}Zft^`*uµ\f`*Z$_¥`rh^YR°f²
= >
@?1@A3¨CB CB# 7 #! #:#DAEBy #&5*)+,:#GF
H¸mB¯¸{¶
ê`½wYRi±h^`s$`*}h^Z$Y[t]qum|_]¢h^YRik}~`*t´lmt[ikum\5e{Zq¡p|¡k`rh[h^`~Y[t*nJ_=]h^YRik}*`*t+e{`rikum\/wYRi±h[h^`*ui±h^8}]Wzoi§h]¢¡m¡k`h[h^`*Y[t~²
Ç`(|ml]¢¡ktyZq¤-sf`*}rh^ZfY[t/]qY[`(Y[`*zmY[`*t^`*u$h^`~|]qt'h^m`(h^Y^]qumt^zgZ$t^`,Zq¤½]s$`~}rh^Z$Y/]Wum|9t^}]¢¡®]qY[t'ipui±h]¡±ip}W²wÇm`
umZqh]h[ikZ$u,IKJMLONQPIRL9}~Z$Y[Y[`*t^zgZfum|t4h^Z/h^m`'}*Y[Zft^tÈ zmY[ZB|ml}h~n¢h^`|mZqh[È zmY[ZB|lm}rh:eg`ikum\TYRi§h[h^`*u8]qtSIUTL ²
P
I£ikt/]WVXV=t^¹q`rÈ t°__`rh^YRip}5_=]h^YRi»ZY,²TÇm`ip|`~u$h[i±h °_=]¢h^YRi±»1ipt'wYRi±h[h^`*u[q² %`*Zf_`rh^YRip}5ZfeBv[`*}rh^t
t^lm}]WtzgZWiku$h^t~ng¡±ipu`~t*ngzB¡¯]Wum`*t/]qY[`,wYRi±h[h^`*ui±h^9}]WzBi±h]¢¡4¡p`rh[h^`*Y[tikufÒ(ng]qum|t^_=]¢¡§¡¡k`rh[h^`~Y[tiku$Ò(²
ê`Y[`*zmY[`*t^`*u$h,h^m`=}*Z$_¥zgZ$um`*ufh^tZW¤]µ_=]h^YRi»ZfY5]8s$`~}rh^Z$Y,lmt[ikum\t^lmzg`*Y[t^}*YRipzBh^ty¤¦Y[Zf_ (h^ZFBn`W²\m²&
I\N^]*_a`cbd_
Y
be_af)g*T²
ê`TYRi§h^`ihkjml£i±¤Chµipt'`*jolO]¡h^Z3l lmzh^Z8]t^}]¢¡p`¤@]q}rh^ZfYnoi@²`W²on&pbdhkNmpl½²
q
0Sr0sMr0sutvr0wxzy${1x|{~}u6}~*rR !ssMrxw-Rs{1xwy${)U~:{)w*{)sMrxr0w/{ 1$@0{ 1K{1|{:tvrw/r0$w*r0/r 1xr0~tMxy$r
0w//*$w/!:$x1&{u)r0xz)w!ra-S1xy:rSw/s
wR/sr
/ ªËJ ¸VÏKË )-¶4Ï ¢ ˸ TË Ëo¢Ë¶fË
ê`lmt` )*Zv0 #' !!'m¤¦Z$Y(]µ}¢]q_`*Y^]n]qt^t^lm_ikum\h^`=}¢]q_`*Y^]zg`*YR¤¦ZfY[_tc]µzg`~YR¤¦`*}rh
zg`~Y[tz{`*}rh[i§s$`8h^Y^]qumt[¤¦Z$Y[_%'i§h^¬}*`*ufh^`*Y"!
;
h^m`1}]q_`~Y^]9Z$zBh[ik}}*`*u$h^`~Y<]¢h¥]|oipt[h]qum}*`$#
;
h^m`8¤¦ZB}]¢¡
¡k`~u\Wh^<5Zq¤h^m`9Y[`h[iku]¢¡wzB¡¯]qum`W² Ç'm`zBipumZW¡k`_¥ZB|`¡T}]WuÂt[h[i±¡±¡weg`1lmt`~|¬¤¦Z$Y=]«*ZBZ$_%¡k`~uti§¤h^m`
Z$eBv[`~}rh[ÈHh^ZWÈHip_=]q\f`T|Bikt[h]Wu}~`iktTumZWh'}~Z$umt[ik|m`*Y[`*|F]qt+º»`*|¼²
À ¡±¡{}*ZBZ$Y[|Biku]h^`*t+]qY[`wY[`r¡¯]h^`*|h^Z]Wu8]¢¾=um`¤¦Y^]q_`wZq¤Y[`r¤¦`~Y[`*um}*`&% N]! bICbLb('g6/*v) /3
0!#Zqn*'=eg`ikum\=]¢¡§ik\fu`~|i±h^h^`,Zfzoh[ip}]¢¡]»oipt*nI ]Wum| Lªeg`ripum\=]¢¡§ik\$um`*|8i±h^µh^m`,mZ$YRip«*Z$u$h]¡4]qum|
sf`*YRh[ik}]¡4]»Bikt+iku8h^m`ik_=]W\$`W²-Ç`yY[`rh[iku]¢¡zo¡®]qum`Tipt½h^Jlmtzg`~Y[zg`*um|Bik}*lB¡®]qY+h^Zh^m`Z$zBh[ip}]¢¡]»oipt!,+Bnm]qt
t^mZ~wu8ikuµº\flY[`=$²
-
-.
/0000000000000000000000000
1 2
23
0000000000000000000000
4
/
5 5 5 6 6
687
9 :
9 : 0
; ; ; ;;<
<
<
<
< 0 =
=
=
=
=> =
=
=
=
=> ? ? ? ? ? ?
? @
? ? ? ? ? ?
? @ A
A
A
A
AB B B BB
CC
CC
CC
CC
CC
00000000000
DD DD DD DD DD DD
EGFIHKJMLONQPSRPTNLF UWVXYXF[Z\R V L(]F^L(_`F[Z
EGFIHKJMLONQPSRPTNLF
a XbVdcF[_eHYJV L fg8hYiH
XKj
_`H j(X
F
kml
n o p
q p l
r r l
EGJsdJT]t V HYJV LuYvwYxQy
a XbVdcF[_eHYJV L o l
q l
n l
z
k
żip\$lmY[`=#&´¿¡p`*_`*u$h^tylt^`*|8ikuh^m`|m`rºuBi±h[ipZ$u1Zq¤4h^m`zmY[Zfeo¡p`*_
¦¶ ´¸ ¦¶gm K! kOËo#
ê`5Y[`*zmY[`*t^`*ufh(]µfÒTÈ z{Zqikufh{ e$°1h^m`s$`~}rh^Z$Y| N !,{} N ]~b~b9g*T lt[ipu\1¿-lm}r¡§ik|m`]qu}~ZBZ$Y[|Bi±È
u]¢h^`*t~²/XZWiku$h^tipuh^m`Y[`rh[ipu]Bng'i§h^zoi±»`r¡:}*ZBZ$Y[|BipuO]h^`*tT}~ZBZ$Y[|Biku]¢h^`~t,]^Rb(g'i±¡±¡Ke{`Y[`*zmY[`*t^`*u$h^`~|]qt
mZ$_Zf\$`*um`*Zflmt,¢ÈÒ sf`*}rh^ZfY[t"& N !} N ]^bO&bg*TKn}*ZfY[Y[`*t^zgZfu|Bipu\1h^Z¡±ipu`~t5ZW¤T]1\qi±sf`*u
|BikY[`*}h[ikZ$u1z]qt^t[ikum\5h^mY[Z$lm\fµh^m`,Z$zBh[ik}]¡}*`*ufh^`*Y
;
ÈRÒ6zmY[ZWv[`*}rh[i±sf`,t^zO]W}*`$<^²
Th^m`*Y,zmYRik_i§h[i±sf`*ti±¡§¡eg`=Y[`*zmY[`*t^`*u$h^`~| lmt[ikum\t^`rh(Zq¤zgZWiku$h^t~²9Ç'Bikt,i±¡±¡e{`=|Bikt^}*lmt^t`~| ipuh^m`
t^`*jJlm`r¡ ²
% km )¯Ë ª¸VÏË )´¸4Ë ¦¶g¦¶4¯ m Ë$Ëo¢(¸ '4Ëf ªËJ
Ru h^Bikt8t[h^lm|o°Jni \ ,1 `1(/ # '-/.0/1q² 5TZ`rs$`~Yn` ]qY[`ipu ]£t^zg`*}ri§º}
t[i±h^l]¢h[ipZ$ueg`*}¢]qlmt^`'`/]*s$`/}mZ$t^`*u1]}¢]qumZ$uBik}¢]¢¡\,¤¦Y^]q_¥`,]¢h[h]q}m`*|=h^Zh^m`/Y[`rh[iku]²:Çm`*Y[`r¤¦Z$Y[`$no`
}*Zfut[ip|`~Y+Z$uB¡±°=h^m`/_=]h^YRi»Zq¤h^m`ikufh^YRikumt[ik},z]qY^]q_¥`rh^`*Y[t
;
}]¢¡§¡k`*|TÈ _=]¢h^YRi±»Z<-iku8h^m`/zY[ZWv[`*}rh[ipZ$u]qum|
N | b N # `
# `
;
$<
À }*Zf_zB¡k`rh^`,Y[`rsJip`r6}]Wuµe{`/¤¦Z$lmum|ipu2±)4@²
uh^m`TzmY[`*t^`*u$h _ZB|m`r¡@n&]^
`
b(
`
g¼ipt-h^m`'zmYRipu}ikz]¢¡{zgZWiku$h~nB]qum|"#=h^m`½¤¦ZB}]¡B¡k`*um\Wh^$¤¦Zq¡§¡kZikum\32±f14 n
`w]qt^t^l_¥` h^]h-`/¹JumZÆh^m`,Y^]¢h[ikZ¥eg`rh `*`*uµh^m`,mZ$YRip«*Z$u$h]¡K]qum|8s$`*YRh[ip}]¢¡¤¦ZB}¢]¢¡V¡p`*um\qh^ ]Wum|h^]¢h
`8]qt^t^lm_`h^]¢h,h^m`/h Z=Y[`rh[ipu]¢¡4}*ZBZfY[|oipu]¢h^`*t]qY[`/ZfYRh^mZ$\$Zfu]¢¡ ² h(]qt,eg`*`~ut^mZTu£`»z{`*YRik_`~uoÈ
h]¢¡§¡±°(h^]¢h´h^m`*t^`w]qt^t^l_¥zoh[ipZ$umt´]WY[`½sW]¡±ip|¤¦Z$Y:th]Wum|O]WY[|}]W_`*Y^]qt2±f14{]qum|=]¡kt^Z¤¦Z$Y:Bik\$BÈ@¡k`rsf`r¡msJiptl]¡
t^`*umt^Z$Y[t92±¢:4@²+ÉTt[ikum\(h^oiptTt[ik_¥zo¡p`,_ZB|m`r¡Vi±¡±¡K]¡±¡pZ~ lmt½h^Zip_zmY[Z~sf`/h^m`ZfeBh]¢ikum`*|Y[`*t^lB¡±h^t~²
ê`c]¢¡kt^Z]qt^t^lm_`5h^]hh^m`iku$h^YRipumtip}z]qY^]W_`rh^`*Y[t,]WY[`|Bi±Ä¼`*Y[`*u$h,¤¦Z$Yy`]q}}]q_¥`*Y^]z{Z$t[i±h[ipZ$u¼n]qt
|mlmYRikum\8]«*ZBZf_²Ruµh^m`,}*Zfut^`*}~loh[i§s$`/¤¦Y^]W_`%N]! bI*bLbO'g´`TYRi§h^`#&
N | ;
8<
8ËKËJ*ËB¶g¢o!¯¸g¶ ¸w¯Ï·Ï ¯)¯m$Ë ªËB¶g#
ê`/}*Z$umt[ik|m`*Y_Zqh[ipZ$uZq¤:YRik\Wik|ZfeBv[`*}rh^t]qum|h^`,`*\fZqÈ _Zqh[ipZ$u8Zq¤Kh^m`,}]q_`~Y^]Bn|#\ #)0!*1²
ê`h^JlmtTY[`*zmY[`*t^`*u$hw_ZWh[ikZ$uh^mY[Z$lm\$YRik\Wik||BiptzB¡®]q}*`*_¥`*u$h^t~²
h_`]Wut+h^]¢h+h^m`h^Zf¹q`*umt+iku=h^m`t^}*`*um`/]WY[`lmum|`~Y[\$Zqipum\](YRik\qip|8|oipt^zo¡®]q}*`~_`*u$hz]qY^]W_`rh^`*YRip«*`*|
e$°1]Y[ZWh]¢h[ikZfu_=]h^YRi» ]qum|](h^Y^]qumt[¡¯]¢h[ipZ$u8s$`~}rh^Z$Y &
|
N |
;
8<
Q !" $# &% ' ()
Ç`,\fZJ]¢¡Zq¤Kh^`,z]qY^]W_`rh^`*YRip«]¢h[ipZ$u1Zq¤:_Zqh[ipZ$uµipt'h^m`/¤¦Zq¡§¡kZ'ipum\ &´\qi±sf`*u]t^`rhwZq¤Kz{Zqikufh^t'ikuF}*Z$Y[Y[`*t[È
zgZfum|`~u}~`'e{`rh `*`~uh Z/sJip`rTt~n$i@²`W²´]yt^`rh Zq¤{_=]¢h^}m`*t+* -,.0/T`½]Wu$h-h^Z(]WuO]¡±°B«~`T]¡±¡m}*Zfut[h^Y^]iku$h^t
woip}Y[`r¡®]¢h^`h^m`h Zz{Zqikufh^tyi ²`W²5ºum|h^`¥`*jJl]¢h[ipZ$umt/Zq¤+h^m`¤¦ZfY[_&12* -,.0/vb#R]^%bO3 g N4B²Ru
z]qYRh[ip}*lB¡¯]qYn`=Zflo¡p| ¡§ik¹W`h^Z9zmY[`*|Bik}rh(h^m`=¡kZB}]h[ikZ$uZW¤w]zgZWiku$h(\qi§s$`~u i§h^t5}*ZfY[Y[`*t^zgZfu|m`*ufh~ni@²`$²]
Y[`r¡®]¢h[ikZfuZW¤h^m`/¤¦Z$Y[_512* -,.0/vbO3N6]^ g^²@5]*sJikum\=t^lm}1zO]WY^]q_`h^`*YRik«]h[ikZfu9]¢¡§¡kZwt½h^Z=`»]q}rhy]¢¡§¡
ikuB¤¦ZfY[_=]¢h[ipZ$u]*sW]¢i§¡¯]Weo¡p`¤¦Y[Zf_ h^m`Y[`h[iku]¢¡:|Bikt^zB¡¯]q}~`*_`*u$h^t~ngTBip}9ipt_`]WtlmY[`*|9h^mY[Zfl\fh^m`t^`rh/ZW¤
_=]h^}m`*t~²
7 4Ë Í^ËKËJ*ËB¶gB¯¸{¶¬¶Ï 4Ë Í B98
³ Z$umt[ik|m`*YRikum\h^m`fÒ }~Z$Y[Y[`*t^zgZfum|`~u}~`*tTe{`rh `*`~uh ZzgZWiku$h^t%]Wum| 3Vikuh Zµ|Bi§ÄV`*Y[`*ufh¤¦Y^]q_`~t*n
`,Z$eBh]¢ipu¼n}*Z$_(eBikuBikum\=`*jolO]h[ikZfut
;
$<^n
;
8<]qum|
;
8< &
N ;:
Y
< = > ?
@BA
C
< = > ?
D ;
a<
w`~Y[`Th^m`wÈ _=]¢h^YRi±».EFÆ}~Z$Y[Y[`*t^zgZfum|t´h^Z(h^m` lmum}]¢¡§ikemY^]¢h^`~|Y[ZWh]¢h[ipZ$u]¢¡{}*Z$_¥zgZ$um`*ufhZq¤h^m`YRik\Wik|
|Bikt^zB¡¯]W}*`*_`*ufh(mnZfY_¥Z$Y[`=\$`~Z$_`rh^YRip}]¢¡§¡±°G k'#'-#Z HG ,U' vM#JIC(qn{wBi±¡p`h^` rÈ
sf`*}rh^Z$Y+}~Z$Y[Y[`*t^zgZfum|t´h^Z(h^m` lmum}]¢¡§ikemY^]¢h^`~|h^Y^]qumt[¡¯]¢h[ipZ$u]¢¡{}*Zf_zgZfu`~u$h+Zq¤¼h^`/YRip\qip|=|oipt^zo¡®]q}*`~_`*u$h(On
]¢¡pt^Z}¢]¢¡±¡p`*| ¤¦ZB}~lt:Zq¤`r»z]qumt[ikZ$u/e$°tZf_`]WlBh^ZfY[t~no]Wu|=_¥Z$Y[`T\f`*Z$_¥`rh^YRik}]¡±¡§° Z&v'²Çm`*t^`
}]Wt`$²
¤`/`¡±ik_ciku]¢h^` 6]qum| ipu`*jJl]h[ikZ$u
;
a<
;
e$°8h]q¹$ipum\h^`,}*Y[Zft^tÈ zmY[ZB|ml}h½i±h^(]qum|µ_(lB¡±h[i§È
zB¡±°Jipum\=e$°$ lT <:`,Zfeoh]iku&
lTPEF
< = > ?
N ;
8<
Çm`_=]h^YRi» N PE F·ipt´h^m` 3*v'a3v]qum|=ikt]¡kt^Z,}]¢¡§¡k`*|=h^m` `~tt^`*ufh[i¯]¢¡{_=]h^YRi»
ikuh^m`8lum}]¡±ipeY^]h^`*|£}]qt^`SO²¥ ¤`=}*Z$umt[ik|m`*Yh^]h5h^m`=Z$uB¡§° ipuB¤¦Z$Y[_=]h[ikZ$u£]*sW]¢i§¡¯]Weo¡p`ikt(Y[`r¡¯]h^`*|h^Z
h^m`Y[`rh[ipu]¢¡}~Z$Y[Y[`*t^zgZfum|`~u}~`*teg`h `*`*uÂz{Zqipu$h^t~n 'i§h^mZ$lBh8]quf°Â¹JumZ'¡p`*|m\$`1]qegZflBhh^m`|m`*zBh^mt ,n
`*jJl]h[ikZ$u
;
8<´ikth^m`ZfuB¡±°8`*jJl]h[ikZ$uh^]¢hw}]queg`/|m`*YRi§s$`*|O2±$4@²
³ Z$umt[ik|m`*YRipum\]Tt^`rh:Zq¤_=]h^}m`*tKY[`r¡¯]h^`*|ef°5`~jJl]¢h[ikZfu
; <{h^m``*jJl]h[ikZ$u
;
8<Vikt4`r¡§¡m|`ºOum`*|(i±¤{]qum|
Z$uB¡§°=i±¤
;
i<N ]Wum|
;
i§i<´h^`~Y[`yipt'umZ¡§ikum`]WY'Y[`r¡®]¢h[ipZ$umteg`rh `*`*u9]¡±¡ ]qum| ²´Ç'm`/|m`*\$`~u`~Y^]¢h^`*|
}]Wt`~t5ZB}*}~lY,Zfuo¡§°i±¤h^`=h^Y^]Wut[¡®]¢h[ikZfuipt5«*`~Y[Zmn-Z$Y,i±¤y]¢¡§¡zgZqipu$h^t(eg`r¡pZ$um\h^Z9h^m`µt]W_`=zB¡¯]qum`2±f14 f~²
Çoipt'z]WYRh[ik}*lB¡¯]WY'}¢]qt^`'i§¡±¡4e{`,]qu]¢¡§°B«*`*|8iku1|`h]¢i±¡ ²
À
t|oipt^}*lmtt^`*|wiku2±¢c4]qu/`r¾=}ik`*u$hK}*YRi§h^`*YRikZfu/iktVh^m`+]*s$`~Y^]q\$`:Y[`rh[iku]¡B¿-lm}r¡§ik|m`]qu,|Bikt[h]Wu}~`*teg`rh `*`*u
`]W}zgZWiku$hy]qum|8i±h^tT`~zoipzgZW¡¯]qY+¡§ikum`W²´Ç'm`/¤¦Zq¡§¡kZ'ipum\t[°B__`h^YRik},¡k`]Wth[È t^jJl]qY[`t^lm_©ikt_ikuBip_ik«*`~| &
~N 6
!#"
$&%
]
b' g f % ] b')(
g
f'*
< = > ?
+-,
u. y&/
021
11
354
76
8!#"
03
< = > ?
9:<; u. y>=
/ ;
8<
w`~Y[`
"
ipt,]¥`rip\$$h^`~|}*Z$Y[Y[`*t^z{Z$um|Bikum\=h^Zh^m`zmY[`*}ikt[ikZfuZq¤´h^m`_]¢h^}VnViku¤@]q}hTh^m`ikufs$`*Y[t^`ZW¤
h^m`'sW]WYRi¯]qum}*`Zq¤{h^m`TzmY[`*}riptipZ$uZW¤gh^m`T_]¢h^}V²-Çm`TjJl]qufh[i±h ° "
ikt \qi±sf`*uipu@?A/_CBED
: f nfwoi§¡k`GF
]7 g^n
h^m`W"$0IH#)/1,*W Z&'niktiku1zBi»`r¡ ²
À
}¢]q_`*Y^](¤¦Z$Y+TBip} ]qteg`*`~u}*Zf_zmloh^`~|iptT}]¡±¡k`~| KJ1v'/.d/1 0²
Çm`s$`~}rh^Z$YL/iktT|m`rºum`*|F]qth^`,e]qt[ipt sf`*}rh^ZfY'ZW¤4h^`,¹W`*Y[um`r¡KZq¤M~T²
7
4Ë9$m*˸ T Ë¢¸mB¯¸{¶ON´¶ÏÂ4Ë )¯¶m8$m*Ë
À twzgZqipu$h^`*|1Z$lBhTzmY[`rsoikZ$lmt[¡±°Jnmipuµh^m`(}]qt^`/Zq¤ ]zmlmY[`5Y[ZWh]¢h[ipZ$uZfY½i§¤h^m`(t^`rhTZW¤KzgZqipu$h^tTe{`r¡kZfum\$th^Z8]
lmuBikjJlm`zB¡¯]Wu]qY´t[h^Y[lm}rh^lmY[`Wnf`y}]qumumZqh `*t[h[ik_=]h^`'h^m` È _]¢h^YRi»8eg`*}]Wlmt`w]¢¡§¡gz{Zqipu$h^t´iku=Zfu`sJik`E]WY[`
Y[`r¡®]¢h^`*|h^ZzgZWiku$h^tiku8h^`,ZWh^`~Y½sJip`r6e$°1]Y[`r¡®]¢h[ipZ$uZq¤4h^m`y¤¦ZfY[_ &
j E
;
<
woip}1}*Z$Y[Y[`~tz{Z$um|mt½h^Zch Z=`*jJl]h[ikZ$umt¤¦Z$Y`]W}1_=]¢h^}¼²
Çm`*Y[`Wni§¤-h^m`5_]¢h^YRi»PEiptlmu|m`rºum`*|¼nO`,th[i§¡±¡K}]Wu`*t[h[ik_]¢h^`/h^m`5_=]h^YRi»E&]qt'ipu 2±f14 nglt[ipu\
E N [/]qtikuBi§h[i¯]¢¡sW]¡klm`W²
QSR
w*)s{1>T)r0t:w/{1-1x&1$-rCrSU${1x/- 1VXWY8y:{)&1KT!-{)w*-cx/- 1$8v{ 1$u 1!Cxy$r0w*rrc-xa{ 1$r0{ww/r-{1x/- 1
trx#|r0r 1[Z { 1$\Z^]-rS{Mw/r-{1x/- 16&xzy$rw/s_Z^]a`PbcZWedRy!-Sxz${1x/- 1 0w/w*r0/ 1:$xzuxy:rC0{/r|r0w*r xy$r
1xU{w/r w/r-{1xr0Mt)6{~011$r0{1x/- 1v!rZ0w/w*r0/ 1:ux~{o!-{ 1:{)wUxzw/$xz$w/rR{Rw/r-rUr0@1Kxzy$r /rSU$r
Y[`*t[ik|ml]¢¡|oipt^zO]WYRi±h °9]W\J]¢ipu¼n]qtiku 2±f14K]Wu|Z$eBh]iku;E3h^Y[Zflm\$&
E ~N# 68 7
@
! "
E
]0]
f g T g
f
< = > ?
+ , u@my/ 01111 3 4
! " 03
< = > ?
9:
u@my=/ ;
8<
w`~Y[`y`/wYRi±h^` E N]`cb Y bSfg´ikuZ$Y[|m`*Yh^Z=]*s$`(]}*Zf_z]q}rhumZqh]h[ikZfu²
ê`,um`*`*|]¢hy¡k`]Wthya8uZfuBÈ }*ZW¡±¡§ikum`]qYzgZWiku$h^t~nVt[ikum}*`]µÈ _=]h^YRi»1ipt/]8»O=_=]h^YRi»lz9h^Z1]=t^}]¢¡p`
¤@]q}h^Z$Y+h^JlmtT|m`rºum`*|ef°czO]WY^]q_`h^`*Y[t~nTBi±¡p`,`]q}µ_]¢h^}zmY[ZsJik|m`*ty`*jJl]¢h[ipZ$umt~²
Çm`5`~Y[Y[Z$Y@F
@ ] Eg^n\qi±sf`*uikuzBi±»`r¡@nV'i§¡±¡:eg`(}]¢¡§¡k`*| d1 &' #[&(kHG/,3 0 &!
ikuh^m`t^`*jol`¡@²
d`*}ripzY[ZB}¢]¢¡±¡§°fnT]qt8t^ZBZ$u ]Wt=h^`z{Zqikufh^te{`r¡kZfum\$t=h^ZÂ]¢h8¡p`]qt[h=h Z zo¡®]qum`*t~n'`}]qu |m`rºum`*|·]
È _]¢h^YRi»2a4@²´Çoipt'|m`*\f`*um`*Y^]¢h^`~|µt[i±h^l]h[ikZ$uh^JlmtTZfuo¡§°8`»oipth^tikuh^`,}]Wt^`Zq¤:]qu1lmuoipjJlm`,zo¡®]qum`W²
4 ¼ /'£.9¼c'y 8 !f#¨ #:# (5*7F4oF
&`rh=lmt=umZ"|oipt^}*lmtt=t[i§h^lO]h[ikZfutc¤¦Z$Y5wBik}Âh^` È _=]h^YRi» ZfY5h^m`µÈ _=]h^YRi» ]*sf`9]zO]WYRh[ik}*lB¡®]qY
¤¦Z$Y[_² ³ Z$umt[ik|m`*YRikum\]Y[ZfegZWh[ik}8t[°Bt[h^`*_n-i±h(ikt5sf`*YR°ªZq¤¯h^`*u£h^]¢h¥]9|oipt^zo¡®]q}*`~_`*u$h(iktcuZWh]9\f`*um`*Y^]¢¡
|Bikt^zB¡¯]W}*`*_`*ufh8elBh]}*Z$umt[h^Y^]¢ipum`*|Â_Zqh[ipZ$uÂt^lm}Á]Wt8] zmlmY[`h^Y^]qumt[¡¯]h[ikZfuVn]Fº»`*|Á]¢»oikt=Y[ZWh]¢h[ikZfu¼n
`rh^}W²§²±²+]qti±¡§¡klmt[h^Y^]¢h^`*|ikuµº\flY[`,²
Ñ9ZfY[`*Zs$`~Y `,}]Wuµ_]q¹W`yh^m`/¤¦Zq¡§¡kZikum\]Wtt^lm_zBh[ikZfumtT]WegZ$lBhh^Bikt¹$ikum|9ZW¤KO]WY[|B]qY[`32±!(c4 &
Çm`/|Bikt^zB¡¯]q}~`*_`*u$h^ty]qY[`/Y[`*zmY[ZB|mlm}rikeB¡p`W²
ê`}¢]qu£_`]qt^lmY[`h^m`8]qum\W¡k`*t/ZW¤+h^`=Y[ZWh]¢h[ipZ$u¼²ÅmZ$Y/h^`*}muoip}]¢¡ Y[`]qt^Zfut/`|mZ1uZWhc]qt^t^l_¥`
h^m`=t]q_¥`h^Bikum\¤¦Z$Yh^Y^]Wumt¡®]¢h[ipZ$umt
;
i±h(ikt,umZqh(t^lY[`h^]h`=}¢]qu£`*t[h[ik_=]h^`h^m`=uZfY[_¨Zq¤h^m`
¡§ikum`]WY´h^Y^]qumt[¡¯]¢h[ipZ$u=ZW¤K]5«*ZBZf_ ¤¦Z$Y´ipumth]Wum}*` 2§(!4VTBi§¡k`Th^m`zmY[`*}ript[ikZ$u8ZW¤h^`wh^Y^]qumt[¡¯]¢h[ipZ$u8Zq¤]
_¥Z$eBi±¡p`/Y[Z$egZWhiktTumZWh½sf`*YR°1Bik\$<^²
À
¡±¡{`»oh^YRikumt[ik}/z]WY^]q_`rh^`~Y[t]qY[`lmum¹JumZTu¼nO]Wu|8`*jolO]h[ikZfut]WY[``»z{`*}rh^`*|=h^ZczY[ZsJip|m`lmut[h]Weo¡p`
`~th[ip_=]¢h^`~t'ZW¤h^m`*_ 2§14 ²
Çm`*t^`z]qYRh[ip}*lB¡¯]qY,}*Zfumth^Y^]iku$h^t(]WY[`¤@]qY¤¦Y[Z$_¨]*sJipu\1um`*\J]h[i±sf`=zY[Zfzg`*YRh[ip`*t~²u h^m`=}*Zfu$h^Y^]qYR°Jn
h^m`r°ikum|mlm}*`8]q|m|Bi±h[ipZ$u]¢¡½`*jJl]¢h[ipZ$umt/TBik}£`¡kz£tZW¡±sJipum\µh^m`=Y[`*}*Zfut[h^Y[lm}rh[ipZ$u£Z$Y/}]¡±ikemY^]h[ikZ$uzmY[ZqÈ
eB¡k`*_²
dRy$rw/r-{1x/- 1GZ^]K`
-S{ur0xw-{1w/s )w"!
#$
%
$&('
] ` )+*,*-/.0)1*3254.)+*
) * -/.0)
2
4.) ,
6 ] ` )72*-/.0)82,254.)72
) * -/.0)
2
4.) ,
9 ` 9
a
b
c
A robotic arm A mobile robot A turret
d
e
f
Åik\$lmY[`('&´¿4»]q_zB¡k`~t'ZW¤Y[ZfegZWh[ik}_`~}]quBipt_ wBik}\f`*um`*Y^]¢h^`*tzmlmY[`/h^Y^]qumt[¡¯]¢h[ipZ$umt~nozmlmY[`,Y[Zqh]¢h[ipZ$umt
Z$Y=º»`*|·]»Bikt8Y[Zqh]h[ikZ$umt~² GW \0 .dv\ 0. "$ G&1/"$'- & 0
0'k! 1 G|'(# H 6) 91 .e1!'-KHG63 .'6d8.eS#Z &1
'-) 0)'v 3v Gkv'Z@.kv'ZM 30 .dv1 #Z &1, IM1
E#~0v*v^#^|'v1 Z, G|'(# H `6 &* 13Z .dv`1!'-HGM,38.'
0 .dv '-3# &K IM3E#6d/ 10! G9130W #Z &1 Z d 0v*vaK# &
,'G0 ZW U'RZ/
ÅmlmYRh^m`*Y[_Z$Y[`$n:h^m`µ`~th[ip_=]¢h[ipZ$uªZq¤h^`|Bikt^zB¡¯]W}*`*_`*ufh=]qY[`8`]Wt[ik`*Y,iku h^m`*t^`8}]Wt`~t*n-e{`*}]qlmt^`=`
]*s$`/h^Z`rsW]¡kl]¢h^`/¡p`*t^t'z]qY^]W_`rh^`*Y[t~²
5wZ~`s$`*Yngh^m`t[°Bt[h^`*__5lmt[h/e{`]qeB¡p`h^Z8Y[`*}*Zf\$uBik«~`i§¤´h^m`|Bikt^zB¡¯]W}*`*_`*ufh}*ZfY[Y[`*t^zgZ$um|mtTh^Z8t^lm}
]z]qYRh[ip}*lB¡¯]WY'}]Wt^`Wnt^Z5h^]¢h`,_5lmt[hw}]qY^]W}rh^`*YRip«*`/h^`,t[i±h^l]h[ikZ$u8iku1`]q}}]qt^`W²
Åiku]¡±¡±°Jnh^m`|Bi±Ä¼`*Y[`*u$h}r¡¯]WttyZq¤+|Bikt^zB¡¯]W}*`*_`~u$h^t_ip\$$h,]*s$`ct^`rs$`~Y^]¢¡Kik_zB¡±ip}]¢h[ipZ$umtZfu9h^`czg`*YRÈ
}*`*zBh[ipZ$ut[h^Y^]h^`*\q°fnBTBik}µiptT]¡kt^Z5h^Z=e{`/|Bikt^}*lmt^t`~|V²
ÇBiktikth^m`\fZJ]¡Zq¤4h^Biktt^`*}rh[ikZfu¼²
' d ! " $#)'%
¤`w}*Z$umt[ik|m`*Y½]\f`*um`*Y^]¢¡{YRik\Wik|8|Bikt^zB¡¯]q}~`*_`*u$h ¤¦Z$Y-wBik}¥`yO]*sf`'h^m`T¤¦ZW¡±¡kZikum\,|m`*}*Z$_¥zgZ$t[i§h[ikZ$u=ZW¤
h^m`wÈ _=]h^YRi» & N P : Y
6 V V V N %
,&% ,b# , ;
8<
Çm` È _=]¢h^YRi±»ikth^Jlmt4Y[`r¡¯]h^`*|/h^Zmnqz]qY^]q_¥`rh^`*Y[t¤¦Z$YVh^m`´zmY[ZWv[`*}rh[ikZfu/Zq¤Jh^m`´h^Y^]Wut[¡®]¢h[ikZfu\9N
;
|m`rºum`*|9lmzh^Z8]t^}]¢¡p`¤@]q}rh^ZfY<^nVzO]WY^]q_`h^`*Y[t'¤¦ZfY½h^m`(Y[Zqh]¢h[ipZ$uF]qum|µh 'ip}*`z]WY^]q_`rh^`~Y[t'¤¦Z$Yh^m`
ikufh^YRikumt[ik}}]¡±ipeY^]h[ikZfuz]qY^]q_¥`rh^`*Y[t~² h´ipt´h^Jlmt+}r¡k`]WY-h^]¢h´`w}]qu¥uZWh+Y[`*}*Zsf`*Y+]¡±¡h^`~t`z]qY^]W_`rh^`*Y[t
¤¦Y[Z$_©h^m`(z]qY^]W_`rh^`*Y[tZq¤4h^m`wÈ _=]h^YRi»V²
ê`5}¢]qu|m`*YRi±sf`=]=z]qY^]W_`rh^`*YRip«]¢h[ipZ$uZq¤ ]WtT¤¦Zq¡§¡kZwt*²
ê`TYRi§h^` ·ikuµh^m`/¤¦Z$Y[_ & N P
%
< = > ?
P ;
!(8<
i±h^
f N
f N f f f % f N $nfwoi§¡k`G ikt+|m`rºum`*|8]qt´h^m`e]qt[ipt-s$`~}rh^Z$Y+ZW¤Vh^m`T¹W`*Y[um`r¡
Zq¤M²
ÇBiktczO]WY^]q_`h^`*YRik«]h[ikZfuiktct[ikum\$lB¡¯]WYipu h^m`µ}¢]qt^`=Tm`*Y[` fkNC9Z$Y lfkNCB² 5wZ~`s$`*Yn-h^Bikt
}]Wt`}*ZfY[Y[`*t^zgZ$um|mth^Zc]/Y[`rh[iku]¡Oh^Y^]Wut[¡®]¢h[ikZfuZ$Y½]y}~Z$uBº\$lmY^]¢h[ipZ$uwm`*Y[`'h^m`T`~zoipzgZW¡k`*t+]WY[`]h-ikuBºuBi±h °fn
woip}ipt/Zq¤´zmY^]W}rh[ik}]¡ipu$h^`*Y[`*t[h(]Wt/|oipt^}*lmtt^`*|1ikuh^Bikt/z]qz{`*Yn]Wu|9h^olt(]WuO]¡±°B«~`*|lmtipum\]8t^zg`*}ri§º}
z]qY^]W_`rh^`*YRip«]¢h[ipZ$u¼²¿¡kt^`(`}]qu9wYRi±h^` NQ] ` b Y
b$gT]Wum| CN ] ` b Y b $g½h^Z1Z$eBh]¢ipu]z]qY^]W_`rÈ
h^`*YRip«]¢h[ipZ$u9ZW¤h^m`(`*zBikzgZW¡k`(]qum|9t[ip_i±¡®]qYR¡±°JnO|oipt[h[ikum\$lBikt^i§¤´`ri§h^m`*Y[mn¢n
ZfY
%
}]qu1eg`,t^`rhTh^Z;ZfY $²
Ru£h^m`}¢]qt^`Zq¤w]Y[`h[iku]¢¡+h^Y^]Wut[¡®]¢h[ikZfu i ²`W² f N µ`=}]Wulmt^`=h^`=|m`*}~Z$_z{Z$t[i±h[ipZ$u£Zq¤wÅ i±h^ª]
zg`~Y[_5lBh]¢h[ipZ$u1Z$u8h^`/¡§ikum`*t]Wum|µY[Zwt'ZW¤ ²
ÇBikt4z]qY^]W_`rh^`*YRip«]¢h[ipZ$uc]¢¡±¡pZTth^Z|BikY[`~}rh[¡±°(`*t[h[ik_]¢h^`´h^m`+`*zBikz{Zq¡k`~t ]Wu| ®²-¿´]W}(lmuO]WYR°,s$`*}h^Z$Y
ikt(|m`rºum`*|ef° 1zO]WY^]q_`h^`*Y[t~nTBi±¡p`=h^`=_]¢h^YRi»6ikt(|m`rºum`*| e$°ªzO]WY^]q_`h^`*Y[t~²Çm`=`r¡k`~_`*u$h^t
Zq¤4h^m`/_=]h^YRi» ]*sf`,]\$`*Zf_`rh^YRip}iku$h^`*Y[zmY[`rh]h[ikZfuVnOt[ipu}~`h^`°µ|m`rºum`h^m`,Zf_Z$\fY^]qzmBik}Y[`¡¯]¢h[ipZ$u
eg`h `*`*uh^m`yh Z=zg`*um}ri§¡ktZq¤K`*zBikz{Zq¡®]qY+¡±ipu`~t 2a$4@²
À t]=}*Z$umt^`*jJlm`*um}*`$nmi±h^1h^oiptz]qY^]W_`rh^`*YRip«]¢h[ipZ$u¼ng`rs$`~u9i±¤O¥]qum|P ]WY[`5|m`rºum`*|9lmzh^Z]=t^}]¢¡p`
¤@]q}h^Z$Y(Z$uB¡±°fn´h^m`µY[`r¡®]¢h[i§s$`t^}]¢¡p`e{`rh `~`*u¬h^m`*t^`¥h ZjolO]Wu$h[i±h[ip`*t}]Wu¬eg`=º»`*|¼n´Tm`*u¬lmt[ikum\h^Bikt
|m`rºuBi±h[ikZfu¼²
Ñ9ZfY[`*Zs$`~YnW\Wi±sf`*u8]qu¥`*t[h[ik_=]h[ikZ$uÂZq¤ È _=]¢h^YRi±»c¤¦ZfYwoip}`_ip\$$h+]*sf`
%
B]9g[N ]Wum|i±h^t
t[ikum\$lB¡®]qY4sW]¢¡klm`|m`*}*Z$_¥zgZ$t[i§h[ikZ$u N
Y
f
`}]quc`]qt[i§¡±°(`*t[h[ik_=]h^`]qu ^Z$zBh[ik_]¢¡\
_=]h^YRi» t^lm}1h^O]h
%
B]76gKN 8]qum|h^m`(h ZY[`r¡¯]h^`*|9`*zBikz{Zq¡p`¢²
À
t/]=}*Zfumt`~jJlm`*um}*`WnO`]¡±]*°Bt
}]Wuµ`*t[h[ip_=]¢h^`(]qulmuJeBi¯]Wt`~|sW]¡klm`,Zq¤4h^m` È _=]¢h^YRi±»µ¤¦Y[Z$_]qu`*t[h[ik_=]h^`
/²
Ë )HÍ^f)¯KB¯¸g¶ ¸,Ë Í B98 &`rhlmt'umZE}~Z$umt[ik|m`*Y+h^m`/zY[ZfeB¡k`*_©ZW¤4Y[`*}*Zs$`~YRikum\h^m`
ikufh^YRikumt[ik},}]¢¡§ikemY^]¢h[ipZ$uz]qY^]q_¥`rh^`*Y[t~²
rx:USwxr !
`
q"!
Q"!
"#
< = > ?
$ 03 % q & &
& % Q &
& & % ('
q)!
'
Q"!
'
)#
< = > ?
* 03 +
V-,.,'Y
Rxy0/12/
+
`3/
+
12/ `54e7681-6
+
`96
+
1:6c`34S{ 1$
%
q<;
%
Q=;
%
=;>&
AdRy!-U$r00s)x/- 1v10{-r0
Ö@?(ACB×EDGFIH
ÜIF)D×JLK.J-MON^Ø4ÝPNÖ?§Ú(?QN)A
8-1!>U$r { 1$60{ 1Ktr rR-r 1x/Kr0x/-sM{xzr0 1$sr0w-0{TSW)U dRy:rCw*r0{)$r0wZ0{ 1 r0{@y:r0
xy:{x xy$rMs{1xwV `W/
% q & &
& % QX&
& & & 6 +
r0wZYr0 [C\)]
# ` & { 1$s~1!-so_^0r0a`Z`
cb> `Z`80 1:-$r0w1KT@xy$r
1$w/s`Z` `Z``cd
'
egffhffi q
`Z`
`Z`kj w/r0)r0w
-|xy$r)r0xw T)r 1:r0w/{1x/1KT xy:r r0w 1$r8gml
+
:r
+ ` & { 1:
'
-Rxzy$rSr0xweTr 1$r0w*{x*1KT xy$rr0w 1:r 1g :rn91
' ` &
ê`,TYRi§h^` N ]qum| CN l
T4²¿´]W}È _=]¢h^YRi±»FiktipuZ$um`rÈ@h^ZqÈ Z$um`5}~Z$Y[Y[`*t^zgZfum|`~u}~`
i±h^ h^m`
À È _=]¢h^YRi±»2§$4@² ¤(``»zB¡±ip}ri±hh^m`¤@]q}rh8h^]¢h; ipt]Wu ZfYRh^mZ$\$Zfu]¢¡_]¢h^YRi» ipu h^m`
|m`rºuBi±h[ikZfu"E F ZW¤`~jJl]¢h[ikZfu
;
a<^n`,Z$eBh]¢ipu &
j EF E TF ;
¢8<
woip}¡k`]W|mt½h^Z
;
_(lB¡±h[ipzo¡§°Jikum\=¡k`¤¯h]Wu|1YRik\f$hTef° P< &
P
Pij T ;
~a<
woip}Â}~Z$Y[Y[`*t^zgZfum|t(h^Z #&-`*jJl]h[ikZ$umt¹ouZwu ]qth^m`/Y[lzmz]`*jJl]¢h[ipZ$umt~²£Çm`*t^`
`*jJl]h[ikZ$umt}]qu e{``]qt[i±¡§° _=]q|m``»mzo¡§ik}ri§h}*Z$umt[ik|m`*YRipu\ªh^`t[ipu\flB¡¯]qYRÈ@sW]¢¡plm`|`~}*Z$_z{Z$t[i±h[ipZ$u Zq¤@
\qi§s$`~uµiku1`*jJl]¢h[ipZ$u
;
$<^² À ¤¯h^`~Y½t^Zf_`,]¢¡p\$`*emY^]Bnm`*jJl]¢h[ipZ$u
;
8<+Y[`*|mlm}*`*th^Z &
TY Y
TY f
Tf f 01
3 J ] Y
gzf UT
Y
Y
Y f UT
Y
f
] f
gzf UT
f
f 01
3 N ;
¢8<
woip}¼nV]qtw]}*Y[Zftt[È zmY[ZB|lm}rh~niptT`*joloi§sW]¢¡p`*u$hTh^Z`~jJl]¢h[ikZfumt*²Ç'm`r°°Jik`¡k|jolO]WYRh[ik}(`*jJl]¢h[ipZ$umt'ipuh^m`
ikufh^YRikumt[ik},z]qY^]q_¥`rh^`*Y[tuZWh`]qt[i±¡§°=}]¡k}*lB¡¯]WeB¡k`32a$4VwBik}9]qY[`h^m`/Zfuo¡§°8`*jJl]¢h[ipZ$umt`/}]quZ$eBh]¢ipu=¤¦Z$Y
t^`r¡±¤¯È }]¡±ikemY^]h[ikZ$u=ipuµh^m`,\$`*um`*Y^]¡}]qt^`W²
Çm`*t^``*jolO]h[ikZfut¥O]*sf`]qu¬ip_zgZfYRh]qu$h8um`*\o]¢h[i§s$`1}*Z$umt^`*jJlm`*um}*` &O# ` HZ0v'~1 zZ
/M'-/.0v &d3!/'( Z01!#"$Wv* @#3&1/.'W* )!'G1v'/.d/
(/(n´`rsf`*u¬'i§h^ÂZ$lmYt[ik_¥zo¡p`_ZB|m`r¡ZW¤/`*jJl]¢h[ipZ$u
;
<^² ê`h^Jlmt=_(lmth¥iku$h^Y[ZB|mlm}*`9]WumZqh^m`*Y
]qt^t^lm_zBh[ikZfuVn$t^lm}8]Wth^m`'¤@]W}rh-h^]h-h^m`*t^`'z]WY^]q_`rh^`~Y[t+]qY[`}*Z$umt[h]qufh@2a4Z$Y-|Bipt}~lt^t-h^m`w}]¢¡§ikemY^]¢h[ipZ$u
lmt[ikum\=]qumZWh^`~Y'_`~}]quBipt_¥t*n]qt|`s$`r¡pZ$z{`*|ipuµh^Biktwz]qzg`~Y²
Q ' #)' ! " $#)' %
&`rhlmt]qt^t^l_¥`'h^]¢h]¡±¡Vz{Zqipu$h^teg`r¡pZ$um\$t-h^Z¥]fÒEzB¡¯]qum`¥noi±h^&{ T { N %
wm`*Y[` n
N $noikth^m`,zo¡®]qum`,umZ$Y[_=]¡4]qum|
%
5i§h^tT|Bikt[h]Wu}~`h^Zh^m`ZfYRik\Wiku¼²
¤´`umZ }*Z$umt[ik|m`*Yy]\f`*um`*Y^]¢¡:zB¡¯]qu]WYYRik\Wik||Bikt^zB¡¯]W}*`*_`*ufh¤¦Z$YTwBik}`]*s$`h^m`(¤¦Zq¡±¡pZ'ipu\
|m`*}*Zf_zgZfti§h[ikZfu 2§$4 & E N : Y 8T
V V V 6 V N
% ,% ,b# , ;
¢ 8<
`]*sf`=z]qY^]q_¥`rh^`*Y[tT¤¦ZfY'h^m`zmY[ZWv[`*}rh[ikZfu9Zq¤:h^m`5h^Y^]qumt[¡¯]h[ikZfuPWn=z]qY^]W_`rh^`*Y[tw¤¦Z$Y'h^m`cY[Zqh]¢h[ipZ$u
]qum|h ik}*`8z]qY^]q_¥`rh^`*Y[t,¤¦Z$Yh^m`iku$h^YRipumtip}8}]¢¡§ikemY^]¢h[ipZ$uz]qY^]q_¥`rh^`*Y[t~nzB¡klmt(z]qY^]q_¥`rh^`*Y[t/¤¦Z$Y/h^m`
zB¡¯]WuO]WYth^Y[lm}rh^lmY[`(Y[`*zmY[`*t^`*u$h^`*|1e$°WN : Y 4 %
nJ'i§h^ T N W² hwiktw]¢¡kt^Zc}r¡k`]WY+h^O]h'`,}]WumuZWh
Y[`*}*Zsf`*Yw]¢¡±¡¼h^`~t`,z]qY^]W_`rh^`*Y[tikuh^m`\f`*um`*Y^]¢¡}]qt^`W²
¡ 16):w|0{/r|r y${)r ! !
'#"
`%$
" Q 6 "
`%$
q Q'&
Q
`($
")"
b*$
Q
" Q
`%$
q/q b+$
Q
q Q
,.-
]0/ $
Q7Q
` 9 $ " q
`$
" Q $ qQ
V-, 4 Y
/xy${1xUxy$r r-r0sr 1xU1xy$r
Ö21Ø+Ø JÚ(H ?M
s{1xw3 r0wZYr04 U${):w/{1x/- 0 1$xw/{11x ,1$r0{wR0 1$xzw/{11)xR{ 1$
{1-0 x~r0x/-s{1xrUxzy$r ${)w*{)sMrxr0w*&xzy$r 0w/w*r0/ 1:!1KT £S s{1xw
ÅmlmYRh^m`*Y[_Z$Y[`$no`rsf`*ui±¤¼`ri±h^m`*Y i<h^m`T}¢]¢¡±ipemY^]¢h[ikZfuz]qY^]W_`rh^`*Y[t´Y[`~_=]¢ipu=}*Z$umt[h]qu$h
N
<o2±f14 n
Z$Y
;
i±i<4h^`~Y[`'ikt+umZ,Y[Zqh]h[ikZfu
; N [!<4'i§h^=}]¢¡§ikemY^]¢h[ipZ$uz]qY^]W_`rh^`*Y[t:sW]qYRi¯]h[ikZfut´`w}]qu¥uZWh+Y[`*}*Zsf`*Y
h^m`*t^`,zO]WY^]q_`h^`*Y[t~²C5wZ~`s$`*YnOt^`rsf`*Y^]¡_Z$Y[`/ipu$h^`*Y[`*t[h[ikum\=t[i±h^l]h[ikZ$umt}]quZB}*}*lmY]qt|m`rh]¢i§¡k`*|1umZ~5²
Çm`zO]WY^]q_`h^`*YRik«]h[ikZfu5ZW¤Oh^m` µÈ _]¢h^YRi»5iptsf`*YR°t[ip_zB¡±° EN
% B #
6
t[ikum}*`+¤¦ZfYY[`]¡±ipth[ip}
|Bikt^zB¡¯]W}*`*_`*ufh^t
ff
iktum`rsf`*Y'uolo¡§¡~2±$4@²
"'d $#)'d% ! % * 'd
&`rhlmt/}*Zfumtip|m`*Y'h^]¢hy`5]*s$`¥]=|oipt^zo¡®]q}*`~_`*u$h/ZW¤-h^m`}¢]q_`*Y^]i±h^umZ8h^Y^]qumt[¡¯]h[ikZ$u¼nOi@²`W²yZfuB¡±°F]
Y[Zqh]h[ikZfuµ]Wum|µ]/sW]qYRi®]¢h[ipZ$uZq¤Vh^m`ikufh^YRikumt[ik}/z]qY^]W_`rh^`*Y[t~²Ru=h^]¢h}]Wt`$n]qt |oipt^}*lmtt^`*|=zmY[`rsoikZ$lmt[¡±°Jno`
]*s$`#&
N iN
%
EF^j EP
;
q<
ÇBiktwti§h^l]¢h[ikZfuipt'h^Jlmt}]qY^]W}rh^`*YRik«~`*|e$°h^m`/¤@]q}rhh^]¢h/]¡±¡Vh^m`(Y[`rh[iku]¡4|oipt^zO]WYRi±h °}]Wue{`zmY[`rÈ
|Bik}rh^`~|e$°1]lmuBikjJlm`,}*Zq¡§¡±ipu`¢]¢h[ikZfu¼² À t'|Bikt^}*lmt^t^`*|eg`r¤¦ZfY[`Wnoh^Biktwti§h^l]¢h[ikZfu
}]WuumZWh'|Bipth[ipum\$lBikt^µ¤¦Y[Zf_ h^m`y¤@]W}rhh^]¢hy]¢¡±¡zgZqipu$h^tTe{`r¡kZfum\h^Z=]lmuBikjJlm`(zB¡¯]qum` nflmuB¡k`*t^t+]Wu=]q|m|Bi±h[ipZqÈ
u]¢¡VipuB¤¦Z$Y[_=]h[ikZ$uiktw]q|m|m`*|¼²
uZfY[|`~Y½h^Ze{`,tlmY[`h^Z=e{`ikuµh^m`,}]Wt`/ZW¤:]zmlY[`,Y[ZWh]¢h[ikZfu`,_(lmth"&
`i±h^m`*Y\$`rhh^m`/ikuB¤¦Z$Y[_=]h[ikZfu¤¦Y[Zf_ ]Wuµ`r»oh^`*Y[u]¢¡4t^Z$lmY[}*`$nt^l}9]Wt½h^m`,Y[Z$e{Zqh[ip}/t°th^`~_ i±h^t^`r¡±¤n
ZfY]Wtt^lm_`,h^]¢hTh^m`ct}~`*um`5ikty_=]q|m`(Zq¤+]h¡k`¢]qt[hTh ZµzB¡¯]Wum`*t~nt^Z=h^]¢hi§¤-`ct`~`] lmuBikjol`
zB¡®]qum`Wnoi§hT}*ZfY[Y[`*t^zgZfu|mth^Zh^m`/¤@]q}rh`,]sf`(]zmlmY[`Y[ZWh]¢h[ipZ$u¼²
u]qu$°8}]Wt^`WnWh^m`/_=]iku8zmY[Z$z{`*YRh°=ipt h^]h½h^m`}~Z$Y[Y[`*t^zgZfum|`~u}~`*t+eg`rh `*`*u8h^m`h Z5ip_=]q\f`*t+|mZB`*t
umZqhc|m`*zg`*um|ªZ$uh^`|m`*zBh^ ZW¤TZfeBv[`*}rh^t~nt^Zh^]¢h(h^`8t[°Bt[h^`*_%}]Wu Y[`r¡®]¢h^`=h^m`¥soikt^l]¢¡´ipuo¤¦ZfY[_=]¢h[ipZ$u
eg`¤¦Z$Y[`,]qum|1]¢¤¯h^`*Y|Bikt^zB¡¯]W}*`*_`*ufh~ng]qt\qi±sf`*u8iku1`*jJl]¢h[ipZ$u
;
a<^²
Ñ9ZfY[`*Zs$`~Yn{i±¤`=]WY[`ikuh^m`=}]Wt`cZq¤]zmlY[`=Y[ZWh]¢h[ipZ$ulmtipum\µ`*jolO]h[ikZfu
;
¢8<'`}¢]qu`*t[h[ik_=]h^`
h^m`,u`Æiku$h^YRipumtip},}]¢¡§ikemY^]¢h[ipZ$uzO]WY^]q_`h^`*Y[t½¤¦Y[Zf_©h^`,zmY[`rsJipZ$lmtTZfum`32±$4@²
ÅmlmYRh^m`*Y[_Z$Y[`$n{i±¤:h^Bikt/_ZWh[ikZ$u9iptTsf`*YR°jJlBik}¹nVh^`¥]q|m|Bi±h[ipZ$u]¢¡4sW]qYRi®]¢h[ipZ$umtikuh^m`(ik_=]W\$`(|lm`(h^Z
umZ$uBÈ th]h[ikZfuO]WYR°=Z$eBv[`~}rh^t+eg`rh `*`*uh^`/e{`*\qipumuoipum\]qum|=h^m`/`*um|µZW¤4h^`/_¥Zqh[ikZfu]qY[`/`»z{`*}rh^`*|8h^Ze{`
t^_=]¢¡§¡@²
³ Z$umt[ik|m`*YRipum\]q}rh[i§s$`=sJipt[ikZ$u¼n-h^Bikt5°oik`r¡p|t(h^Z9h^m`¤¦ZW¡±¡kZikum\ )1v,_`*}]quBikt^_ & d//
3d J &1/.'1 &)\`@ k H &'&&1 HG` /H!M#3v'H %
|'RI#^²
"'d $#)'d% ! % *#,
Ruh^m`=}]qt^`wm`*Y[`h^m`=}]¢¡§ikemY^]¢h[ipZ$uz]qY^]W_`rh^`*Y[t(]qY[`=}~Z$umt[h]qu$h~n]Wum|¹JumZikum\"E `}]Wu`¢]qt[i±¡§°
}]¡k}*lB¡¯]h^`h^m`yipu$h^YRikumt[ik},}]¡±ipeY^]h[ikZfuµz]qY^]W_`rh^`*Y[twt[ikum}*``,]sf`#&
N
EP
%
B] E g
#
% N
%
B] g N : Y
6
N|]8g P
;
¢8<
w`~Y[` N n
iptyh^m`=lmu]qYR°9sf`*}rh^ZfY,Zq¤´h^m`8]»Bikt,Zq¤´h^m`=Y[ZWh]¢h[ikZfu]qum| h^m`8]Wu\W¡k`cZq¤+h^m`
Y[Zqh]h[ikZfuV²uh^m`\$`*um`*Y^]¡B}]qt^`´`]*s$`
%
B]
g N a
B]
guN /]Wum|5`}]qu(Y[`*}*Zsf`*Yh^m`+ikufh^YRikumt[ik}
z]qY^]W_`rh^`*Y[tZ$uB¡±°1]¤¯h^`*Y+h Z=Y[Zqh]h[ikZfutumZqhy]qY[Zflum|8h^m`t]W_`,]»oipti2§$4@²
ê`/]¡kt^ZY[`*}*Zsf`*Y
lzh^Z8]t^}]¢¡p`T¤@]q}h^Z$Yng]qt+h^m`,uJlB¡±¡4sf`*}rh^Z$YZq¤
t[ikum}*`/`,O]*sf`&
N B²
ÃÁi±h^8h^m`,_ZB|m`r¡4Zq¤K`*jJl]h[ikZ$u
;
$<´`,Z$eBh]¢ipuh^m`/¤¦Zq¡§¡kZikum\`*jolO]h[ikZfut"&
#$$$$$$
%$$$$$$&
``
`
f`
N
YY
` f Y N
] ` Y Y ` g ` f Y `
f`
N
f`
#afB
``
` ` Y `
`f
N
f Y
#afB Y ` `
YY
` Y f N ;
¢8<
woip} ]¢¡±¡pZh^ZY[`~}*Zs$`*Y ]^
`
bO
`
gy¤¦Y[Z$_%h^m`ºY[t[h¡§ikum`]qY(`*jJl]h[ikZ$umt=]Wum|Vn´¹JumZ'ipum\ ]^
`
bO
`
g^n#
`»}~`*zBh'i§¤ &
f`
N 7 ] g
#
N #
% f Y N
] g
#
9N ; (8<
Çoipt+t[ikum\$lB¡¯]WY-}*ZfuBºO\flmY^]¢h[ikZfu}*ZfY[Y[`*t^zgZ$um|mt-h^Zc]/Y[Zqh]¢h[ipZ$u8]WY[Z$lmum|h^m`Z$zBh[ik}¢]¢¡{]»oipt+Z$uB¡±°cTBip}i±¡§¡
eg`ip|m`*u$h[i±º`*|1ikuµh^m`,t^`*jJlm`r¡ ²
À t+]}~Z$umt^`*jJlm`*um}*`WnG&G1# H3 090/ '#'C6/#d1!/'('-/.0/9`61()*
#&|' 3!v!'²´Ç'Bipt½iptTumZqhh^m`,}]qt^`i±h^9]WumZqh^m`*Y}]¢¡§ikemY^]¢h[ipZ$u_ZB|m`r¡u2±f14 ²
"'d $#)'d% ! % * ' '
Çoipt+Zqh^m`*Y´t[i§h^lO]h[ikZfuikt+t[ik_zB¡§°=}]WY^]q}rh^`*YRip«*`*|=e$°ch^m`T¤@]q}rh h^O]h´h^m`Th^Y^]qumt[¡¯]h[ikZfuikt+z]qY^]¡±¡p`r¡Oh^Z,h^m`
ik_]q\$`/zB¡®]qum`Wnoi ²`W² fN ²KÇBiktiktw`*jJlBi±sW]¡k`*u$hwh^Z &
f N ;
m$<
t[ipu}~`¤¦Y[Z$_©`*jJl]h[ikZ$u
;
$<^n fj )f
uh^]¢h+}]Wt^`Wnqh^`wZ$YRip`*u$h]¢h[ipZ$u ,Zq¤{h^m`'h^Y^]qumt[¡¯]h[ikZfuikt N#
S# ] Y 4
`)g^²-Ç'Bipt´ikt´|mlm`'h^Z,h^]¢h
¤@]q}hTh^]¢h¤¦Y[Zf_ `~jJl]¢h[ikZfu
;
$<^n`6N U]#`
`
f)gT]Wu| Y N U]# Y `
fcg't^Zh^O]hi±¤=fiN n
`,]sf` Y 4
`uN Y 4
`¢²
¤T`1]qY[`umZqhipu¬h^Biktt[i±h^l]h[ikZ$u¼n´`µ}]Wu¬z]qY^]W_`rh^`*YRip«*`h^m` rÈHsf`*}rh^ZfYlmt[ikum\ )`]qum| Y ]qum|
]qt^t^lm_ikum\£h^O]h )fON wm`*Y[`]Wti§¤`]WY[`umZqh8ikuÁh^oiptµt[i§h^lO]h[ikZfuVnT`}]Wu z]qY^]W_`rh^`*YRip«*`9h^m`
rÈHsf`*}rh^ZfYlt[ipu\ )`y]qum| Y ]qum|9]Wt^tlm_ipum\5h^]¢h f~N W²
dRy$rr$c-x rSU${x*- 1:{w/r !
#$
%$&
`
.
.
.
.
.
` b
.
!
.
.
" Q ` b
.
$#&%
.
b
.
'(%
.
b
)
.
*
.
&`rhlmt'umZÆ}*Zfumtip|m`*Y+h^O]h`]*sf`,]|Bikt^zB¡¯]q}~`*_`*u$hZW¤h^m`/}]W_`*Y^]5wBik}iptT]czlmY[`/h^Y^]qumt[¡¯]h[ikZfuVn
i@²`W² h^m`*Y[`µiptumZY[Zqh]h[ikZ$u ]qum|¬umZ9sW]qYRi®]¢h[ipZ$u¬ZW¤'h^m`µipu$h^YRikumt[ik}z]qY^]W_`rh^`*Y[t~² Ru¬h^]h}]Wt`$n4¤¦Y[Zf_
`*jJl]h[ikZ$umt
;
a<^n
; < & N P #
% E Fjm[
;
f8<
ÇBiktt[i±h^l]¢h[ipZ$u8iktTt[ip_zB¡±°}]WY^]q}rh^`*YRip«*`*|e$°h^`¤@]W}rhh^O]h'h^m`È _]¢h^YRi»µipt't^¹W`r'È t[°B__`h^YRik}W²
³ Z$umt[ik|m`*YRipum\Th^m`½Y[`~}*Z$umt[h^Y[lm}rh[ikZfuzmY[Z$eB¡k`~_nq`½t^`*`´¤¦Y[Zf_ `*jJl]¢h[ipZ$u
;
a<{h^]h-t^Z$_¥`´h^Y^]qumt[¡¯]¢h[ipZ$u]¢¡
_ZWh[ikZ$u=ipt½Y[`~jJlBikY[`*|h^Z5ikuB¤¦`*Y+t[h^Y[lm}rh^lmY[`/¤¦Y[Z$_ _¥Zqh[ikZfu]qum|=h^ZY[`r¡®]¢h^`h^m`,$ÒEt[h^Y[lm}rh^lmY[`/z]qY^]W_`rh^`*Y[t
h^Zh^m`,zmY[Zqv[`*}h^`*||Bikt^zB¡¯]W}*`*_`~u$h~²
&ZBZf¹$ikum\5¤¦ZfYZ$zBh[ik_=]¡h^Y^]qumt[¡¯]h[ikZ$u]¡V|Bikt^zB¡¯]W}*`*_`*ufh~ni±hikt]¡kY[`]W|B°8¹JumZ~wuµh^]h'h^m`,Z$YRip`*u$h]¢h[ipZ$u
Zq¤+h^m`h^Y^]Wumt¡®]¢h[ipZ$uikt,eg`h[h^`*Y$Z$YRh^mZf\$Z$u]¡h^Z1h^`$Ò zgZWiku$h^t(\2±!(:4@ni@²`$²¥Z$YRip`*u$h^`*|£t^lm}h^]¢h,h^m`
ikum|mlm}*`*||Bikt^z]qYRi±h °=ikt_=]¢»oik_=]¡ &-}*Z$umt[ik|m`*YRipum\]¡§ikum`t^`*\f_`*u$h~no¤¦ZfY´ikumt[h]qum}*`Th^m`/zmY[ZWv[`*}rh[ikZfu8Zq¤h^m`
h^Y^]qumt[¡¯]h[ikZfuipt'Zfzoh[ip_=]¢¡i§¤4i±hikum|ml}~`*t]umZfY[_=]¢¡4|Bikt^zB¡¯]W}*`*_`~u$hZq¤4h^m`Y[`~}rh[i±¡§ikum`]qY`*|m\$`$²
Ñ9ZfY[`*Zs$`~Yyi§¤}]qu`=Y[`*}*Zsf`*Yh^m`8|BikY[`*}h[ikZ$u£Zq¤h^m`=h^Y^]qumt[¡¯]h[ikZ$u¼n-]Wtt^ZBZfu]Wt]1}]¢¡§ikemY^]¢h[ipZ$uikt
ikt^t^lm`*| &
ij
: Y ;
f8<
Çm`8zO]WY^]q_`h^`*YRik«]h[ikZfut(Zq¤ ]qY[`=s$`~YR° t[ik_¥zo¡§° N Y
`
Y `
¤¦ZfYºuBi±h^``*zBikz{Zq¡p`
i±h^t[ip_i±¡®]qYzO]WY^]q_`h^`*YRik«]h[ikZfui§¤ f N ²
"'d $#)'% ! $% #, #)'d
'
&`rhlmtumZ6}*Zfumtip|m`*Y'h^]¢hw`5]*sf`]=zmlmY[`h^Y^]Wut[¡®]¢h[ikZfu¼nemlBhT¤¦ZfY]zB¡¯]Wu]qYTt[h^Y[lm}rh^lmY[`W²/ÉTt[ikum\h^m`
t]q_`/`~jJl]¢h[ikZfumt½`,`]Wti§¡±°8t^`*`h^]¢h`(]qY[`¡pZBZ$¹$ipu\c¤¦Z$Y]_=]h^YRi»"E¨Zq¤Kh^m`¤¦Z$Y[_ &
EEjm[
T ;
Wa<
³
Z$umt[ik|m`*YRipum\ E T
`]*sf`yh^m`/¤¦Zq¡§¡kZikum\`rip\$`*uBÈ@sW]¢¡pl`,|m`*}*Zf_zgZft[i±h[ikZfu &
EkT
N
j
EkT
N ]O 8T
DD g ;
f8<
Ð lm}]}*Zq¡§¡±ipu`¢]¢h[ikZfuiptZ$uB¡§°µ|m`rºum`*|9ef°ºms$`(z]qY^]W_`rh^`*Y[t
;
¤¦Z$Y'h^m`(zmY[Zqv[`*}h[ikZ$u1Zq¤Kh^m`yh^Y^]WumtÈ
¡¯]h[ikZfu|m`rºum`*|£lzh^Z]t^}]¡k`¤@]W}rh^Z$Y,]Wum| µ¤¦ZfY/h^`=z]WY^]q_`rh^`~YZW¤h^`=zB¡®]qum`$</]qum|£}]quh^Jlmt5e{`
}O]WY^]q}rh^`~YRik«*`*|·]qtt^ZBZ$u ]Wth^mY[`*`\$`~u`~YRik}zgZWiku$h^t1]qY[`F\qi±sf`*u¼ntipum}*``]q}Á_=]¢h^}E\f`*um`*Y^]¢h^`*t=h Z
`*jJl]h[ikZ$umt\qi§s$`*u1e$°-& J E N BnmZ$Y_Z$Y[`,zmY[`*}ript^`r¡±°-&
J ] T g
J
N #
%& b b D
D N
] 8T,Og N D
D T u l ly : u l y l
l
/ ;
f 8<
t^Z/h^O]h+\qi§s$`~u8]¢h´¡p`]qt[h´h Z5umZ$uBÈ t[h]¢h[ikZfu]qYR°czgZqipu$h^t-`w}]qu=}]¡k}*lB¡®]¢h^` D
D
]Wum|h^`~uVnB\qi§s$`*u8]h´¡k`¢]qt[h
h^mY[`*`,umZ$u}~Zq¡±¡§ikum`]WY½z{Zqipu$h^t½`,}]Wuµ}¢]¢¡k}~lo¡®]¢h^` ¹JumZ~ikum\ DD ²
H z"$'- &6 v) 0 &v'²
u5ZfY[|m`*Yh^Z}r¡¯]WYRi±¤¯°/h^Bikt4¡¯]Wt[hz{Zqipu$hK}*Z$umt[ik|m`*YK]quf°,_=]¢h^YRi±» E 'i§h^
Y ]Wu|
Y
h^m``rip\$`*uBÈ@s$`*}h^Z$Y[t
}*ZfY[Y[`*t^zgZ$um|Bikum\h^Zµh^m`=t]q_``ik\$`~uoÈ@sW]¢¡plm` Y
Zq¤E T ]qum|
`
h^m`=`rip\$`*uBÈ@s$`*}h^Z$Y,}*Z$Y[Y[`~tz{Z$um|Bikum\8h^Z
]qumZWh^`~Y½`ik\$`~uoÈ@sW]¢¡plm` `
ZW¤ E T ²-Rufs$`*YRh[ipum\`~jJl]¢h[ikZfu
;
f8<-`,`]qt[i§¡±°8Z$eBh]iku &
ij
Y J
Y WN
` 4 Y
D
D T ` ` ;
o<
]qum|(s$`*YRi§¤¯°5h^]h E©ikt:Zq¤h^`+¤¦ZfY[_ ZW¤g`~jJl]¢h[ikZfu
;
Wa<^²Ç`~Y[`r¤¦Z$Y[`E # GM`GQ GM &
GiZWZ'-(3G m kH"$'- &@ v) 0 &v'
hikth^JlmtKzgZ$t^t[ikeB¡p`h^Z'ip|m`*u$h[i±¤¯°/i§¤]'\Wi±sf`*u µÈ _]¢h^YRi»5}~Z$Y[Y[`*t^zgZfum|tVh^Zy]'zmlmY[`-h^Y^]qumt[¡¯]h[ikZfu
;
h^`~th[ipum\
i±¤Kh Z¥`rik\f`*uBÈHsW]¡klm`*tw]qY[`,`*jJl]¢¡*<+]qum|µi§¤h^Y[lm`WnOh^ZY[`~}*Zs$`*Yh^m`,`r¡k`*_¥`*u$h^tTZW¤4h^`,}*ZW¡±¡§ikum`]¢h[ipZ$u
;
t^`*`32±)4
¤¦Z$Y]Y[`rsoik`r6ZW¤4h^`,}]¡±ipeY^]h^`*|}]qt^`$<^²
"'d $#)'% ! % ' $#)'%
&`rhlmtw}*Z$umt[ik|m`*Yh^m`5z]qYRh[ip}*lB¡¯]WY'h °zg`ZW¤-|BiptzB¡®]q}*`*_¥`*u$h¤¦Z$Y'wBik}h^m`5Y[`h[iku]¢¡KzB¡¯]Wu`/iptTiku$sW]WYRi¯]Wu$h~²
³
¡k`]WYR¡±°fnVh^oipt,}*Z$Y[Y[`*t^z{Z$um|mth^ZµYRip\qik|_ZWh[ikZfu9'i§h^ & fN `,N Y N BnVi@²`$²,`¥O]*sf`=]8Y[Zqh]¢h[ipZ$u
]qY[Zflmu|9h^m` +1]»oipt/Z$uB¡±°]Wum|Zq¤]Wu\W¡k` ]Wu|£]=h^Y^]qumt[¡¯]h[ikZ$u9i±h^ f,N Bn¼wBi±¡k`(h^m`=}]¢¡§ikemY^]¢h[ipZ$u
z]qY^]W_`rh^`*Y[t_ik\f$hweg`,}*Z$umt[h]qufh'ZfY'umZWh~²
uµh^]¢hw}]Wt`$nf`,]sf`(] È _]¢h^YRi»ZW¤h^m`/¤¦Z$Y[_ &
N LeY
`
+ l
+ ]
9`f )] g Y
f |]8g0g + l
+ ] 9`f |] g Y
f )] g0g 9ff
" 9ff~N
] 9`f ` 9f` ` Y f
` 9f
Y ` g ;
f8<
ÇBikt È _=]h^YRi»µikt}*Zfut[h^Y^]ikum`*|ef°-&
``
N ` Y N Y` N
YY
N ;
f8<
]qum|8`,Z$emt^`*YRs$`~|Vn¤¦Y[Zf_©`*jJl]¢h[ipZ$u
;
$8<^nBh^O]h"&
#
# N
]
f`
g f ] f Y g f
]
`f
g f ] Y f g f ; (8<
t^Z'h^]¢h`+}¢]qu,`*t[h[ik_=]h^`-h^m`´sW]qYRi®]¢h[ikZfu,Zq¤Bh^m`´¤¦ZB}]¢¡W¡k`~u\Wh^¼n¢TBi±¡p`-`+Y[`*}*Zsf`*Yn¢¤¦Y[Z$_ `*jJl]¢h[ipZ$u
;
$ <^n
h^m`(]qum\q¡p`/Zq¤4h^m`Y[ZWh]¢h[ipZ$u1]qt"&
N ]
9f Y
f`
g
|]
Y f
`f
g ;
m$<
ê`8]¢¡kt^Z9Y[`~}*Zs$`*Y(h^m`¥h^Y^]Wumt¡®]¢h[ipZ$u lmz£h^Z]t^}]¢¡p`¥¤@]W}rh^Z$Y)%j j ] `fb Y fb 8g
T
n ]Wum| Z$eBh]ikuª]
`ri§h^`~Y'}*Zfumth]Wu$hZ$Y+sW]qYR°oikum\mnh^m`,|Bikt^zB¡¯]q}~`*_`*u$hiptT]|BiptzB¡®]q}*`*_¥`*u$h¤¦Z$Y+woip}h^m`Y[`h[iku]¢¡zB¡®]qum`ikt
ikufsW]qYRi¯]Wu$h~nOi±¤ ]qum|ZfuB¡±°=i±¤ `` N ` Y N Y ` N YY N tipum}*`i±¤K`,|`ºOum` \N
6
f
`
]*s$`#&
9``
9` Y
Y `
YY
j ] 6
v` f
Y g Y ] f
6
` Y g f
] 6 Y f `cg Y ]^` ` vf vf
Y Y
g f
] 6
` f Y g ` ]^` v`
vf f
Y Y g f
] 6 Y f
`)g ` ] f
6
` Y g f
;
f8<
woip}Y[`¢]¢¡:tZW¡klBh[ikZfumt]qY[`cZ$uB¡±°1`ri§h^`~Y ` N Y N f N =Z$Yv` N
Y N f N Bn]qt`¢]qt[i±¡§°µsf`*YRi±º`*|
i±h^9]ct°_5e{Zq¡±ip},}]¢¡p}*lB¡¯]¢h^ZfY²
Çm`*Y[`r¤¦ZfY[`T],um`*}*`*t^t]qYR°¥]qum|=t^lB¾=}rik`~u$h+}*Zfu|Bi§h[ikZ$uh^Z(eg`ikuh^Bikt+t[i§h^lO]h[ikZfuikt~nW¤¦ZfY-h^m` È _]¢h^YRi»¼n
h^Ze{`ZW¤4h^`/¤¦ZfY[_2^N
9`f
Y f
f` f Y ff
²
¤-umZ5nm`c]qt^t^lm_`h^]¢hw`5]*s$`(]=¹JumZ'¡p`*|m\$`,Zq¤Kh^m`5zB¡®]qum`(]¢hikuBºuoi§h °fngh^m`5Y[`¡¯]¢h^`~|_=]h^YRi»
EF6ikt\qi§s$`~ue$°-&
EFj + l
+
)] g + l
+ |]8g + l
+ ]
)]8g8
` U] g8
`
g `
+ l
+ |] g + l
+
)] g + l
+ ]
)]8g8
` ] g8
`
g
`
;
f8<
Ruh^Bikt(}]qt^`Wn`=]¢¡ptZ1|BikY[`*}rh[¡§°Z$eBh]¢ipuh^`=Y[ZWh]¢h[ipZ$uª]qum\q¡p` nh^`sW]WYRi¯]h[ikZ$u£Zq¤+h^m`¤¦ZB}]¡¡p`*um\qh^
# 4
#n']qum| }]quÂ`~th[ip_=]¢h^`1h^`Fu` ¡pZB}]¢h[ipZ$uÂZq¤yh^`FZ$zBh[ik}]¡T}~`*u$h^`*Y ]^ ` b(
`
giku¤¦lmum}rh[ikZfuÂZq¤/h^m`
zmY[`rsJipZ$lmtsW]¡klm` ]^
`
bO
`
g^nJ]WtsJipt[ikeB¡k`+ikuc`*jJl]¢h[ipZ$u
;
$8<^² ¤Oh^m`}]¢¡§ikemY^]¢h[ipZ$u(z]qY^]q_¥`rh^`*Y[t´]WY[`+}*Z$umt[h]qufh~n
`=|BikY[`*}h[¡±°£Z$eBh]¢ipuh^`¡pZB}]¢h[ipZ$uZq¤+h^m`=zmYRikum}ripz]¢¡+z{Zqikufh~²¥Ru ]qu$°}]Wt^`WnumZµipuo¤¦ZfY[_=]¢h[ipZ$uZ$uh^m`
]qemt^Zq¡plBh^`sW]¢¡klm`,Zq¤4h^m`/¤¦ZB}]¢¡{¡k`*um\Wh^µiktZ$eBh]ikum`*|¼²
ÇBikt´}~Z$Y[Y[`*t^zgZfum|tKh^Z(] 0!#' |'ZM0v*vm²Çm`'z]WYRh[ik}*lB¡¯]WY µÈ _=]¢h^YRi±»ch^Z,eg``*t[h[ik_]¢h^`*|
iktZq¤4h^m`/¤¦Z$Y[_ & EN
%
²
À
t ¤@]WY]qtY[`*}*Z$umt[h^Y[lm}rh[ikZfuipt'}~Z$um}*`*Y[um`*|¼ni±h]qteg`~`*uµ|m`*_¥Z$umt[h^Y^]¢h^`*|h^O]h`}¢]quY[`*}*Z$umt[h^Y[lm}rh
h^m`,t}~`*um`,]qti±¤Ki±h]qtzY[ZsJip|m`*|e$°1]WuµZfYRh^Zf\$Y^]WzBip}/}]q_`~Y^] 2$4@²
³ Z$umt[ik|m`*YRipum\]q}rh[i§s$`soikt[ikZfuVnh^Bikt(°Jik`¡k|mt5h^m`=¤¦Zq¡§¡kZ'ipum\9_`*}]quBikt^_ & #Z &1k\0a)''
3vm# G#0!m HZv'@/G`\"$0IH%/ H!'!1v # ` # EH ZO#
&d'#'!'R*W d!#'G|'Z W1&&v*G,v#9#^&1( # H30/'/8.'-cvm²
À tµ|Bikt^}*lmt^t^`*|Á`r¡kt^`rwm`*Y[`G2±(!4@ni±¤(h^m`Fh^Y^]Wumt¡®]¢h[ipZ$u iptz{`*YR¤¦Z$Y[_`~|Et^lm}Áh^O]hµi§h^t}*Zf_zgZfum`*u$h
]¢¡pZ$um\h^m` 'ÈR]¢»oiktcikt=«*`*Y[ZOn h^m`9Y[`rh[ipuO]¡T|Biptz]WYRi±h ° ikt=umZqh8|m`*z{`*um|`~u$h8lmzgZ$u¬h^m`¡pZB}]¢h[ipZ$u¬ZW¤h^m`
zmYRikum}ripzO]¡mzgZWiku$hK2±4@² À t:]}*Z$umt^`*jJlm`*um}*`Wnq`s$`*uci±¤h^oipt-jJl]Wu$h[i±h °5ipt-umZqh:¹JumZTu('i§h^=]Bik\$(zmY[`*}riptipZ$u
;
]qzmzmY[Z~»oik_]¢h^`,}]¢¡§ikemY^]¢h[ipZ$u<^noh^m`,Y[`*t^lB¡±h'i§¡±¡4umZqheg`,]ÄV`*}h^`*|¼² Ñ9ZfY[`*Zs$`*YnBh^`,Y[`rh[ipu]¢¡º`r¡k|1]qtumZ
t[ikum\$lB¡®]qYRi±h °µipuµh^m`,ik_=]W\$`woip}Ftip_zB¡±i§ºO`~t'i±h^ty`*t[h[ik_=]h[ikZ$u¼²´ hTipt'h^Jlmt/]\fZBZB|µt[h^Y^]h^`*\q°8h^Zh^YR°h^Z
zg`~YR¤¦Z$Y[_©h^Y^]qumt[¡¯]h[ikZ$uz]qY^]¡±¡k`¡Vh^Zh^m`,Y[`rh[iku]¢¡4zB¡®]qum`/iku8h^oiptT}]Wt^`W²
#)' %
&`rh8lmt=umZ~ }*Zfut[ip|`~Yh^m`¤@]q}rh¥h^O]h=`]qY[`FZ$emt^`*YRsJikum\ª] zB¡®]qu]qYt[h^Y[lm}rh^lmY[`WnTlmum|`~Y8]qu Y[`rh[iku]¡
|Bikt^zB¡¯]W}*`*_`*ufh~ng]qt|oipt^}*lmtt^`*|8zmY[`rsJipZ$lmt[¡±°f²
u=h^oipt+}]qt^``T|mZ5umZWhO]*sf`'h^Zc`*t[h[ik_=]h^`'h^m``rip\$$h+z]WY^]q_`rh^`~Y[t+Zq¤Vh^m`}*ZW¡±¡§ikum`]¢h[ipZ$u¼nJelBhZfuo¡§°
t[i»Zq¤4h^m`*_"t[ikum}*`h^m`,_=]¢h^YRi±»"E ipt'ZW¤4h^`/¤¦ZfY[_ &
E N
%
% %
;
Wa<
i@²`W²-`}¢]qu1]qt^t^l_¥`h^O]h fj ] b bg*TwBik}µ¡k`¢]q|mt+h^Z8]Y[`rh[iku]¡4|oipt^zo¡®]q}*`~_`*u$h~²
ÇBikt¤@]q}rh}]Wuµe{`,`]qt[i±¡§°=s$`~YRi±º`*|i±h^h^`,_ZB|m`r¡Zq¤K`*jJl]¢h[ipZ$u
;
$<+t[ikum}*`/`/]sf`#&
f` j ` f ]O
)] g0g
|Y |]8g8 f `
f Y j Y f ]O
)] g0g ` |]8g f Y ;
f8<
wO]h^`rsf`*Y½h^m`,}]¡±ikemY^]h[ikZ$uz]qY^]W_`rh^`*Y[tw]qY[`W²
Ð
ZW¡±sJipu\8h^m`*t^``*jolO]h[ikZfut`c`]qt[i§¡±°9|m`*_¥Z$umt[h^Y^]¢h^`h^]¢hyh^`~t`ch Z8sW]¢¡klm`*t/sW]Wuoipt^9i±¤]qum|Zfuo¡§°
i±¤ `0# 0v*vm U 0 |'E# z j ] b bg
T
O
0'#&d'#'!'/ 30!#' U'z f j f N k3 U'3#, G10Z/ Y&0v'#'!'
U' z @ ,Z1 'RHG `|'Z \j ] b b$g T q²
uh^m`'\f`*um`*Y^]¢¡m}¢]qt^`Zq¤gsW]WYRi¯]Weo¡p`'}¢]¢¡±ipemY^]¢h[ikZfuz]qY^]W_`rh^`*Y[t~nqi±h:ikt´umZWh´zgZft^tipeB¡k`+h^Z/Y[`*}*Zsf`*Y-h^m`T¿:loÈ
}r¡§ik|m`]qucz]qY^]q_¥`rh^`*Y[t~n$tipum}*`+`'t[h[i±¡§¡O]*sf`/$z]qY^]W_`rh^`*Y[tKh^Z/`*t[h[ik_=]h^`W² 5TZ`rs$`~Yni§¤gh^m`}]¢¡§ikemY^]¢h[ipZ$u
z]qY^]W_`rh^`*Y[tw]qY[`/}*Zfumth]Wu$h~ng]qt\Wi±sf`*uµipu2!4@n`/}¢]quY[`*}*Zs$`~Y½h^m`,|BikY[`*}rh[ipZ$u1Zq¤4h^m`yh^Y^]Wumt¡®]¢h[ipZ$u¼noh^m`
]qum\W¡k`ZW¤-h^m`Y[ZWh]¢h[ikZfu]qum|9h^m`zB¡¯]Wu`cumZ$Y[_=]¡´lmz9h^Z9]Wu9ikum|m`rh^`*Y[_ipuO]h[ikZfuV²5u 2c4:h^m``*jJl]¢h[ipZ$umt
]*s$`,eg`~`*uµ\Wi±sf`*uµ¤¦ZfY't^_=]¡±¡|BiptzB¡®]q}*`*_¥`*u$h^tw]qum|h^m`r°1}]Wuµe{`/`]qt[i±¡§°\$`*um`*Y^]¡±ik«~`*|]qt\qi±sf`*u1uZ &
#$$$$$$$$$$$$$
%$$$$$$$$$$$$$& N 6
#
S ]9g
"
u
Y
:
yKq
/ f u :
yYq
uY :
:
:
y
`
` N )]g
Y N |] g
\N
Yf
#
S# ] 6 u y
: u
yYu
y
"!
u yKu
:
y
uKu
y/ u y/ : u y/ : u y/ y: f u
#$
u yKu
H:
y %!
u yYu
yYy
g
U` N & u
:
y & u : y
u&
y./
u&
y&/
Y N & u :
y & u : y
u& y/ u& y/ ;
f 8<
ê`]*s$`h Zµt^ZW¡klBh[ikZfut¤¦ZfYTh^m`|Bikt^zB¡¯]W}*`*_`*ufh~n]qtipuh^`¥}*Z$u$h[ipuJlmZ$lmt/}]Wt`$²5Ç'm`5ipu$h^`*Y[zmY[`rh]h[ikZ$u
ikt/|Bipt}~lt^t^`*|ipuG2!4@²ÅmlYRh^m`*Y[_¥Z$Y[`Wn¼h^m`(h^Y^]qumt[¡¯]¢h[ipZ$u9ipt,]¢¡kt^Z8\qi§s$`~ulz9h^Z1]qu9ipum|`h^`*Y[_iku]h^` Vn4]qt
`»z{`*}rh^`*|¼²
ÅmlmYRh^m`*Y[_Z$Y[`$nf`T]*sf`Z$um`w]q|m|Bi±h[ikZfu]¢¡¡±ikum`]WY´`*jJl]h[ikZ$u¤¦ZfYh^m`Tipu$h^YRikumt[ik}wzO]WY^]q_`h^`*Y[tK]^
`
bO
` g &
|] g
`f `
]O
``
g ` ` Y N )] g Yf ` Y` `
]O
YY
g ;
o<
]qtikuh^m`}~Z$u$h[ipuJlmZ$lmt'}¢]qt^`,]q\o]¢iku¼²Ãª`/|Z=umZWh']*sf`5]Wu$°}*Z$umt[h^Y^]¢ipu$hwZ$u8h^`/¤¦ZB}]¡V¡k`~u\Wh^#nOtipum}*`
u¬`rsf`*u _Z$Y[`1|`~\$`*um`*Y^]h^`*| ¤¦Z$Y[_Zq¤h^m`1Y[`rh[iku]¢¡wzB¡¯]WuO]WY|Bikt^zB¡¯]W}*`*_`*ufhikth^Z£]}*Z$umt[ik|m`*Y¥]
/@0!#Zv'u3On:i²`W² GN
% N 1]qum|
NX N 9ikuÂ`~jJl]¢h[ikZfu
;
qa<^² ÇBikt`»Bh^Y[`*_`
t[i±h^l]¢h[ipZ$u¬ipt=tZf_`rh[ip_`*tlmt^`*|¤¦Z$YczO]WumZ$Y^]q_cik}|BiptzB¡®]q}*`*_¥`*u$h^t~² h8}¢]quÂeg`1`]qt[i§¡±°¬|m`*_¥Z$umt[h^Y^]¢h^`*|
h^]¢hh^Biptt[i§h^lO]h[ikZfu9}*Z$Y[Y[`~tz{Z$um|mtTh^Z Z 03d!#'S0' G G10/ K&0'#'!'U'o
/ '-/.0 &03!/1noi±h^ ij ]
%
b
% b 8g^²
"'d O$#)'% "! % *
&`rhlmt+umZ~·}*Zfut[ip|`~Y-h^]¢h+h^m`/`r¡k`~_`*u$h]WYR°=|Bikt^zB¡¯]q}~`*_`*u$hZW¤Vh^m`/}]q_¥`*Y^]yipt]º»`*|]¢»oikt+Y[ZWh]¢h[ikZfu¼n
woi§¡k`(iku$h^YRiput[ip}z]qY^]q_¥`rh^`*Y[t,]qY[`c}*Z$umt[h]qufh~²w h/ipt/¹JumZTu9h^]¢h/h^Bipt/ti§h^l]¢h[ikZfu9ikt}]qY^]W}rh^`*YRik«~`*|e$°
h^m`/¤@]q}rhh^]¢hh^m`yh^Y^]Wumt¡®]¢h[ipZ$u8iktzg`*Y[z{`*um|oip}*lB¡¯]WY½h^Zh^m`(]»oipt'ZW¤KY[Zqh]¢h[ipZ$u¼²Ã `/]*sf`#&
%
B]7 T g N ;
f8<
hw]qteg`~`*uµ|m`*_¥Z$umt[h^Y^]¢h^`*|8h^]¢hh^oipt'}~Z$um|Bi±h[ikZfuipt'um`*}~`*t^t]WYR°8]qum|t^lo¾}rik`*ufh½¤¦ZfY+h^`È _=]¢h^YRi±»h^Z
}*ZfY[Y[`*t^zgZ$um|8h^Zt^lm}F]|Bikt^zB¡¯]q}~`*_`*u$h
;
t^`*`32$4<^²
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
000000000000000000000000 66
5 5
5
1
B B B B B B B B B B B
{
!
Åik\flmY[`5 &wZqh]¢h[ipZ$umt+¤¦Z$Yw]5º»`*|F]»oipt'Y[ZWh]¢h[ikZfu
ê`,lmt`,h^m`5umZWh]¢h[ikZfumtTZq¤:º\$lmY[`(B²'à `,}*Zfumtip|m`*Y]sf`*}rh^Z$Y
]¢¡§ik\$um`*|'i§h^h^m`Y[ZWh]¢h[ikZfu9]¢»oikt
]qum|8h^`,z{ZqikufhZfuµh^m`(]»oipt
nOtlm}µh^]¢h N }
!
²´Ç'm`,Y[Zqh]h[ikZ$u1]qum\W¡k`ikt ²
ÅmY[Z$_©`~jJl]¢h[ikZfu
;
<^n
;
a<]qum|
; <-ikuµh^BiptT}]Wt`$noh^m` È _=]¢h^YRi±»µiktZq¤4h^m`Y^]h^m`*Y'm`]*sJ°8¤¦ZfY[_ &
j
$ |] g P` ]O
)]8g0g
$ Y T
f f T
Y * *
` N f f
!#"
&ur y
%$
$
#
% Y N : Y T
% f N : Y T $
$
;
f8<
woi§¡k`/`/]*s$`#&
T
` Y N ; a (8<
woip}ikth^m`ZfuB¡±°}*Z$umt[h^Y^]¢ipu$hweg`rh `*`*uµh^m`*t^`h^mY[`*`/sf`*}rh^Z$Y[t'&~²
(*)
1$-$r0wZxzy$w/r0r T)r 1$r0w-Sr0xw/,+
"
+
q { 1$+
Q
/$zy@xy${1x-+
" . + q { 1$@1xw*!$$0rS{o)r0xw0/ `2103 254
3*
32 32 b q Q6
1 # 3 4 3*
32 3
*~xzy${x,/
+ + " ` & { 1:/
+ +
q07
+
Q)#
` 3* 3
Q
wS{ 118 dRy:r0w/r- {1|{0!{/1-!x*- 161rSU${1x/- 1V98 Y