HAL Id: hal-00341655
https://hal.archives-ouvertes.fr/hal-00341655
Submitted on 25 Nov 2008
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 teaching and research institutions in France or abroad, or from public or private research centers.
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 recherche français ou étrangers, des laboratoires publics ou privés.
The Reduced Automata Technique for Graph Exploration Space Lower Bounds
Pierre Fraigniaud, David Ilcinkas, Sergio Rajsbaum, Sébastien Tixeuil
To cite this version:
Pierre Fraigniaud, David Ilcinkas, Sergio Rajsbaum, Sébastien Tixeuil. The Reduced Automata Tech- nique for Graph Exploration Space Lower Bounds. Oded Goldreich, Arnold L. Rosenberg, Alan L.
Selman. Essays in Memory of Shimon Even, Springer Berlin / Heidelberg, Volume LNCS 3895, p.
1-26, 2006, Lecture Notes in Computer Science, �10.1007/11685654_1�. �hal-00341655�
" #%$&')(*&+ ,-/.&01+-324657#.98
:;=<?>@>A<BC>@DE;=FHGI;=DHJIKCLMNMHOIPQDSRT;=KUWVYX-;YGIZSD\[@]QM@M^OC_^<`>AFH;badcDEeA[gfIDHJIhdiMjMkM^OlD\GlK
_m<?fIDH[Ang;b<`G!o);bpq<?Jq;=Vbrs
t!uvxwxyIz\{jw|gz\}x~\SN ^)?by\^lzHT ?~^@
H??SE```\j`
{jw|gz\}x~\SN ^?by\^lzHT ?~^@
?E`-S\ ¢¡ S`\j£S
¤ |~^W \ ¥Q\ ¦§ N¨©-W=@`@zT}ª~Hq«\v)`Ab¥?~T-¬9ª\q¥`~H¥`¨H ¦®@¯Eb@¥HzT¦d@¯Eb@¥
E S°¢¡-±E ²`³\ ³\ ?´`µ¶£²`\ -³·¸³¢¹
º {jw|»¼|vªwª|zE}ª~HSN ^?by\^lzHT ?~^@
´\-¹E ²H?`S`\j£S
½¿¾kÀNÁÃÂÃÄTÅ?Á`ÆÇ
g¥`~Tb\N3 ÈHA?É¥?Ê@¯\Ë\¬b¥?~^ÌÍÌ` Ë^ÈT Î, È7 ~^¥?~EÏ\¨0¥?T
~H¥EHÃТϿ Ã?¨Ñ¥ Ê9~^¥?~H@¥¢¥?ËqN WS)W¥?Ðq¥?A@z\¨0¥EHg¬bN?ÒT~H x?H ¥?¨ AE«
T¥?)@¯\ËH¬¥? W¥`~Í ¥Ðq3@¥?¨0ËH¬@ ÃIzqÃ` È!ÃHÌ?¥?ʶ È^Ì` Ë^È!ÈT?ª ¥Ðq3
S@ çÐEϧ )¬Ã?¥`~HW¥`Ðq¥ ëI|~§ ÈHbxË^?ËqNNzq ÈH3W¥?Ðq¥?AxÈ^ÃS3~H¥#Ë^¥?
ÉE~^¥ÃÎ,¬Ã\Ì`0¥?Ê È^ ¥?Ëq¥?¬¥`Ì Ï¥?Ê È^QÌ? ?Ë^Èlzj~H¥`¥ ÊAÓN?zk ~T!Î?WQ~H
NWN Ã~ ÈH?¨0¥?^~¢¥ Ê9¨0N¨0¥`Ï0 ÈH)W¥`Ðq¥ A~^NN¿ ¥0?N@¥`¨0Ë\¬=È@¯\ËH¬¥?
-Wb¥?~Cz
Ç
~¢ W¥EH^@ È^Q¥?N ¬¬Ã7ÔWÕWÖ?×HØgÕWÖÙ?×\Ú¸Û?Ü0Ù`Ú¸Ù!Ú£ÕWØ@ÝSÞ^߸à@×^Õgzk?~TÍÎ
ÈH¥-μÈ^¥ÃÎá ¥T ÈHb, à È^~Hbâ¢^Ê=¥`\NE~HÌ@SN ¬9ËT`g¬¥ÃÎNxÐq¥`^~^^
Ê=¥`¿@¯\ËH¬¥` -Wb¥?~C«|~HÊ=¥`W¨-¬¬ÏãËqÃ?É¢~^Ì\z ÈHdWÃH^@é H ¥?¨ A à È^~\bâEH
@¥?~TbAx~§WÃH^g~^Ì0W¥`Ðq¥?ª ¥#¨0ËH¬NÊY¥?W¨ä ÈT-)ËHWÃNWSÃåA0æAg¥`WÃç
ÐqNÈ^ÃE¥?¥`~¥?¨0QÌ` Ë^È^@«j}xb~HÌ È\=x NAÈH~Hbâ¢^`zqÎÒT ÈH¥-Îè È^ ~EÏ
@¿¥ Ê)éãêìëd~H¥`~H@¥¢¥?ËqN WS§W¥?Ðq¥?A@z·WÃâ¢HWÃ#íîY¬b¥?Ìqî-ïðIñWñ¨0N¨0¥?ÏÐHA
¥!@¯\ËH¬¥`W# ¬¬åòq£~^¥EH¿Ì` Ë^È^@«óÈHËHW¥¢¥?ʪb¨0Ë\¬bN ÈT-Ãz9ÊY¥?0?~¢Ï@¥?Êxé
ô
A W¥?Ðq¥?A@zH È^NW)g¯\bAåÌ? ?Ë^È#¥?ÊÓN õQîöé
ô
ñ ÈT ~H¥W¥`Ðq¥ ¥?Ê9 ÈHb
@@?~!@¯\ËH¬¥`W`zIÎåÈ\= ÈÍb¨0ËHW¥-Sê ÈHõQî
ôÍ÷¶ø ðAù
ñªÐq¥`H~T§Ð¢Ï§w¥?¬¬bÉîëNú`û`ü`ñg«
ý
H3¨-b~WÃ\¬b ~7 Ë^Ë\¬bN-W¥`~þ¥?Êå ÈHb¬b-W NWÃ\¬Ãz¶@¥`~^@NW~H~HÌþÚ£ÕgÔgÿ
Ü3ßYÞqÙ`ÚYß=ÞÌ? ?Ë^Èg¯HË\¬¥` W¥?~Î, È¥?~^W¥`Ðq¥ Ãzk¸«?«z9~ÎåÈ\= È È^W¥?Ðq¥?=
WÃâ¢Hà Ã# ¥¿ ¥`Ë! Êb N)g¥`¨0ËH¬@W~HÌ0@¯\ËH¬¥` -Wb¥?~C«IT¥?ª È\=,A`ÉqzT ÈH W¥`Ðq¥?
bËHW¥ ¢bHN3Î, ÈËqNÐHÐH¬`zS È^ ·N ~¿^ ¥ ¨ WÉ3~H¥EHÃîYÎ, ÈH¥`\,T È
¨ WÉSNNz\NSN~¿ NW¨Q~T-Wb~HÌ@¯\Ë\¬b¥? W¥`~§¥ ÊgÏHg¬ÃåN ~^~^¥ Ðq` ÈHNSNTñg«
Ç
ËHW¥ `x ÈT- NW¨Q~T-Wb~HÌ@¯\Ë\¬b¥? W¥`~WÃâ¢HWÃxíîY¬b¥?ÌòCñÐHA¥ Ê9¨0N¨0¥`ÏÊY¥`
W¥?Ðq¥?ª` ÈHN¢~^Ì3 ÈHbA`Éb~# ¬¬kòq£~^¥E\Ì` Ë^ÈT@«
ÑË^W@¬¨Q~T Ï*S@ b¥?~¥?Êå ÈHb ËT?Ëq@ Ë^Ëqà ~ È^Ë^W¥EgNÃ\~HÌS3¥ Êå È^§ëà È|~¢ N
~T-Wb¥?~T-¬0u¥ ¬¬¥Eâ¢HH¨ ¥`~¼yE WTA ^ ¬ |~HÊ=¥`W¨ W¥?~¼?~^áu¥?¨0¨H~HbN W¥?~¼u¥?¨0ËH¬@¯EÏ
î£y\|w
ý
u,u
ý
ñgz^¦d¥?~¢)y\ ~¢W¦#= È^g¬£zHT ~T@`z^¦§NÏ? Ez ü`ü¢zq?Ë^?å¥?Ê븫
y\HË^Ëq¥` N)ÐEϪ È^¶|vªwª|*Ë^W¥ÃAªæx ~T {k?WÌ?Ãç\z? ~T) È^¶Ë^W¥ÃAAåæ -b 窥 ÊH ÈH
u|ªæA¦§`WN,H)¥`~H~,NNWç\z\?~^!æ 9wªx|{·ç¥?ÊI È^u|ªægyÃ@HH@|~HÊ=¥`W¨-W=â¢HÃç\«
y\HË^Ëq¥` N)ÐEÏ){kª¦d|l ~Tlª¶|W|óËHW¥ ÃgA@« ?j¥?Ê\ ÈHbCÎ¥`WÉxÎ`9H¥?~^ÎåÈH¬¢bWb~HÌ
{jw|gz\}x~\I«\ =ªy\^lz
ý
WNÏ¢«
y\HË^Ëq¥` NáÐ¢Ï ÈHþ|vxw|ìË^W¥Ãg æx ~T {k WÌ`ÃçE« xH\W¥`~T-¬^ËHËq¥`ÍÊYW¥?¨ ÈH
oq<I>gaHfqV=<?h6a<-p qV=aH>g;YGqFD\G©JIGIZTGqa G©<`G^R^;Y>gaHGIh#<?G^n0aqX X?JI>@[0;=G DR¢DH>A;=< n7a [A;=n
JIDEng;ba^GI[ O)V=;=Z\<7>gaHfCa\nGIDSRT;bF^DEng;ba^G9OªGq<?nªa^>gZáhdDE;YG^nA<?GlD\GIX <\O>A<`[Aa^JI>@X-<þKq;Y[@X-a¢R\<`>HOªDHGIK
[g<?DH>gX "!U Gán#I<?[g<[g;=ngJID\nA;=aHGI[dn$q<<?G^nA;=nA;=<?[%C<?>¸aH>@h#;=GIFã< p qVba^>gD\nA;=aHG X D\GáfC<
< ;=n#q<`>D&'(q[g;=X?DEVxha^fq;=Vb<!KI< RT;=X <!a^>¿D[ga¸n)D\>g<ÍDEFH<?G^n)!·U G n#q;Y[*ID+C<?>?O,x<>g<?[gng>g;=X n
aHJI>DEnAng<?G^nA;=aHG nAaþn$q<X D\[g<-.q<`>A<!n#q<*<?G^RT;=>gaHGlh<`G^n;=G/.q;=X n#q<h#aHfq;=Vb<<?G^nA;=nA;=<?[
D\>g<h#a¢R^;YGqF;=[xh#aTKI< V=<?KÍDH[ªD¿FH>@D+ "!0)nxDHGÍD\fl[An@>gDHX-nåV=< RH< VOHF^>gD( §<-p qV=aH>@DEng;ba^G#;=[xn#I<
ngD\[@Z1.q<`>A<§a^Gq<daH>0h#aH>g<§h#aHfq;=Vb<§<`G^nA;=nA;=<?[?O¶X D\VbV=<?K32#45#4687§;YGãn#q;Y[9ID(l<`> O¶DH>A<dn@>T;YGqF
nAadX-a\V=V=<?X-ng;bRH< V:dng>@DSR\<?>@[g< < RH<?>##<`KqF\<3a·DFH>@D+'"!HU GD\KIKI;bng;ba^GÍnAa#n#I<D¸aH>g<?h#<?G^nA;=aHGI<?K
D+ qV=;YX DEng;ba^GI[?OCF^>gD( < pIVba^>gD\nA;=aHG;Y[3;Yh;la^>An@D\G^nQKIJq<dnAa*;bn@[Q[An@>Aa^GqF>g< VYDEng;ba^GnAaX-a^h<
qVb< pq;bn7n#q<?aH>#\OD\GlK7;YG=IDH>Ang;=X?JqV=DH>nAan#I<!JIGIKq;Y>g<?X-ng<?K=>@?AX aHGIGI<?X-ng;bRT;=n/B8C0_ToDEFHG
I>Aa^fqV=<?hIBXJ!bO9<(!FK!bOMLNO8GP!RQ3;=R\<?G7D\GJlGIKq;Y>A<`X-nA<`KþF^>gD( TS DHGIKnxa*R\<?>gnA;YX-<`[U>dDHGIK&?ÃO
n#q<*CQ_ToDEFVI>gaHfqV=<?h ;Y[nAaKq<?X ;=Kq<<.q< n$q<?>W>dDHGIK1?DH>A<;=Gþn#q<d[gDHh#<X-a^GIGq<`X-nA<`K
X-aHh;CaHGq<`G^naS*!9oq<¿KI;=>g<?X nA<?KR\<?>@[g;ba^Ga+ån#q<*I>gaHfqV=<?h ;Y[Kq<`Gqa\ng<?K7_ToDEF<!CUWn3;=[
Z^GIa Gdn#ID\n_ToDEF ;=[xX-a^h;qVb<?nA<¸aH>XFYOTn#I<3X-VYD\[@[åa+¶GqaHGKq<?nA<`>gh#;YGq;=[gnA;YX V=a\F+[$IDHX-<
[AaHVbR¢D\fIVb<;I>gaHfqV=<?hd[@!KZq<?n#q<`>HCQ_ToDEF4;Y[X aHh;qV=< ng<[¸a^>YªO9n#q<dX-VYD\[@[a\l>Aa^fqVb<`hd[
[AaHVbR¢D\fIVb<xf(0Kq<?nA<`>gh#;YGq;=[gnA;YXåV=a\F+[$IDHX-<åDEV=F\a^>A;=n#lh#[?O@lD\[fl<?<?G¿D3X IDEV=V=<?GqFH;=GqFa(C<?G9I>gaHf
Vb<`h]¸aH>_^^JI;bng<D¿Vba^GqF¿ng;=h#<\OIDHGIK§;=nª;Y[xaHGqV:dR\<`>d>A<`X-<`GHngV`dn$IDEnxc < ;YGqFHa\VYKI>ga¢R\<`Kdn#ID\n
CQ_ToDEF;Y[Q;=GIKI< <?KãX-a^h;qVb<?nA<*¸aH>HYaLcbedOf!gFaHnA<dn#lDEnQn#q<d< pT;Y[gnA<?GlX-<da)D-hCGI;bng<Í[A<?n
ahjGq;bng<JW[An@DEng<D\JqngaHhdDEn@D7DHfqVb<nga <-p qV=aH>g<*D\VbVF^>gD( I[*ªa^JqVYKiIDSRH<1IJqn%CQ_qoDEF
;=GjYªOD\GIKl>Aa¢RT;YGqF©aH>§Kq;Y[#l>Aa¢RT;YGqF©n#q;Y[Í< pT;Y[gnA<?GlX-<&IDHK n$q<?>g<J¸a^>A<h#aHnA;=RSD\nA<`K^^JI;bng<
D§Vba^GqF![g<@^TJq<`GIX-<a+[An@JIKq;=<?[@!"DªaTa^Z!D\GlKcD\XÃZ\ak3LNO< RH<?G^ngJlDEV=V`lI>Aa¢RH<?K*n#lDEn<?R\<`GD
ha^>A<Caª<`>£JIVThdDHX q;=GI<\OEX D\VbV=<?K;m(0QO¸aH>Mnm\JIh;q;YGqFH0JqngaHhdDEngaHG<¸aH>Q>@D+'I[#nlO¢X D\G
Gqa\n3<-p qV=aH>g<¿DEV=V·F^>gD( I[[BDom(0Qä;Y[3D-hCGq;=nA<d[A<?naåFHVba^fIDEV=V:*X a^al<`>gD\nA;=R\<WhjGq;bng<JW[An@DEng<
D\JqngaHhdDEn@D<?G IDHGIX-<`Kp;bn$©n#q<!DHfq;=Vb;=n\O"¸a^>0< RH<?>#þD\JInAaHhdD\nAaHGOnAa&n-eAJIh; nq£>gaHh ;=ng[
X JI>@>A<`G^n[la^[A;=nA;=aHG©ngaþD\G©GqaqKq<!aqX?X J q;=<?K f©D\GqaHn#q<`>¿DHJqnAa^h#D\nAa^GKGP!,_^;=GlX-<!n$q;Y[VYDEn
nA<?>>A<`[gJqV=n Oln#q<< p qVba^>gD\nA;=aHG!FH>@D+ qI>gaHfqV=<?h ;=[r¸aqX?JI[g[g;YGqF§aHGKq<?nA<?>@h#;=GI;=GqF§n$q<¿[$ID\X <
X-aHh;qV=<-pq;=nÍa,>gaHfCa\ng[)DHfqVb<0ngad<-p qV=aH>g<QD\VbV9F^>gD( I[@!
0[£D\>QD\[J C<?>QfCaHJIGIKl[3;YGþX aHGIX <?>@Gq<?KOCc <?;=GIF\a\VYK[$qax<?K;YGiLcbedsOn#lDEnHq;=[V=a\F+
[#IDHX-<*DEV=F\aH>g;=n#Iht¸aH>*C0_ToDEF ;Yh;qV=;b<`[dn#q<*<-pq;Y[Ang<?GIX <a+VbaHFW[#lD\X-<X-aHGl[An@>gJIX nA;YfqV=<
uv'wyxz 2P7){|
z$})~
|c42#{6
w4 v 7 z$)u'z)vPz
7*B8CQ_ Gªa+RlaHV`qGqa^h#;=D\VjV=<?GIF\n#!qc aHJqFqV:Í[#C<?DHZH;YGqFCO
DWC0_&Lcb)Oj;=[ªD¿[g<@^TJq<`GIX-< a+9;=G^nA<?F\<`>g[n#ID\nBbGng< V=VjD>gaHfCa\n\qa¼nAah#a¢RH<£>Aa^häGIaTKI<
nAaþGqaqKq<;=G®DFH>@D+ 3Bn#q<<-pq;bn*la^>AnDEn¿n$q<oTn$ [gnA<@ an#q<ng>@DSR\<`>g[@DEV,;Y[a^fqngD\;=Gq<`K
f(DHKIKq;YGqF!n$q<*Tn$;YG^nA< FH<?>an$q<[CQ_nga!n$q<<`G^ng>#qCaH>gnPGÃOjDHGIK=BA (G FHJIDH>gDHGHng< <0nga
<-p qV=aH>g<0< R\<`>*GqaqKq<0aåD§F^>gD( *aåD+'I>AaI>g;=D\nA<0[A;: <%BD%C0_*;Y[Kq<)hCGq<?Kl¸a^> D§FH;bRH<?G
[A;: <HO^DHGIK!D¿F\;=R\<?G§KI< FH>g< <GP!^c <@'I>gDH[A;YGqFn$q;Y[ªVYDEngnA<`>ª>g<?[@JqV=n O^n#q<`>A<;=[xD<*BVbaHFRGA[$ID\X <
>Aa^flaHnån#ID\n< pIVba^>A<`[åDEV=VCn$q<F^>gD( I[,a+¶[A;: <M!^oq<<-pqnA<`GIK§nAa<.q;YX dn#q;Y[ªfCaHJlGIKÍX DHG
fl<0Kq<`X >g<?D\[g<?KfÍJI[A;YGqF§D#[A<?nxa+<bQX-aTal<`>gD\nA;=R\<3>gaHfCa\n@[)>A<`h#D\;=Gl[ªal<`G"! 0 VY[galOqn#I<
^^JI<?[gnA;=aHG§a+n#q<<-pq;Y[Ang<?GIX <aV=a\F+[$IDHX-<X aHGI[gng>@JIX-ng;=fIVb<
uv'wyxz 2P7){|6f2#{
xz 2P7J{+|K7
zP)u'zJvgPz
7
B8C3o_'GrLb)Ol>A<`h#D\;=Gl[·al<`G-BDCo_¿;=[DQ[A<e^TJq<?GIX <ªa+CaH>gnWGTJIh¿fC<?>@[[Aan#ID\nn#q<)aHJIn#IJqn
la^>AnDEnn$q<[Tn$*[gnA<e*a·n$q<0ng>@DSR\<`>g[@DEVj;Y[n#q<9Tn$*< V=<?h#<?G^nan#I<[A<e^^JI<?GIX <sGP!
0[£D\>*D\[ÍV=ax<?>!fCaHJlGIKI[*D\>g<7X-a^GIX-<`>gGI<?K9Oxha^[AnlID+C<?>@[*D\>g<þKq<?D\Vb;YGqFi;bn$èn#I<
Kq<?[g;bF^G a[@hdDEV=V6f2#{
~
7-¸a^>DH>gfq;=ng>@D\>#þng<?DHh#[a>gaHfCa\n@[ O;f!<(!bO[ghdD\VbVxFH>@D+ l[n#lDEnGIa
>Aa^flaHna+¿n#q<©ng<?D\h X?D\G <-p qV=aH>g<+!HB£BCaH>@h#D\VbV:\OD ng>@D+ X-aHGl[A;Y[An@[!a+#D FH>@D+ D\GIK D
[An@DEnA<d>gaHfCa\n;=[F\<`Gq<?>@DEV=V:D\nAn@>A;YfIJqng<?Knga)JlKID\X LdsOBn#q<dng>@D+þ;=[QDHX-ngJlDEV=V`DlqVYD\GIDH>
FH>@D+ KG !oq<Ín@>gD(7X aHGI[gng>@JIX-ng<?K©fJIKIDHX þ;Y[9qax< RH<?>a)VYD\>gF\<§[A;: <HO¶D\GlKãDhJIX
[ghdDEV=V=<?>n@>gD(W)D\[¶KI<?[@X >g;=fC<?KQ;YGLcbe sO .q;YX 9I>ga¢R\<`K3n$IDEn?O)¸a^>·DHG&[gngD\nA<>gaHfCa\n?O n#I<?>g<
<-pq;=[gng[¿Dng>@D+ãaDEnh#aH[gn bÍGqaqKq<`[)!¶U GZLbeNOO9c a\V=Vb;YZpI>Aa¢RH<?Kþn#ID\n¿GqaqhCGq;=nA<[A<?n
ahCGI;bng<3V=aqX DEV=V:(WX-aTal<`>gD\nA;=R\< D\JInAaHhdD\ngDIO^;f!<(!bOqD\JInAaHhdD\ngD0n$IDEnx<-pIX IDHGqF\<3;=G ¸a^>ghdD\nA;=aHG
aHGqV:W.q<?Gn#I<)¿h#< <?n,DEnDGIaTKI<\O¢X DHG¿< pIVba^>A<xDEV=VqFH>@D+ I[@!`U G¿n$q<I>AaTa+laln$q;Y[,>A<`[gJqV=n O
n#q<DHJqn#IaH>JI[g<?[¶D\[DngaTa\V\D)n@>gD(¸a^>¶D[g< na+ )Gqa^G WX-aTa(C<?>@DEng;bRH<&[gngD\nA<,>gaHfCa\ng[XB[@JIX
>Aa^flaHng[0hdDsTIDSRH<dKI;ckk<?>g<?G^n0ng>@D\Gl[A;=nA;=aHGT£JIGIX nA;=aHGI[?O,q<`GIX-<§n$q<) ;bV=VM¸a\V=V=aäKq;`kj<`>A<`G^n
IDEn$I[å;YG§n#I< <-p qV=aH>g<?K#FH>@D+'KGP!^oq;=[V=D\nAng<?>ån@>gD(d;=[a[g;`?<*B GGqaqKq<`[)!Hc a\V=Vb;YZ[
ng>@D+q¸a^>X-aTal<`>gD\nA;=R\<>gaHfCa\ng[3;Y[ < RH<?GVYD\>gF\<`>;B
GGqaqKq<?[?O';=n#p b¿V=< RH< VY[
a)<-p la^Gq<?G^ng;=D\V=[W.I<?>g<#n$q< GqaHngDEng;ba^Gq;=KI<?[0V=a\F^D\>g;bn$Ih#;=X<£D\X nAa^>g[@!9U G©n#q;Y[9ID(l<`> O
ª<-I>g<?[g<?G^nDGq<@Vbax<?>0fCaHJIGlK©nA<?X lGq;:^TJq<;¸a^>0FH>@D+'7< p qVba^>gD\nA;=aHG9OX?DEV=Vb<`K32
zu'Pz
{ u
64! %{6{&6
zP#"v'w8)u'z
!·c aHJqFqV:\O¶n$q;Y[nA<`X IGq;^TJq<!X-a^GI[g;=[gng[¿;=G >g<?KIJlX-;YGqFD>gaHfCa\n0nAa7D
[A;Yh;qVb<`>M¸a^>ghän#ID\n\I>g<?[g<?>gR\<`[;bn@[$@X-a^>A<enfC<@lDSR^;=aH>åaHG§[gaHh#< FH>@D+'I[\<-pIX-<eqnX¸a^>[gaHh#<
<?D\[g;=V`ÍKq<`[gX?>A;YfC<?KX-V=aH[g<?KoIDEn$I[ Oqn$q<>g<?KIJIX <?K*>Aa^flaHn¸aHVbV=a [)n#I<HlDEn#*a+·n#I<0aH>g;bFH;=GID\V
>Aa^flaHn OqaHG*D\G![@JIX FH>@D+ !
oq<Í;YGHng<?>g<?[gnA<`K >A<`D\Kq<`>X DHGhCGIK a\n#I<?>[Ca\;YG^nA<`>g[¿nAaþn$q<!V=;=nA<?>@DEn@JI>g<Í;=GO·<(!FK!bOL%!&
dqO('qO)IO)be sOA!·o·aþX aHh;qV=< nA<n#q<lq;YX-ngJl>A<HODHGIK fl<)¸aH>g<!Kq<`[gX?>A;Yfq;YGqFaHJl>¿>g<?[@JqVbn@[;YG h#aH>g<
Kq< n@DE;=V=[?OHV=< n)JI[_laH;=G^nxaHJqnªn#ID\n)_ I;=h#aHG+*RH<?G9O(.qaHhn$q;=[xfCa^a^Z#;=[xKq<?KI;=X?DEnA<`KÍngalOxDH[
;=G^nA<`>A<`[Ang<?K©;YG FH>@D+'©<-p qV=aH>@DEnA;=aHGI>gaHfIVb<`h#[¿<?DH>AV:7a^G©;=G q;=[#X DH>A<?<?>@!U G/IDH>Ang;=X?JqVYD\>?O
;=G/I;=[ob-,.'N[A<`h#;=GID\V_lD+C<?>9;=n#®o·DH>¸eADHGZLb(bJOORq<l>A<`[A<`GHng<?K DTxDs7aGTJIh¿fC<?>g;YGqF
GqaqKq<?[QKIJI>g;YGqF*DPBå_ng>@DSR\<`>g[@DEV·n#ID\nWI>Aa¢RH<?Knga*fC<§JI[g<J£JqV;YG7hdD\GD\VbFHaH>g;bn$Ihd[)!jU G
X-a\V=VYD\fCaH>@DEnA;=aHGl;=n#&0[!gY¶;=nghdD\GDHGIK:M! ;=GIZ^V=<?>;Lb0/OOKq<n#q<`G[gngJIKq;=<?Kþng>@DSR\<`>g[@DEV9;YG
Kq;=>g<?X nA<`KGq< nxaH>@ZT[)! ;=n#pQ<!lUWngZ^;Y[DHGIK7_!CcD¢eA[@fID\Jlh L,OOKq<Kq<?[@X >g;=fC<?KDÍng>@DSR\<?>@[@DEV
[An@>gD\nA< F(.¸a^>JIGIKq;Y>g<?X-ng<?K0F^>gD( I[kn$IDEnX-aHGl[An@>gJIX ng[D[gJIfIFH>@D+ ;bn$0F\aTaqKQX-a^GIGq<?X nA;=RT;bn
fIJqn¸<@ <`KqF\<`[)! 03GIK>A<`X-<`GHngV`HOq;=GX a\V=V=DHfla^>gD\nA;=aHG-;=n#þ_g!1IDEngn OIP*!Q>g< <?GTfC<?>gFlOIDHGIK
c9!Eo·Ds^D\>@K-L OOI<x[gngJIKI;b<`K¿n$q<I>Aa^fqV=<?hÑakJI[g;=GqFQD>Aa^flaHnDH[[g;Yh*IVb<)D\[ CaH[@[A;YfqV=<B;bn$
D\X X <?[@[xnAa§[Aa^h#<V=aqX D\Vh<`h#aH>#![AngaH>g<?K!;=G*n#I<0R\<?>gnA;YX-<`[PGånAa*hCGlK*DHG+*xJqV=<?>g;=DHGX)TX Vb<Q;YG
h#D+ <`[D\GIKFH>@D+ l[)!
243 2 56!748:9 ;=<?>-;=@@0ACB:D4>
0[ ;YG=LNlO)beNOOª<DH>A<0;YG^nA<?>g<?[gnA<`K*;=G*<-p qV=aH>@DEng;ba^G!a+åJIGIKq;Y>A<`X-ng<?K*FH>@D+ l[r.q<?>g<GqaqKq<?[
D\>g<!Gqa\n#JIGq;^TJq< V:©V=DHfl<?Vb<`K"! Fa\ng<!n$IDEn?OfC<?[g;=KI<?[n#q<*n#q<?aH>g< ng;=X?DEV;YG^nA<`>A<`[Ana+JIGIKq<`>
[An@D\GIKq;YGqF<.q<?G!aH>xDEn.lDEn)X-aH[gnª[@JIX §F^>gD( I[ªX D\G!fl<<-p qV=aH>g<?K9O^n#I<JIGIV=DHfl<?Vb<`K GIaTKI<
[A<?nAnA;YGqFÍX?D\G*aqX X Jl>);=GqI>@D\X nA;YX-<\OIKlJq<0nAaCOI<+!F'!=O'I>g;bR¢DHXJ!X aHGIX <?>@GI[ OqV=;Yh;=nA<`KX D(ID\fq;=V=;bng;b<`[
a,n#q<#>Aa^flaHng[?OIaH>3[A;Yh;qV:*DHGqaHGqh#aHJI[<`KqF\<0;YG^nA<`>g[g<?X nA;=aHGI[@!Coq<>Aa^flaHng[?Olh#aTKI< V=<?KDH[
D Kq< ng<?>@h;YGq;Y[Ang;=XþD\JqngaHhdDEn@DIOåX DHGqax< R\<`>#;=Kq<`G^nA;` n$q<<?KIF\<?[Í;=GIX ;=KI<?G^n§nAa®D GIaTKI<
n#I>gaHJqFJIGq;^TJq<*CaH>gn VYD\fC< VY[ OK£>gaHh b¿nga!n#I<Kq<?FH>g< <a+ån#q<#GqaqKq<+!7<dX-a^GI[g;=Kq<`> nxa
n C<?[ a·< p qVba^>gD\nA;=aHGE
F
:,<?>$l<?ngJID\V9<-p qV=aH>@DEng;ba^G9OT;=Go.q;YX n$q<QngDH[gZ§a+·n$q<>Aa^flaHng[);Y[)nAaCOq< R\<`G^ngJID\VbV:\Oqn@>gD
R\<`>g[g<D\VbV¶<?KqFH<?[@!
F
o¶<`>gh#;YGIDEng;=GIF#< p qVba^>gD\nA;=aHG9OT;YGl.q;=X n#I<>Aa^flaHng[?OID¸nA<`>X-a^h*IVb<?nA;YGqFd<-p qV=aH>@DEnA;=aHGO
U G!D\X)qX-V=;=XFH>@D+ I[?O^nA<?>@h#;=GlDEnA;YGqF#<-p qV=aH>@DEng;ba^Gd;=[)[gng>g;=X nAV:Íha^>A<Kq;§X?JqV=nxn$ID\Gol<`>
l<?ngJID\V9<-p qV=aH>@DEnA;=aHG!HU GoID\>gnA;YX JqVYD\>?O^;bn);Y[x[$qa G§;YGL'sOkn$IDEn)ng<?>@h;YGID\nA;YGqF< p qVba^>gD\nA;=aHG
;=GHgWGqaqKq<åfCaHJIGIKI<?KQKq< F^>A<?<,ng>g< <`[9>A<e^^JI;=>g<?[9D>gaHfCa\n";=n#0h#<?h#a^>[A;: <*B£V=a\FåV=a\FVbaHFXRGNO
.q<?>g<?DH[9l<`>#C< n@JIDEVx<-p qV=aH>@DEng;ba^Gã;=[<la^[g[g;=fIVb<-;=n#i*BbsGfq;=ng[@!·U G DH>gfq;=ng>@D\>#F^>gD( I[?O
nA<?>@h#;=GlDEnA;YGqFQ<-p qV=aH>@DEng;ba^GX DHGIGqaHnfC<D\X q;=< RH<?K"!SU GIKI< <?KOE;bn;Y[<?DH[0ngaQ[g< <)n$IDEn,DQ>Aa^flaHn
X D\Gn@>gDSRH<?>@[A<0D\VbV·<?KqFH<?[ a+å[Aa^h<¿FH>@D+ I[?Ol[@Ds*D!XJqX-V=<\OjfIJqnn$IDEn3;bnX DHGIGqa\n3>A<`X-a\F^Gq;: <
.q<?G;=nIDH[)R^;Y[g;bng<?KD§GqaqKq<0n;YX-<HOCfC<?X DHJI[g<GqaqKq<?[ DH>A<GIa\n JIGq;^TJq< V:!VYD\fC< V=<?K!CoID\n
;=[?OHn$q<?>g<3DH>A<3FH>@D+ l[ån#lDEnªD>Aa^flaHnªX?D\G§< pIVba^>A<C<?>$C< ngJlDEV=V`HOTflJqn;=nxX?D\GÍGI< R\<`>[gnAaI[)!
o^Jl[ OjD\[ ;YG1I>g< RT;=aHJI[xaH>@ZÍ;YGn#I;=[[A<?nAng;=GqFCOl<(!FK!bO L%lOlO)OO'x<¿D\[@[gJlh<0n$IDEn?O'¸a^> ng<?>
h;YGID\nA;YGqF<-p qV=aH>@DEng;ba^G9O>gaHfCa\ng[¿X D\G©hdD\>@ZþGIaTKI<?[-·D>gaHfCa\nX DHG KI>ga(©D1l<`fIfqV=<Í;YG D
GqaqKq<D\GIKVYDEnA<`>);=KI<?G^nA;`!;=n D\GIKqq;YXÃZ§;=n J "!
Bla\V=V=a;=GqF7n#q<X aHhdh#aHG®X aHG^R\<`G^nA;=aHGI[¿;=G n#q<V=;bng<?>@DEn@JI>A<HOn#q<>gaHfCa\ng[#DE;Yh#;=GIFãD\n
l<`>¸a^>gh#;YGqF=l<`>#C< n@JIDEV < p qVba^>gD\nA;=aHG D\>g<GIa\ndF\;=R\<`GiC<?fIfIVb<`[ OX.I<?>g<?D\[§>gaHfCa\n@[dDE;Yh[
;=GqF*DEnC<?>¸aH>@h#;=GIFÍnA<`>gh#;YGIDEng;=GqF<-p qV=aH>@DEng;ba^G*DH>A<¿F\;=R\<?Ga^Gq<a^>h#aH>g<[C<?fIfqV=<?[@!"0[3D
X-aHGl[A<e^^JI<?GIX <\Oln$q<¿nxa-I>gaHfqV=<?hd[3fl<`X-aHh#<`[ ;YGIX-a^h*lD\>@D\fqV=<+!CU GIKq< <`K9Olng<?>@h#;=GID\nA;YGqF!< p
qVba^>gD\nA;=aHG ;Y[dh#aH>g<Kq<`h#DHGIKq;YGqFãn#IDHG C<?>$l<?ngJID\Vx< p qVba^>gD\nA;=aHG9OfIJqn#n#I<qnHhdD\X q;YGq<?[$n
Kq<?[g;bF^Gq<?K¸aH>)n$q<?[g<0nxa#n@D\[@ZT[Kqa§Gqa\nIDSRH<n$q<[@D\h#<Wlax<?>@!
0 6z
{! a+x>gaHfCa\n@[3;Y[0D[A<?nQaxKI< nA<`>gh#;YGq;Y[Ang;=XdD\JInAaHhdD\ngDo;bn$ CaH[@[A;YfqV:þKq;`kj<`>A<`G^n
ng>@D\GI[g;bng;ba^Gi£JIGIX-ng;ba^GI[?OªDEV=V[gngDH>Ang;=GqF£>gaHh n#q<ã[gDHh#<[An@D\>gnA;YGqF=laH;=G^n)!\Zq<?G [g< n@[Ía^>
nA<?DHhd[,a9>Aa^flaHng[,DH>A<X-a^GI[g;=Kq<`>A<`K9O¢n#I< >Aa^flaHng[a9DQnA<`D\häX D\GdX aHhdh¿JIGI;=X?DEnA<);YG#RSDH>A;=aHJl[
h#DHGIGq<`>g[@!qBla^JI>X DH[A<`[xDH>A<0X aHGI[g;=KI<?>g<?K;=Gn#q<0V=;=nA<?>@DEn@JI>g<
F
Fa^G X aTa(C<?>@DEnA;=R\<0>gaHfCa\n@[Cn#q<¿>gaHfCa\n@[ D\>g<0aHfIVb;=RT;ba^JI[ a+<`D\X *a\n$q<?>?OCDHGIK<?DHX *a
n#q<`hìDHX-ng[);YGIKq<el<`GIKq<`GHngV`o£>gaHh n$q<0a\n$q<?>@[)!
F
Y¶aqX D\VbV:dX-aTa(C<?>@DEng;bRH< >Aa^flaHng[-H>gaHfCa\ng[h<?< ng;=GqF#DEnxDGqaqKq<3X?D\Gd< pqX lD\GqFH<;=G ¸a^>ghdD
nA;=aHG9Ol;=GIX V=JlKq;=GIF§n#q<?;=>);YKq<?G^ng;bng;b<`[ D\GIK*n$q< ;Y>X JI>@>g<?G^n[An@DEnA<`[)!
F
Q3Vba^fIDEV=V:*X a^al<`>gD\nA;=R\<¿>gaHfCa\n@[Cn#q<#>Aa^flaHng[3D\>g<[l<`>#C< n@JIDEV=V:Ds)D\>g<Qaån$q<[gngD\nA<?[
a,n#I<a\n$q<?>@[ OlaM.q< n$q<?> n#q<@*h#< <?nD\GlKq.qa§n#q<@*h#<?< n OjD\GIKa+n$q<¿Kq<?FH>g< <`[
an#q<GIaTKI<?[)aqX X?J q;=<?KfÍn#q<>gaHfCa\n@[)!
F
m\Jlh*I;=GqFl0JqngaHhdDEngaHGECn#q<#>Aa^flaHng[3D\>g<F\V=aHfID\VbV:X aTa(C<?>@DEnA;=R\<HOCDHGIKD\G>Aa^flaHn ;=[
D\fqV=<!ngaÍeAJIh;/£>Aa^h n$q<GqaqKq<!;=n¿;Y[X?JI>@>A<`GHngV`©aqX X?J T;=GqFþnAa7D7GqaqKq<X?JI>@>A<`GHngV`
aqX X J'q;b<`Kf(D\GÍa\n$q<?>>gaHfCa\n@!
U G n#q;Y[lID+C<?>?O\x<þ>g<?[gng>g;=X nÍaHJl>D\nAnA<`G^nA;=aHG nga n#q<ãnxa/ª<`D\Z\<?[gn!h#aTKI< VY[xGqaHG
X-aTa(C<?>@DEng;bRH<>gaHfCa\n@[ OIDHGIK!V=aqX D\VbV:!X-aTal<`>gD\nA;=R\<Q>Aa^flaHng[@!
243 66!;.> :9@0>
U G©n#q;Y[9ID(l<`> Ox<-I>g<?[g<?G^nDGq<)V=aª<`>0fla^JIGIKãnA<`X IGq;^TJq<%¸aH>QF^>gD( 7<-p qV=aH>@DEnA;=aHGO
X DEV=V=<?Kj2
zu'Pz { u
6A4 ;{6A{T6
z$ "(vKw8Ju'z
!:)DH[A<`KãaHG©n#I;=[¿nA<?X lGq;:^TJq<HO¶n$q<ÍV=aª<`>fla^JIGIKI[
I>A<`[A<`G^nA<?K;YG¿n$q;=[ID+C<?>D\>g<)aHfqn@DE;YGq<?K#D\[R¸aHVbV=a [)!03[g[@JIh#< DQ[A<?na+3>Aa^flaHng[;Y[F\;=R\<?G!
oq<?GX aHGI[gng>@JIX-nn#q<#[ghdDEV=V=<?[gnla^[g[g;YfqVb<¿FH>@D+ 9OCX DEV=V=<?KDq6f2#{
~
¸aH> n$q;Y[[g< na+å>Aa^flaHng[?O
[gJIX ãn$IDEn0;`n#q<!>gaHfCa\n@[0D\>g<%qV=DHX-<`K7;YG [gaHh#<§[#C<?X ;chl<`K GqaqKq<?[a)n#q<ÍF^>gD( I[?Okn#q<`G
n#q<`>A<;=[#DEnV=<?DH[AnaHGq<!<?KqFH<!n#lDEn¿;Y[#Gqa\nng>@DSR\<?>@[g<?Kãf( DHG(ãa n$q<>gaHfCa\n@[)!·UAn#I<o
>Aa^flaHng[IDSRH< [gngD\nA<?[ <?D\X OID\GIK*n#I<0ng>@D+qID\[
B GxGqaqKq<?[?OIn$q<?G*n#I<[#IDHX-<0V=aª<`>
fla^JIGIKo¸aH>Dd[g< na >gaHfCa\n@[)<-p qV=aH>g;=GIF#D\VbV"gWGqaqKq<0FH>@D+'I[x;=[*B£V=a\F9L BRGGxfq;=ng[@!
oq<>g<?KIJlX-<?K®D\JqngaHhdDEn@DnA<`X IGq;^^JI<-¸aH>n#I<*Kq<`[A;=FHG a[$ID\X <ÍVbax<?>fla^JIGIKI[<¸a^>
FH>@D+ < pIVba^>gD\nA;=aHG*;=[Kq<`[gX?>A;Yfl<`K;=Gã_^<?X nA;=aHGT !Coq;Y[V=ax<?> fCaHJIGlKnA<`X IGq;^TJq<¿DEV=V=a [
JI[ångaX-a^GIX-<`G^ng>@DEnA<a^G§D[@JIfCX V=DH[g[a9FH>@D+'I[ OHX DEV=V=<?K
" 4 ;4 zJvgz
4 u
7k<?KqFH<JWX-aHVba^>A<`KDHGIK
>A<?FHJqVYD\>@!HBCaH>x[gJlX ÍFH>@D+'I[ OTD#>Aa^flaHnxX?D\G!fC<QKq<?[@X >g;=fC<?KfÍD¿RH<?>#d[g;Yh*IVb<0D\JInAaHhdD\nAaHGO
.qaH[g< ng>@D\Gl[A;=nA;=aHG<£JIGIX nA;=aHGÍX aHGI[g;Y[An@[,aD0F^>gD( <¸aH>@h<`K§f#DKI;=>g<?X nA<?K%lDEn#*¸aHVbV=ax<?K
f(©DKq;Y>A<`X-ng<?K XJqX Vb<(!·oq<!>g<?KlJIX-<`K D\JqngaHhdDEn@DnA<?X lGq;:^TJq<D+ qV=;=<?[ngaTqa^haHF\<`Gq< a^JI[
FH>@D+ I[@!lcaHJqFqV`[$l<`D\Z^;YGqFlOkD&2
zu'$z
2#45#46IDH[n$q<;I>Aal<`>An*n#lDEn;c;=nng>@DSR\<?>@[g<?[
D\Gã<?KqFH< dD\n[Aa^h<§[gnA<e7a+xn$q<§<-p qV=aH>@DEng;ba^G9O9[gDs&£>Aa^h nAajO¶n$q<?Gã;=ng[Gq< pqn
ha¢RH<-;=VbV)Gqa\n#fl<*ng>@DSR\<`>g[g;YGqFn#q<<?KqFH<fIDHXÃZþnga!oq;Y[*I>Aal<`>Anã;Y[¿D\X I;b<?R\<?K f
ng>@D\GI[¸aH>@h#;=GqFD>gaHfCa\n3;=G^nAa*D>g<?KlJIX-<`K>Aa^flaHn.qa^[A<ng>@D\GI[g;=nA;=aHGq£JIGlX-nA;=aHGãGq<?R\<?>UIDH[
nªaãX-aHGl[A<`X Jqng;bRH<!<?KIF\<?[<;=n# n$q<[gDHh<V=DHfl<?V ! ã<*X aHGI[gng>@JIX nDi6 2#{
~ 42
z
Kq;Y>A<`X-ngV`
£>Aa^h n#q<dn@>gDHGI[A;=nA;=aHGT£JIGIX nA;=aHGãa)D>g<?KlJIX-<`K7>gaHfCa\n?O".q;=X 7;Y[Qn#q<`Gþ<`D\[g;bV:<-pqng<?GIKq<`K
nAaÍD#ng>@D+¸aH>)n$q<0aH>g;bFH;=GlDEV9>Aa^flaHn)!
U G!_^<?X nA;=aHG%Wx<JI[g<n$q< nA<`X IGq;^TJq<a+9>g<?KlJIX-;YGqF¿D>gaHfCa\n,nga¿X-a^GI[gng>@JIX-nD¿Kq< F^>A<?< %
ng>@D+¸aH>D1W[gngDEng<>gaHfCa\n?Oqa,[A;: < % !loI<Hl>AaTanA<`X IGq;^^JI<X D\G*fC<0F\<?GI<?>@DEV=;`?<?K
nAa%I>gaTKlJIX-<ng>@D+I[xa+·D\GÍKq<?FH>g< <\OTfIJqnr¸a^>x;bV=V=Jl[An@>gD\nA;YGqFn$q<QnA<`X IGq;^^JI<\OT;bn);Y[[gJ §X ;b<`G^n
nAa;ªa^>gZ;;=n#Kq<?FH>g< < %#FH>@D+ I[@!TU GIKq<?<?K9ORLcbe O,I>g<?[g<?G^ng[)D#ng>@D+a[A;: < jbHO qVYD\GIDH>
D\GIK7R¢DEV=;=KT¸aH>QF^>gD( I[3axDHGKq< F^>A<?<+!9oq<-I>gaTax<%I>A<`[A<`G^n3;Y[0[Aa^h#<).ID\n[g;=h;qV=<?>
n#IDHG§n#q<3aHGq<aLbs sOOHDHGIKÍh#aH>g< a¢RH<?>?O¢;bnå;=V=V=JI[gng>@DEng<?[n#q<3nA<?X lGq;:^TJq<JI[g<?KdnAa*I>ga¢R\<aHJl>
>A<`[gJqV=ng[);YG*n#q<H¸aHVbV=a;YGqF#[g<?X nA;=aHGI[@!
U G!_^<?X nA;=aHG*9x<.I>A<`[A<`G^n,aHJI>åGI<) >A<`[gJIVbn@[åD\fCaHJqnng>@D+I[ ¸a^>X a\V=Vb<`X-nA;=R\<< p qVba^>gD\nA;=aHG
f(*D§[A<?n a
v 4 v
X a^al<`>gD\nA;=R\<0>gaHfCa\ng[@!Ioq<¿>gaHfCa\n@[KqaÍGqaHnX-a^h#hJIGq;YX D\nA<DEn D\VbVOlDHGIK
< R\<`><`KqF\<§hJI[AnfC<§ng>@DSR\<`>g[g<?Kþf(7DEnQVb<`D\[gnQaHGq<§>gaHfCa\n)!"ã<Í[$qa BXJ!·oq<?aH>g<?h G
n#ID\n[¸a^>#DHG©[g< n#aUGqaHGX a^al<`>gD\nA;=R\<+&[gngD\nA<*>Aa^flaHng[?O·n$q<?>g<!< pT;Y[gng[dD %>g< F^JqVYD\>
FH>@D+ 1S#OkD\GIKnxa-ID\;=>@[dD\GIK¿a+,GI< ;=F(Tfla^>A;YGqF!GIaTKI<?[?OC[@JIX n#ID\n3DHG(
>Aa^flaHn¿a3n#q<[A<?n O[An@D\>gnA;YGqF&£>gaHh¼aH> O£DE;=V=[#ngaþng>@DSR\<`>g[g<§n#I<<`KqF\< !oI<
FH>@D+ %S ID\[\*B !pG,GqaqKq<?[@!Hoq;Y[å;Yh;I>ga¢R\<?[n$q<*B GfCaHJlGIKda9c aHVbV=;=ZlLbeNO,BX !
DªaH>ga\V=V=DH>- (G !
_ [g;=h;qV:/qVYJqF\FH;=GIFþn#I;=[§Gq<@ ng>@D+=¸aH>dGqaHGX a^al<`>gD\nA;=R\<!>gaHfCa\n@[¿;YG^nAa7c a\V=Vb;YZ[
X-aHGl[An@>gJIX nA;=aHG9Ox<FH< n[BX !RDªa^>AaHVbVYD\>#G D*Gq<) ng>@D+q¸a^>3V=aqX D\VbV:X a^al<`>gD\nA;=R\<0< pIVba+
>gD\nA;=aHGaå[g;`?<
;B
G;bn$& bV=< R\<?V=[a,<-p CaHGq<`G^nA;YDEVOlnAafl<#X-aHh;IDH>A<`Kl;bn$
n#q<[ + ZbQVb<?R\< VY[)a.Lcb@NOA!KEJI>xng>@D+*;Y[)n#TJI[ [@hdDEV=Vb<`>xn#IDHGn$q<0aHGI<;YG=LbeNOA!
U Gþ_^<?X nA;=aHG&d;x<¿[$qaÑn#ID\n3oq<?aH>g<?h oID\[3DÍ[A;=FHGI;chCX?D\G^n;Yh*lD\X-n3aHGn$q<[$ID\X <
X-aHh;qV=<-pq;=n©ang<?>@h;YGID\nA;YGqFþF^>gD( ©<-p qV=aH>@DEng;ba^G f©D7[A;YGqFHVb<*>Aa^flaHn)! 0[dh#<?G^nA;=aHGq<`K
D\fCa¢R\<\O".I<?G©nA<`>gh#;YGIDEng;=GIF<-p qV=aH>@DEnA;=aHG7;Y[>A<e^TJq;=>g<?KO9n#q<!>gaHfCa\n0;Y[9I>ga¢RT;=KI<?Kp;bn$©D
l<`fIfqV=<+!ã<UI>ga¢R\<<BXJ!ToI< aH>g<?h dG,n$IDEnxnA<`>gh#;YGIDEng;=GIF< pIVba^>gD\nA;=aHG§>g<@^TJq;Y>A<`[ªD#>Aa^flaHn
;bn$ *B£V=a\F\RGfI;bn@[_¸aH>xn#q<U£DHh;=V:§a·F^>gD( I[\;bn$D\nha^[An_7GIaTKI<?[@! 03[h#<?G^nA;=aHGq<`K
fl<)¸aH>g<\O9;YG7DH>gfq;=ng>@D\>#FH>@D+ l[ O"C<?>$l<?ngJID\V,<-p qV=aH>@DEnA;=aHG7D\GIK7nA<`>gh#;YGIDEng;=GIF*< p qVba^>gD\nA;=aHG
D\>g<3GqaHnxX aHh;ID\>@D\fIVb<fl<`X D\Jl[A<< RH<?G§;`C<?>$l<?ngJID\Vk<-p qV=aH>@DEnA;=aHGÍ;=[)D#[A;Yh;qVb<`>n@D\[@Zdn#IDHG
nA<?>@h#;=GlDEnA;YGqFQ<-p qV=aH>@DEng;ba^G9O`;=Gn#q<VYDEngnA<`>X?D\[g<ªn$q< >gaHfCa\n;=[FH;bRH<?G¿DHC<?fIfIVb<(!Eoq<?>g<J¸a^>A<HO
< R\<`G®;`Qn#q<< pT;Y[gnA<?GlX-<aQng>@D+l[<;=n# D\n§ha^[An *BbsG§GqaqKq<?[*¸a^>§D\G 1W[gngDEng<
>Aa^flaHnx;Yh;qV=;b<`[D\G *B£V=a\FRGxfI;bn@[ V=aª<`>xfCaHJlGIKl¸aH>)n$q<¿h#<?h#aH>#![g;`?<0a,Dd>Aa^flaHnn#ID\n
l<`>¸a^>ghd[C<?>$C< ngJlDEVk<-p qV=aH>@DEng;ba^G;YG!D\VbVjFH>@D+'I[M;=n#!D\nªh#aH[gnGIaTKI<?[?OHn$q< *B£V=a\F\RG
Vbax<?>fCaHJIGlKl¸aH>ng<?>@h;YGID\nA;YGqF§<-p qV=aH>@DEng;ba^G!;Y[GqaHnD§X-a^GI[g<@^TJq<?GlX-<Qa,n#I<WhC>@[An >g<?[@JqV=n
V '
U Gã_^<`X-nA;=aHG !:b[x<Kq<)hCGq<<¸aH>@h#D\VbV:q.IDEnUx<h#<?DHGfD*>gaHfCa\n< p qVba^>A;YGqF!D!FH>@D+ !
U G _T<?X-ng;ba^G= ! x<§Kq<?[@X >g;Yfl<ÍfIDH[A;YX;I>ga(C<?>gnA;=<?[Qa)D>Aa^flaHn)!9U G _^<`X-nA;=aHG= !%oª<Í[$qa
qa nAa#[A;Yh;qVb;`§n#I<[gng>@JIX-n@JI>g<a¶D#>gaHfCa\n O+¸aH>ªn#q<HI>gaTa£[ªan#I<¸aHVbV=a;=GIF[g<?X-ng;ba^GI[@!
E3 2 6> 748 7 @0>1B 6>
0 >Aa^flaHnÍX-a^GI[A;YKq<`>A<`K ;YGán#q;Y[lD+C<?>Ín@>gDSRH<?>@[A<`[dD©FH>@D+ áfáh#a¢RT;=GIF £>gaHh1GqaqKq<nga
GqaqKq<DEV=aHGqFdn$q<0<?KqFH<?[)a+n$q<FH>@D+'"!7<Hhj>g[gn Kq<?[@X >g;Yfl<Qn#I<¿fID\[g;YXh#aqKq<?Va,D§>Aa^flaHn
ng>@DSR\<?>@[g;=GqF#D¿F^>gD( 9OqD\GlK.ID\nrª<0h#<?DHGf!Dng>@D+9OIGlD\h#< V:!D*IDE;Y>HBfS "G.q<`>A<9S
;=[QD*FH>@D+ þD\GIK;BAS9G[gJlX n#lDEn0D>gaHfCa\nQ[gngD\>gnA;YGqFo£>Aa^h X D\GlGqa\n<-p qV=aH>g<;S*!
o¶aX-a^GI[An@>gJlX-nQD!n@>gD(1¸aH>QD*>Aa^flaHn Ogx<[hC>@[gnQKI<?[g;bF^GþDFH>@D+ n$IDEnQn$q<§>Aa^flaHn3X DHGIGqaHn
Vb<`DSR\<\O9X?DEV=Vb<`K7D*ng>@D+ãX-a^>A<HO9D\GIK7n#q<`Gpª<§D\KlKþnga;bnQ<?KIF\<?[Qn$IDEn0n$q<§>Aa^flaHn0KqaT<?[0GqaHn
<-p qV=aH>g<+!7<<-p qVYDE;YG-qa n$q<0Kq<?[@X >g;:InA;=aHG§a+¶D>gaHfCa\nª;=[x[A;Yh;qV=;chl<`K.I<?GÍn@>gDSRH<?>@[A;YGqF
Dh#aH>g<[#qhdh<?ng>g;=X#Z^;=GlKaªFH>@D+ 9OkX D\VbV=<?K qaHh#aHF\<?GI< aHJl[)!koq<d[A;Yh;qVb<`>QKq<?[@X >g;:InA;=aHG
;bV=V¶fC<X >@JIX-;YDEV9;YG!n$q<>g<?[gna·n$q<9ID(l<`>)!
; 81>-A"!< 7;.9 7$#% 6!7 8 7 @ @-6'&; 6!>0ACB:D D46 3
U GDÍFH>@D+'o.I<?>g<¿GqaqKq<?[
IDSR\<Gqa ;YKq<?G^nA;`hl<`>g[?O,nªa©GqaqKq<`[ÍD\>g<;YGIKq;Y[gnA;YGqFHJq;Y[$ID\fqV=<nAa n$q<>Aa^flaHn OåJIGIVb<`[g[dn$q<)
IDSR\<Kq;ckk<?>g<?G^n)Kq< F^>A<?<+!)(ax< RH<?>?O\<?KIF\<?[_IDSRH<V=aTX?DEVgla^>An)GTJIh¿fC<?>@[?O^[gan$q<Q>Aa^flaHnªX DHG
Kq;=[gnA;YGqF^Jq;=[$ÍnxadKq;ckk<?>g<?G^nx<?KqFH<?[x;YGIX-;YKq<?G^nxnAa§D#GqaqKq<+!TU G!h#a^>A<QKq< n@DE;=VOT<`D\X Í<`KqF\<HIDH[
nªa VYD\fC< VY[?O <?DHX aHGq<DH[g[gaqX-;YDEng<?KnAa a^Gq<åa+I;bn@[nxa <?GIK'laH;=G^ng[@!?oI<VYD\fC< VY[aqn$q<<`KqF\<`[
;=GIX ;=KI<?G^nånAaDQGqaqKq< ¿D\>g<D\>@fq;bn@>gDH>D\GIK;ID\;=>#;=[g<Kq;Y[Ang;=GIX nå;YGn$q<[g< n / +*,*+* .-+/101b ^O
.q<?>g<2-+/*Kq<?GqaHnA<`[0n#q<ÍKI< FH>g< <da+ !Zq<`G D*>gaHfCa\n0;Y[Q;YG D*GIaTKI<\O;=n¿[g< <?[Qa^GqV:þn#I<
V=DHfl<?V=[ D\nn#q<0<`GIK Ca\;YG^ng[a+n$q<<?KIF\<?[);YGIX ;=Kq<`G^nnAa§n#I<¿GqaqKq<+!Coq;=[DEV=Vba [xn#I<¿>Aa^flaHn
nAadKq;=[gnA;YGqF^Jq;=[$n#q<Q<?KIF\<?[x;YGIX-;YKq<`GHn)ngan$q<0GqaqKq<Qn#I>gaHJqFÍn$q< ;Y>)JIGq;^^JI<VYD\fC< VY[?OTX?DEV=Vb<`K
|c4
{+|
~
42 6
vKu %5
z
2P743KF3a\nA;YX-<¿n#ID\n3D\G<`KqF\<h#DsqIDSRH<Kq;ckk<?>g<?G^nCaH>gnGTJIhfl<`>g[;=G;=ng[
nªad<?GlK laH;=G^n@[)! ã<>g<J¸<?>xnga§n#qa^[A<QFH>@D+'I[)D\[
~
42 665|c{(5
z | z
+2#{
~4"
7 !
0 >Aa^flaHn0;=[D\G©D\JqngaHhdDEngaHG ;bn$ D[A;YGqFHVb<§;YGq;=nA;YDEVª[gngD\nA<7·DEn0n$q<!fC< FH;=GIGI;=GqFCO;=n;=[
qV=DHX-<`KÍaHGD\GD\>@fq;bn@>gDH>d[gngD\>gnA;YGqF#GqaqKq<Qa¶n$q<QFH>@D+ §;YGÍn$q;Y[[An@DEnA<(! Zq<?G*D>gaHfCa\nª;=[
;=GãDGqaqKq< D\GIKi62${
xz 2P7
z
7dDHGþ<`KqF\< #ngaF\< nQngajO9;=nV=<?DH>gGl[3n$q<§VYD\fC< VåDEn [
<?GIK Ca\;YG^na+n#q<<?KqFH<¿a^GIX-<;=n<?G^nA<`>g[ K!9oq<#>Aa^flaHnKq<?X ;=KI<?[.q;=X <?KqFH<¿nAangDHZE<nga
Vb<`DSR\<fIDH[A<`Ka^Gn#I;=[VYD\fC< VOkDH[Uª<?VbVD\[aHGþn#q<dKq<?FH>g< <¿a+ jOD\GIKþaªX aHJI>@[A<HOjflD\[g<?K
aHGÍ;=ng[)V=aqX D\V[An@DEnA<(! 7<0Kqa§GqaHn)KI<JhCGq<¸aH>@hdDEV=V`Í[@JIX *D>gaHfCa\n)fC<?X DHJI[g<x<H;bV=V[An@JIK
;bn@[fC<@lDSR^;=aH>aHGqV:aHGD[#C<?X ;=D\VX V=DH[g[3aåF^>gD( I[?OCX?DEV=Vb<`K&qaHh#aHF\<?GI< aHJl[ O'¸aH>.q;=X þD
R\<?>#þ[g;=h;qV=<!>g<@I>g<?[g<?G^n@DEnA;=aHG7aD>gaHfCa\n0;Y[9la^[g[g;YfqVb<HOn#lDEn9x<98
w
|y|)Kq<JhCGI<%¸aH>@hdDEV=V`(!
U Gþ_^<?X nA;=aHGTd*x<9;=VbVX-aHGl[A;YKq<?>3D\G*<-pqng<?GIKq<`KKq<)hCGq;=nA;=aHGaåDÍ>gaHfCa\nn#ID\nX DHGKI>AaD
l<`fIfqV=<;=G#DQGqaqKq<D\GIK*q;YXÃZ0;bnåJ'[.q<`G¿;=nå>g< ngJl>gGI[ngan$q< GqaqKq<)nAa0KI>ga(;=n[gaHh#<@.q<?>g<
< VY[A<(!
0 6f2#{
~
¸aH>D![g< n3aª>gaHfCa\n@[;Y[DID\;=><BfS ;:9GNOg.q<`>A<;S;=[QDola^>AnVYD\fC< V=<?KF^>gD(
D\GIK<: ;=[dDã[A<?n¿a+3GqaqKq<?[#a+US#O,[gJIX n#ID\n#;`3D\VbV)n#I<*>gaHfCa\n@[DH>A<lqV=DHX-<`K ;=G GqaqKq<?[
:#O9<`D\X þ;=Gã;=ng[Q;YGq;bng;=D\Vå[An@DEng<\O9n#I<?G7n#q<`>A<;;=VbVåfC<§D\G7<?KqFH< dn#ID\nQ;=[0Gq<?R\<`>
ng>@DSR\<?>@[g<?Kfn#q<§>gaHfCa\n@[)!ko¶ahdD\Z\<¿aHJl>3V=ax<?>fla^JIGIKþ>g<?[@JqV=ng[Q[gng>gaHGqFH<?>?OC[gaHh#< ng;=h#<?[
ª<WI>g<?[g<?G^nDo7 | 6f2#{ GID\h#<?V`-;=n#Gqa%IDH>gD\VbV=< V9<`KqF\<`[D\GIK*[g< V`yV=aTa(I[@!
w u
0
1
1
1 1 0
1 2 2 0 0 1
v
0
2
Core
jÆTÆ
® ?Ë#?~^Ag¥`W
74< 7D;=B:;.7 :> D461:><1B1 @-6 ! 746!;=> 3
7<p;=VbVQ[An@JIK¼n#I<7fC<@IDSRT;=aH>Ía+D
>Aa^flaHnx;YG*DF^>gD( -.I<?>g<QfCa\n$oCaH>gnGTJIh¿fC<?>@[)aD\G<?KqFH<QX a\;YGIX-;YKq<(!qU G[@JIX *DF^>gD(
D>gaHfCa\n0X DHGþfC<§Kq<?[@X >g;=fC<?KãfD*R\<?>#[A;Yh;qV=<dDHJqnAa^hdDEnAa^G9O9D\[Ux<d[$ID\VbV,[g< <§Gq<-pqn@!0
- 5"
4! %4
z)vz 4 u
7JlGIKq;Y>A<`X-nA<`KdFH>@D+ #;Y[DQF^>gD( #n#ID\nå;=[ -e>g< F^JqV=DH>,D\GIK2-e<?KIF\<JWX-aHVba^>A<`K"!
0ÑFH>@D+ ;=[ - 52
z u
|c{2¿;`<`D\X a;bn@[ GqaqKq<`[.ID\[KI< FH>g< < -TOlDHGIK*;bn;Y[ - 5
z z 5 4+|c42
z(
;`
<?D\X <`KqF\<¿;=[3V=DHfl<?Vb<`Kq;bn$aHGI<¿a,n$q<¿;YG^nA< FH<?>@[ ;YGn#I<[g< n 0/ @b ,*+*+* .- 0jb ¿;YG
D9)Ds#n$IDEn)Gqanªa<?KqFH<?[ª;=GIX ;=KI<?G^nªnga¿n$q<[@D\h#<GqaqKq<UlDSR\< n$q<[@D\h#<X-a\V=aH>@!^BlaH>ªn#I<
[gDHZE<a,X-VYD\>g;bnHOª<0hdDE;YGqV:%¸aqX JI[a^G!F^>gD( I[_;=n#hdD¢pq;Yh¿JIh KI< FH>g< <n#l>A<?<+!
Zq<?GD3>Aa^flaHnng>@DSR\<`>g[g<?[9D%qaHh#aHF\<?GI< aHJl[9FH>@D+ O-<?DHX 0nA;Yh#<;=nDH>g>g;bRH<?[knga3DGIaTKI<
n#q<3VbaqX D\Vl<`GHRT;Y>Aa^GIh#<?G^nåV=aTaHZT[å< pqDHX-ngV`#n#q<[gDHh#<D\[;=GÍDHGaHn#q<`>GqaqKq< ^D\VbVjGqaqKq<?[xD\>g<
<@^TJIDEVxD\GIK ;=G <`D\X GqaqKq<*DEV=VV=aqX DEV_la^>An@[DH>A< /lO\bHO¶a^>< !oTJI[ On#I<>gaHfCa\n¿Kq<`X-;YKq<?[
.q;=X <?KIF\<QnAa§n@D\ZE<Qnga#< pq;bnn$q<0GqaqKq<fID\[g<?KaHGIV`Ía^G!;=ng[X JI>@>A<`G^nx[gngD\nA<+!lBlaH>@hdDEV=V`HOqD
2#4(5$46;Y[D\GãD\JqngaHhdDEngaHG B >GNO;=n#©DohCGq;=nA<§[g< n0a+x[gngDEng<?[O·D\G7;=Gq;=nA;YDEV
[An@DEnA<> ODHGIK7Dng>@D\Gl[A;=nA;=aHG&£JIGIX-ng;ba^G !9BCaH>QD*[An@DEnA<-> ;bn$
Bf>G BA>
GÃOEKq<?GIa\nA<"!$#$BA>G >
D\GlK %eBf>G&P!Eoq<)>gaHfCa\n¼ha¢RH<?[·aHGD%>g< F^JqVYD\>
FH>@D+ D\[¸a\V=Vba [@!lU Gq;=nA;YDEV=V:' ;Y[IV=DHX-<?Ka^GD§GqaqKq<a+n$q<¿F^>gD( *;=G[gngD\nA<(>(!CUA) ;=[
;=GDdGqaqKq<Í;YG[gngD\nA<[>Qn$q<?G* h#a¢R\<`[xnAa§n#I<GqaqKq<¶[gJIX n#lDEnn#I<0<?KqFH< 0;=[
V=DHfl<?Vb<`K +%)Bf>GNOjD\GIK*X IDHGqF\<`[ªngaÍ[An@DEng< ,!#PBf>GP!
Zq<?GX aHGI[g;YKq<?>g;=GIF§n#q<<¸aH>@hdDEV·KI<JhCGq;=nA;=aHGaDÍ>gaHfCa\n¸a^>qa^h#a\F\<`Gq< a^JI[F^>gD( I[?O
aHGq< X?D\G#X-aHGl[An@>gJIX nåDng>@D+df9hC>@[An,Kq<)hCGq;YGqF¿DFH>@D+'*S n#ID\nå;Y[,<?KqFH<JWX-aHVba^>A<`K9O`flJqnGqaHn
Gq<?X <?[@[gDH>A;=V` %W>g< FHJIV=DH> OEDHGIK§n#I<?G!DHKIKq;YGqF[gaHh#< <`KqF\<`[ªDHGIKÍGqaqKq<`[ånga¿aHfIngDE;YGÍD¿ng>@D+§;YG
.q;=X n#I<0ng>@D+!X aH>g<3V=aTaHZT[rqaHh#aHF\<?GI< aHJl[ªngadn#q<0>gaHfCa\n)!ã<0Kqa§Gqa\nKq<`hdD\GIKn#ID\nD
ng>@D+Í;Y[ %qa^haHF\<`Gq< a^JI[DH[)Vba^GqF#DH[)D#>gaHfCa\n)Gq<?R\<?>xn@>A;=<?[xnAadn@D\ZE<QD\G<?KIF\<n#ID\nx;Y[GqaHn
;BAC@-AC7B 2 6 746 ; !3
ng>@D+©X aH>g<J42o{&7
z
6H4%2$4(5$467 w 7{
~ { w
2-BAS :9G
=
8 " z 2 z S w 7<{%>5
z z 5 4|`42
z 2#{
~ " { v : w 7<{%7
z
6r4
v 4 +z
7<4S
= 7 u'#"
6"
{6
w
<{+|y|
6
"z
2#4(5$467*{2
z~
|c{
Pz(lwyvv
4
(z
7 :
=rz
{
#"&wyvpw 687
wyv'w 6w
{|R7 6A{6
z4=
6" z)v/z
{
#"
6w z {
2#4(5$46 B >G
w7 wyv
7)4!
zv
4
+z
wyv 7)4
z
7 6A{6
z >
=.w
% BA>sG <6
" z)v { v
z( z
|c{5
z |
z u
7 6r5
z[wyv S23
6!74< @6 ! 7 6!; @07 @-6 3
EGIX <Wª<WIDSRH<0fIJq;=VbnD#n@>gD(*X aH>g<<BAS :9G);bn;Y[ GqaHn
Kq;ÍX?JqVbn3nAaÍX aHGI[gng>@JIX-n DÍng>@D+pBfS :[GNOlfD\KIKq;YGqF§ngaÍ;bn3[Aa^h<0<`KqF\<`[ D\GlK*D!X-aHGl[An@D\G^n
G^Jlh¿fC<?>QaGqaqKq<`[)!F3a\ng;=X <#n$IDEn0;`WBfS ;:9G3;=[¿Dn@>gD(7X aH>g<*¸aH>0D[A<?n0a>Aa^flaHng[?Okn#q<`G
BfS :9G3;Y[D*ng>@D+ ¸a^>Qn#q<![@D\h#<§[g< n0a>gaHfCa\ng[?OfC<?X DHJI[g<S ;Y[D[An@>A;YX-n[@JIfqF^>gD( 7a
S Cn$IDEnªn#q<Q>gaHfCa\ng[ªGq< RH<?>ªVb<`DSR\<(!7<hC>@[Anx[#IajIa nAaX aHGI[gng>@JIX n_S K£>Aa^hD %<?KqFH<
X-a\V=aH>g<?KF^>gD( TS#OkfD\KIKq;YGqF*DEn3h#a^[AnH !GqaqKq<`[ OkD\GlKD\KIKI;=GqF<?KqFH<?[3n#ID\n3F^JID\>@D\G^ng< <
n#ID\nå< RH<?>#¿GqaqKq<aS ID\[Kq< F^>A<?<x< pID\X-ngV` %IO\DHGIK*ª< KI<JhCGq<VbaqX D\V la^>AnV=DHfl<?V=[ ¸a^>,n#I<
Gq<)V:D\KIKI<?K7<?KqFH<?[@!koTJI[?O9D\[;YGþB;=FHJI>g<bHO9<?KqFH<?[3n#ID\nUx<?>g<#aH>g;bFH;=GID\VbV:;=GpS IDSRH<
n#q<§[@D\h#<*CaH>gnQV=DHfl<?V=[;YG7fCa\n$ã<?GIK Ca\;YG^ng[*B£<(!FK! §;YGþn$q<*hlFHJl>A<GNOg.q;=Vb<§Gq<@V`
D\KIKq<`K§<?KIF\<?[ªhdDs*IDSRH< Kq;`kj<`>A<`GHn_la^>AnªV=DHfl<?V=[B£<(!FK! ;YG§n#q<hlFHJl>A<GP! 0¸nA<`>)D\>@K
ª<0[$qaqa nAa§X-a^GI[gng>@JIX-nD\Gqqa^h#a\F\<`Gq< a^JI[S ";=n#DEnh#aH[gnWb-%dGq<@ GqaqKq<`[)!
;BAC@-AC7B AC< 9C; 6E@0;=B:>0AC7B !3
wyxsz)v {%>5
z z 5 4|`42
z +2#{
~4"
S
B6 <G
= 6" z
|c{5
z | z
7 w ~ |z +2#{
~ " S VB yG
=
j
=
4(5J6{
wyvz
P2#4 S
wyv 6" z
J4|y|c4 8
wyv 4 v 7P6f2
u'
6w4
v&w 7
{+|y|
z 6" z
[g;Yh*IVb<Qng>@D+<-pqng<?GI[g;ba^G 4.S23
o¶a¿X aHGI[gng>@JIX n\S KhC>g[gnXx<X DHGÍD\[@[@JIh#< n#ID\nn$q<?>g<3DH>A< D\nªh#aH[gn\ GIaTKI<?[åa+¶Kq< F^>A<?<
Vb<`[g[Qn$ID\G % ! E3n#q<`>;Y[A<HO9n#q<`>A<§DH>A<dnxaGIaTKI<?[0a+)Kq<?FH>g< <#Vb<`[g[n#IDHG%*n$IDEnDH>A<§GqaHn
X-aHGlGq<?X nA<?K7fD\G<`KqF\<HO9D\GIKTª<dhdDsDHKIKþDHG<`KqF\<dX-a^GIGq<?X nA;YGqF*n#q<`hO";=n#7D+ l>Aa+
I>A;YDEng<V=aqX D\V CaH>gnV=DHfl<?V=[@!"Fa0Ogx<#DHKIKþD\nh#aH[gn9 !GI<) GqaqKq<`[)!E*xD\X ng;=h#<;x<#DHKIK
DGq<)GqaqKq<\O,ª<ÍX aHGIGq<`X-n0;=nnAaGIaTKI<?[W;=n#©Kq<?FH>g< <dVb<`[g[n#IDHG%lO;=n# D+'I>AaI>g;=D\nA<
VbaqX D\V,CaH>gnV=DHfl<?V=[@!lUAåDEV=V¶GqaqKq<`[aS]IDSRH<QGIa Kq<?FH>g< <Q<-pIDHX-nAV: %lO x<D\>g<KqaHGq<HOI< VY[g<
ª<0D\KlK!DdGq<) GqaqKq<0D\GIK*>g<@C<?DEn)n$q<WI>AaqX <?KIJI>g<+!0)n)n#I<0<?GIKoª<Qa^fqngD\;=G!n#q<Kq<`[A;Y>g<?K
%<?KqFH<#X a\V=aH>g<?KF^>gD( S O".q<`>A<§D\VbV,a^>A;=F\;YGIDEV,GqaqKq<`[WIDSR\<#<-pIDHX-nAV:þKq<?FH>g< < %IO".q;=V=<
n#q<Gq<@ GIaTKI<?[IDSRH<Kq<?FH>g< <0DEnh#aH[gn % !!aH>g< a¢R\<`> OS 9;Y[ Dd[A;Yh;qV=<0FH>@D+ "!
" z
;{2$#3rC[A;YGqFdn#I<Q[@D\h#<nl<QaD\>gFHJIh#<`GHn@[ªDH[)D\fCa¢R\<\OT;=n);=[CaH[@[A;YfqV=<3nga§X-aHGl[An@>gJIX n
D#[g;Yh*IVb<0n@>gD(!< pTng<?GI[g;=aHG¸aH>D\>@fq;=ng>@D\>#ÍKq< F^>A<?<%-TOCf(D\KIKq;YGqFÍD\n)h#a^[An -%0ib0GqaqKq<`[)!
7<!X?D\G X aHGI[gng>@JIX-nDng>@D+©< pTng<?GI[g;=aHG/S&%'( £>gaHhIS n#ID\n;=[*qa^haHF\<`Gq< a^JI[ Of
D\KIKq;YGqF§D<¸<)Ñh#aH>g<QGIaTKI<?[@!
;BAC@-AC7B*)
7< 74D;.B7 :>+,E@-;.B:>-A 74B- 3.
wyxzJv { %5
z z%
4|c42
z +2#{
~ " S
B6 <G
= 6
"z +2#{
~4"
S&%'( B6 yG
=/
0
b-%
=
45 6{
wyvgz
P2#4 S
wyv 6" z
J4|y|c4 8
wyv 4 v 7P6f2
u'
6w4
v&w 7
{|y|
z
6
"z
IaHh#a\FH<?Gq<?aHJI[x<-pqng<?GI[g;ba^G/4.S23
0KIK©nga<?DHX 7GqaqKq<!aS a Kq< F^>A<?< 3V=<?[@[0n#lD\G %IO% 0 UC<?GlKq;=GIF $#ID\Vcy<?KIF\<?[$n
X-a\V=aH>g<?K*Kq;`kj<`>A<`G^nAV:£>gaHh <?DHX aHn#q<`> D\GlK£>gaHh n#I<¿X-aHVba^>g[)a+<`KqF\<`[;YGIX-;YKq<?G^n ngaÍn#I<
GqaqKq<+!CBlaH>1 / @b $ IOIV=< n325476+A?98gB:1eG fl<n$q<<lD\>g;bna,n#q<#GTJIh¿fC<?>aXl<`GIKq;YGqFID\Vcy
<?KqFH<?[)VYD\fC< V=<?K;13;YG*n#q<>g<?[@JqV=nA;YGqFdFH>@D+ <HS f!
= xÎ,¬¬k^) ÈHb,~^¥ Wb¥?~d¥?Êæ Ì` Ë^È^çÎ, Èæ ÈT-¬Ê=£ÃHÌ?ÃWç0NS@ ¬jW¨0Ã~¿ ÈHb,ËT?Ëq@N«
|`{
w
23 BCaH>D\G 1 1 0/ @b P HO 2 46+A?98gB:1eG 2 46+f?98gB1G !
r2#4e4430G <?KqFH<þa;S X D\G fl<©X-a^GI[g;=Kq<`>A<`KèD\[nxaáGqa^G l<`GIKq;YGqF3lDEV`y<`KqF\<`[)!xBla^>
1 0/ )b P ^OVb<?n[?%dfl<n#q<*nAaHngDEV)GTJIh¿fC<?>alDEV`y<`KqF\<`[aS ªVYD\fC< V=<?K 1EOD\GIK 2 %?O
>A<`[#"!(2 %`OHfC<3n$q<3GTJIhfl<`>åa,C<?GlKq;=GIFlOT>A<`[#"!^GqaHGAC<?GIKI;=GqFCO(ID\Vcy<?KIF\<?[aRS CV=DHfl<?Vb<`K
1!0 V=VGqaqKq<?[Q;YG=S åD\>g<d<-pID\X nAV:a)Kq< F^>A<?< %DHGIK©D\>g<;YGIX-;YKq<`GHn0ngaaHGq<%ID\Vcy<?KqFH<da
<?D\X þV=DHfl<?V!9oTJI[U? ?L ?]
OD\GIKþn#q;Y[Q;=[<e^^JlDEVnAa*n#q<§GTJIhfl<`>3a+ªGqaqKq<`[Q;=GpS O
S
!·U G S O;cDTID\Vcy<?KqFH<Í;Y[GqaHn<C<?GIKI;=GqFCOn#q<`G ;=n9¸aH>@hd[DHG <?KIF\<-;=n# D\GqaHn#q<`>
GqaHG C<?GIKq;YGqF*<?KqFH<<;=n#7n#I<d[@D\h#<#V=DHfl<?V!oI<?>g<J¸aH>g<\OkDEV=Vn#q<;2 % [DH>A<#< RH<?G"!¶_^;YGIX <
?% 2 % l2 % O+?% D\GIK.2 % IDSR\<n$q<[@D\h#<.ID\>g;=n\O\DHGIKdn#TJI[ªDEV=Vln#I<32 % [\IDSR\<)n#I<3[@D\h#<
ID\>g;bn(!
7<Gqa X-aHGl[An@>gJIX nån#I<3Kq<`[A;Y>A<`K%qaHh#aHF\<?GI< aHJl[,FH>@D+ %S %'( !Y¶<?n0fl<3n#q<UID\>g;bn
a3n$q<G^Jlh¿fC<?>daUl<`GIKq;YGqF=IDEV`y<`KqF\<`[#a3D7F\;=R\<`G VYD\fC< V;YG3S !,UA;Y[daTKlK9On#q<`G
ª<DHKIKnAaS ·DÍGqaqKq<X-a^GIGq<`X-nA<`KnAa§a^Gq<0a,n#I<[IDEV`y<?KqFH<?[?OqV=DHfl<?Vb<`K[gDs 1EOjD\GIKDHKIK
nªaIDEV`y<?KqFH<?[;l<`GIKq;YGqFp£>Aa^h n#q;Y[§GqaqKq<HO,V=DHfl<?Vb<`K 1 1D\GlK 1 1 1(!X03[dD
X-aHGl[A<e^^JI<?GIX <\O¿fl<`X-a^h<`[x< R\<`G"! Fa0Ox<UlDE;Y>ªn$q<WIDEV`y<?KqFH<?[_;bn$*;=Kq<`G^nA;YX DEVkVYD\fC< VY[ O
D\GIK X aHGIGq<`X-n0n$q<?h nAa&¸aH>@h aHGI<§<?KqFH<+!¶:åDH>gD\VbV=< V,<`KqF\<`[X DHG©fl<!DSRHa\;YKq<?KO¶JIGqV=<?[@[W¸a^>
[Aa^h< 1)n#I<?>g<D\>g<)aHGqV:nxaWl<`GIKq;YGqF[ID\Vcy<?KIF\<?[X;bn$dV=DHfl<?V1EO\DHGIK#n#q<`[A<DH>A<;YGIX ;=Kq<`G^n
nAa!n$q<[@D\h#<<`KqF\<(!CU Gn#q;Y[3X?D\[g<n#I<<ID\;=>;=[X-a^GIGq<?X nA<`Kf(n$q<¿F^D\KqFH< nKq;Y[$qV=DsH<?K;YG
B;=FHJl>A<; qO.q<?>g< 1 / !4r*VYD\fC< V=;YGqF!n$q<<`KqF\<`[a+å< RH<?>#F^D\KqFH< nD( I>ga(I>g;=D\nA<?V` BD\[
;=G*n#I<HhlFHJI>g<sGÃOª<Qa^fqngD\;=GD %qaHh#aHF\<?GI< aHJl[F^>gD( oS&%'([!
|`{
w
23S&%'(aID\[D\n h#aH[gnUb0%dGqaqKq<?[h#aH>g<Qn#IDHG1S*!
r2#4e4437<¿DHKIKq<`K*D\n h#aH[gn9bGqaqKq<0nAaÍX aH>@>A<`X-n)n#I<[ID\>g;=nA;=<?[?OlD\GIKD\n ha^[An %dF^D\KqFH< n@[
nAaÍDSR\aH;=KlIDH>gD\VbV=< V<`KqF\<`[ Ol<?D\X aHGI<9;bn$qÍGqaqKq<?[@!loTJI[n$q<nga\ngD\V¶GTJIh¿fC<?>a,GqaqKq<?[
D\KIKq<`K!;Y[ D\n)h#a^[AnWb0% !
0
2 1
G’ 0 1 2
0
jÆlÆ
óÈHÌS`\Ì`@åÊ=¥`ª@¥`~H~^ÃgW~HÌQÈT-¬Êb£ÃHÌ?Ã
" z
;{2$#3p0[o¸a^>Ín#I<ã[g;=h;qV=<ãng>@D+ < pTng<?GI[g;=aHG9Ox;bn*;Y[!<`D\[#ánga X q<`XÃZán#ID\n!aHGI<7X DHG
X-aHGl[An@>gJIX n3DHGTqa^haHF\<`Gq< a^JI[<-pqng<?GI[g;ba^G1¸a^>3DH>gfq;=ng>@D\>#KI< FH>g< < -TO9f(JI[g;YGqF*D[#C<?X ;chjX