Cake-Cutting is Not a Piece of Cake Malik Magdon

!"$#%$
&('*),+.-/&0'*132547658:9<;>=?'7+.)A@CBD4E;GFH'E;JIJKC;HLNM@O'76C2&PKO-Q-R'*+SUTCVXWH+Y;GMO6Z'*=?4Q47W>F>MQ[
\Jqm]N]N^Qd3_rb`brba<]Ncst_]N]HdR`DauUegevfisxw*hja<eg]Ncn>yE^3d3kEopn!a<]>zA`mdEl7r:a<nNoxopa<]NkEdEa<nN] ]
…G†Q‡gˆŠ‰*{v‹{}Œ|~ ŽŠa<yE‘ŠlR’}ab“E`<’Z]N]H”a}€3†QZ‹Š‹`<e}•ŠwR–v€E“R‚m—7˜ƒ ™*’Š{}‘›„*šœ{}•v~gE| ž›šAŸg‰v
” ¡£¢N¤N¥¦Q§g¤v¨© _ox`n}_gªv]H«œnNkEaba<opd3¬ oprja<yE]J­7ot®*oprbopevdegfU_¯n}_ªŠ]meg`°`<]NrbegkE`<nN]_gcevdE¬
n}e±_fiªŠa<kE]yErb]¹­7]H`<oxn}µOr!_]HrbªŠ`<e]¯]NdRa<n}a<yQ_gsxwR_dºa€7ev_g]}dEdQ_gsp­nGw?y/op¶5dEkE]¹f,egrb]H`<eg`c”¶EaGop_r_ga<opotdEnNegev]}d?dR­a<_]N¶*¶5dRw$eva}kE²C`<a°]}³J»Ry3rbk3e}]H]N·¸`<r:r!a<_¹opc”dEkE¬_Nrbw´kE]H`rb®g]H®g_g`<_gsprJk3spk3a<]Xe0]H_$r¼A­E¬vnHoxkEopµO®Ša<]H]H½d/`<]N^3dR^3opaj]Nop]NnN^QnH]N_]rJ`begega<r ff
a<oprjyE]ma<e¹nN_g­EªŠ]H]¾a<]>op`<dRca<e!otdErb]^5a<]Ny3nNox]m¿Qc]}­XotdE`Gop_cÁa<otk3egcÂrN²EÀJd*k3d3c¹]¶5efC]H`a<yEeg]¾fZnNckEeva<r:riai`<ot]}dR»Ra<k3]Hox`<`<]H]}r:­Xa<otdEa<e¯¬!­Eevop^5®*]No.d­7]D»Ra<k3yE]H]Dr:a<n}oteg_ªŠd3]r
fY·¾_gyEox`<]Hsxa<wRy3²Š]HzÃ`maopegrd3ª7]!dEn}e}_·¾d?d¹­Ea<eÁyQ_¶5ai]HabÄXa<]HÅÆ±Ç`}² spev¬j±ÈUnNkEa<rrbkEÉXnN]NrN€ŠyEe}·°]N®Š]>`}€voxaiotrdEegaª*d3e}·¾d
Ê/^5]H]°`bf,rbegy3`<e}c·0ra<fYyQ_g_ox` an}rb_gegªv`ba<]Hop«Ãd3­E¬op®*nNot_grbopdÁegd¶5]in}`<_]}d/­EkErbenN`b]}a}­¯² a<© eDegn}` _g_”ªv]H¬v«œ]NnNdEkE]Haba<`Gop_gd3s¬7nNËEst_gÌgrbÍ3r!Î e_f°sp¬vn}eg_`<ªŠoxa<]HyE«œnNcÂk7aba<a<y3otdE_¬ a
¶5__ststeg¬g¬gk3egegdQ`<`<oxox­a<a<y3y3egccdPrNr!a<€v¿Ey3·¾a!]Ny3ox`Xopopd*n>a<yXnHeev·jca<]Dy3^3opnNk7r_gaGsp¬g_s›]Na<Ïopd3ÐpevÑ]Hd3ÒH`G_gÓv_s°ÔœsiÏ Õ}nHnHÖGevs.Ï _Ó*crb×vrN^3Òg€›spÏ ]HÒN·¾Ú7Ø3yEox€HaAot·°wRnGy/²U]mÛDevsp]}¶Esp_gsjaG­E_a<r!opyEd”]$kE_grª*d$d3a<eÙ”e}·¾ÅÆnN±¸dPegdgn}spÜ:ev]H_¬jnHªŠa<]H±kE«œnN`<Èk7]Áspabe}a<a<·°y3otdE_]H¬ `a
]Ne®vfE]HnH`bevw cn}^Q_g_ªv`<]Hop«œrbnNevkEd3abrZa<op^5d3]H¬D`Z_gnNspkE¬gaZegop`<r›oxa<¶5y3evcÝkEdQopr­7]}Ï Ðp­ÁÑÒNÅÆÓvÞHÔÆß7Ï Õ}à¯Ö<áÏ ÓRÓv×vÔYÒgÐ âAÏ ßEÒNØ3Ñ}Ö<²>×vzÃfEß7opãRdXÑØR_vÒN­Eؾ­Eox_ga<spop¬vevedC`<€oxa<a<y3yEc]°d*rGÈ>k3€Nc¹a<yE¶5]N]Hd `
·j_st]J¬gegev`<¶7oxa<aGy3_gcopdrD_g_d`<]ٔÞ>ÅÆßE±¸à spáevÓv¬jÔY±Ð â:ßEÈÑ}spÖ<e}×g·°ßE]HãR`°ÑØR¶5ÒNevØ3k3² d3­Xevda<y3]md*k3c¹¶5]H`egfZnNkEa<rN²*ÛmspsQª*d3e}·¾d
Ê/a<y3]D_aX_spa<rbyEe¹]Hr:wPa<k3yQ­7_}w¹®Š]®v_c`<o.eg_`<a<]opevn}d3_riªŠeg]$fCa<]Ny3d*_g®Rd0w*«œf.]N`<®Š]N]H]`bwn}_ªŠega<]Hy3«Ã­E]>op`®*opk3rbrboteg]HdZ`}²£€ŠÊ/·¾yE]$]H`<nH]mevd3]}_gr:abnG`<ykEk3nHarb]Hk7`a<fYot]Hspox]NaAspw r
f,»Rk3k3d3ox`<n>]Na<r?otegd3ٔrÅÆfY±?e`Dæ}Ȕ·¾nNyEk7opn>a<yr_ga<e0dRw$^7_g`<spe*¬v­Eek3`<opnHa<]ºyEcärbkEn>ÅåyçotdEnN­EspopkQ®*­7otrbotdEopeg¬Xd3rNnN²megd*°a<opy3d*]Hk3rbeg]/k3_r¾`<_]´st¬ga<egyE`<]oxa<y3a<y3c]rGÈj¿3`<`<]Hr:a«
ª*_d3d3ege}a<·¾yEd]H` ¬g]N¬vd3]Hd3]H`G]H_`GsU_sispe}nN·°st_]Hrb`Dr¹¶5eevf¾kE_gdQsp­E¬vr¾e`<fYoxea<`Jy3c]Hd7r!®Rw*n}_«Æf,st`<sp]}]N­º] _èEspéE¬vÌgegêH`<ëboxa<ì”yEc_gsp¬vrNe² `<© opa<opdQyEc_gspsxrNwR€Z€3f,·jeg` ]¹·¾r:a<y3k3op­7nGyw
·j·¾]Joxa<yrby3^5e}·íevrboxa<a<yQop®Š_] aj®g]N®Š_g]Nspk3d]vox€EfZa<evy3dE]N]Ddopٔrja<ÅÆe ±¸rbspopevc¬°^3±?sxwXȾ¬gnNkQk7_a<`GrJ_g_dR`<a<]]N]Jd3]N]N_g]}nG­7y]}­$kErbopd?]H`a<_!yE]^Eot·°]HnNeg]J`<r:eaDf›n}n}__rbªŠ]v] ²
î?_d*w$egf›a<y3]]HÚ7opr:a<opd3¬n}_ªŠ]H«œnNk7aba<otdE¬X_st¬geg`<oxa<y3crm_`<]!^3yQ_rb]}­C²
ï ð3ñmò5óOô!õ¹ö¯÷›òOø<ômñ
¾ù WH47ú›ûW>F<[(;GMZ'*WH+.6O1PúCW>4EüO).ûg=;@;>KCLNMý'7;$LNMO47WHû25+,þ3+Y;>+.4E6@+,6OMOûgW>+.FH'76CLû´'7).),45L'RFH+.4E6@'76C2
W>4Q47=ä;>û),ûgLF>+,476@3MC'ŠþEû¹ü›ûûg6ºûÿQFHû6C;>+.þEû),[´;<FHKC25+,ûg2+.6ûgL476O4E=+YL;'76C2´13'*=?û8AF>MOûg47WH[ 7@
1 !MOûg6
@ 5@ O@ :Tù¾WH47ú›ûW>F<[0;>MC'*WH+.6C1úOWH47üC).ûg=?;X'7W>+Y;Gû?
4 åF>û6 +,6 ûgþ7ûgW>[52O'Š[PL4E=?úOK5F>+,6O
25+ UûWHû63FÁKC;GûgWH;¹L4E=ú›ûFHû Æ4EW F>MCû$;H'*=?ûWHûg;>47KOWNLûv;T m[QúO+YL'7)ûÿO'7=úC).ûv; 4 ¾;>KCLNM0úOWH47üO8
).ûg=?;?'7W>û <4Eü ;HLNMOûg2OKO).+,6O1 j;>MC'*WH+,6O10FHMOû(BJù FH+.=?û4 Á'(=$KO)tFH+.úCW>45Lûv;>;>47W$='7LNMO+,6O
û ;GMC'7W>+,6O1F>MCû”üC'*6Z2 !+,25F>M0
4 °'?6OûF D4EW>-/L4E6O6OûgLF>+,476 CûFHL7T MOûW>ûv;G4EKOWHLû¯FH4´ü›û;GMZ'*WHûg2
L'*6çü›ûþQ+.û Dûv2 'E;'PL'7-7û7@'76C2(F>MOû´úCW>4EüO).ûg= 4 !;>MC'*WH+.6C1;>KCLNMý'/W>ûv;G4EKOWNLû+,;”Lg'*),).ûv2
47W
T°9b6 F>MO+Y; J47WH-U@ Dû;GF>KC2O[ œ'*+,WLg'*-7û8:2O+.þQ+Y;G+,476 Jû´'*WHû
+.63F>ûgW>ûv;<FHûg2+.6 3KC'76EFH+Æ[Q+,6O1?MO4 MZ'*WN2'?L4E=?úOK5FH'*F>+,476C'7)£úOWH47üO),û= FHMO+Y;!+,;gT
9b6íFHMOû´4EW>+,17+,6C'*) Æ4EW>=$KO)Y'RF>+,476ç4
JFHMOûºLg'*-7û8:2O+.þQ+Y;G+,476íúOW>4EüO),û=@+,6EFHW>4525KZLûg2ç+,6çF>MCû
;üQ[S3FHû+,6OMC'7KC; A@ KZ;GûgWH; !+Y;>MF>4º;>MC'*WHû”'´Lg'*-7û+,60;>KCLNM0' 'Š[F>MC'*F¹ûv'7LNM
KC;GûgWi1EûFN;j'¯úZ4EWGFH+.4E6
4 5F>MOû!L'7-7ûFHMC'RF¾;>MOûm+Y;°L4E6EFHû63F !+.F>M œ'¹6QKO=ü›ûWj4 ›25û C6C+tFH+.4E6C;j4 L4763FHû63FJLg'*6ºü›ûXL476Z;G+Y25ûWHûg2@3'76C2 Jû !+,).)£25+Y;HLKC;H;¾FHMOûg;>ûÁ=4EW>û Æ47WH='*),).[?)Y'RF>ûgW T ¯;>ûWN;
=?'Š[ þR'*),KOû'(17+,þ7ûg6ýúO+.ûvLû´
4 !F>MOûL'7-7û´25+ UûWHû63F>),[7T O4EWûÿ5'7=?úO).ûE@i;>47=?ûºKZ;GûgWH;=?'Š[
úOW>û ÆûWFHMOûúC'7WGF”
4 DFHMOûºL'7-7û !+.F>MçF>MCû´LNMO45L47)Y'RFHûF>47úCúO+.6C1C@i'76C2 4*FHMOûWN;X='Š[(úOWHû ÆûgW
F>MOû¹úC'*W>F !+.F>MO4EK5FmFHMOû¹F>47úCúO+.6C1CT3S5KOúOú›4E;>û F>MCûWHû¹'*WHû CþEû¯KC;>ûWN;g@E'*6Z2).ûFH;JL4E6C;G+Y25ûgW¾F>MCû
;G+.F>KC'*F>+,476 ÆW>4E=FHMOû CWH;GFKC;GûgW ;DúZ4E+.63F4 þQ+.û T MOû¹WHûg;>KO).FD
4 i'Lg'*-7û8:2O+.þQ+Y;G+,476+Y;DF>MC'*F
ûþ7ûgW>[KZ;GûgWJ1EûFN;!'$ú›47W>F>+,4764 jF>MOûLg'*-7ûE@Q+.6úC'7WGFH+,LKO),'7WDKZ;GûgW Á1EûFN;J'ú›47W>F>+,476T ¹;GûgW !+.),)CLûgWGFN'*+,6O),[”6O4*Fü›û L4E6EFHû63F¾+ ZFHMOû!úZ4EWGFH+.4E6FHMC'RFm;>MOû17ûFH;°+Y; J47W>F>M Æ+,6MCûW47úC+.6O+,476
).ûv;>;¹F>MZ'*6 476Oû åFHM(FHMOû?þŠ'7).KCû œ+.6 MOûgW47úO+,6O+,476 ¯4 DF>MOû?û63FH+.WHûL'*-Eû7T£SQ4+.6 47WN25ûgW¯FH4
=?'7-7ûÁKC;>ûW L4E6EFHû63Fg@ JûX=KC;GF 17+,þ7ûÁMOûW '$ú›47W>F>+,476F>MC'*F!;>MOûL4E6C;>+,25ûgWH;DFH4ü›û J47W>F>M
476Oû åFHM(FHMOû?þŠ'7).KCû$
4 ¾F>MOûLg'*-7ûE@›'76C2(;>+,=+,)Y'*WH).[ Æ47WÁFHMOû?4*F>MCûWÁKC;GûgWH;gTU9 Jû
;GKCLgLûgûg2+.6 Z6C25+,6O1;>KCLNM'25+.þQ+Y;G+,476 Æ4EW !MO+YLNM?'7).)OF>MOû KZ;GûgWH;¾'7W>û!L4763F>ûg6EFv@ Jû ;>'Š[F>MC'*F
+tF +Y; '
T
&P47WHû Æ4EW>='7).),[7@ JûÁWHûúCW>ûv;Gûg6EFJF>MCû”L'*-EûÁ'E;!'*6/+.63FHûWHþŠ'7)
:T úO+.ûvLûX4 jF>MCû
L'*-Eû¯L4EW>WHûg;>ú›476C2O;¾F>4;G4E=ûÁ;GKCü58A+,63F>ûgW>þR'*)›4 £FHMO+Y;D+,63F>ûgW>þR'*)A@Q'*6C2´'$ú›47W>F>+,476´
4 L'*-Eû¯L'76
üZû”þQ+,û Jûg2'7;¯'´L4E).),ûgLF>+,4764 úO+,ûgLûg;gT MOû”KC;>ûW¯476O),[º-Q6O4 ;!MC4 FH4´þR'*),KOûúO+,ûgLûv;¯'E;
;Gú›ûgL+ Cûv2(üQ[0MCûWK5FH+.),+tF<[ ÆKO6CL}FH+.4E6@'76C2(MZ'7;Á6O4-Q6O4 !).ûv2517û?'*ü›47KOFÁFHMOû?K5F>+,),+tF<[ ÆKO6CL}8
F>+,476C;D4 £FHMOû¹47F>MOûgWmKC;>ûWN;gT MOûÁL'7-7û8b25+,þQ+,;>+.4E6?úOW>45Lûg;H; œ'76º'7;H;>+.1E6O=?û63FD
4 úZ4EWGFH+.4E6C;FH4
KC;GûgWH; £+Y;iF>4ÁüZûJû UûgLF>ûv2üQ['¹;>KOú›ûWHKC;>ûW !MO4Á+.6C+tFH+,'7).),[MC'7;i6O4Á-Q6O4 !).ûv2517ûJ'*ü›47K5FjF>MCû
K5F>+,).+.F<[ ÆKO6CL}FH+.4E6C;¾
4 UF>MOû KZ;GûgWH;gT û úZ4E+.63Fm4EK5F¾FHMC'RF¾FHMO+Y;¾='Š[$'7úOúZûv'*W°FH425+,þ7ûWH17û ÆWH47=
F>MOû”'ELLûgú5F>ûv2º=?ûg6EFN'*),+tF<[º+.6F>MOû Zû)Y2£@ !MOûgW>ûÁúOWH4*F>45L47)Y;J'7W>ûXþQ+,û Jûg2/'7;;Gûg) å8:û6 Æ47WNL+,6O1
úO)Y'Š[7ûgWH;¾'7W>û¹'725þQ+Y;Gûv2'7;mF>4MC4 ÇFHMOû[;>MO47KC),2´LK5Fg@5'76C2´'*WHû 1EKC'*WN'*63F>ûgûg2$F>MZ'RFD+ FHMOû[
LK5F¯'ELL4EWH2O+.6O1$F>4?FHMOû”'72Oþ3+YLûE@QF>MOûg6F>MOûWHûg;>KO).F !+.),)ü›û”û 3KO+.FH'7üO).ûÁFH4?F>MOûg=/T MOû J'Š[
;GKCLNM '*),174EW>+.F>MC=?;$KC;>KC'*),),[¸úOWH4QLûûv2¸+Y;F>MC'*FFHMOûPúO)Y'Š[7ûgWH;$='*-7ûLKOFH;g@¾'*6C2 ;G4E=?ûMO4 üC'7;>ûg24E6?F>MOûv;GûXLKOFH;g@Eú›47W>F>+,476C;D'*WHû¯'7;H;>+.1E6Oûg2FH4”F>MCû¹úO)Y'Š[7ûgWH;gTESQ4E=?û¹L4E=?úOK5F>+,6O1$üZ4525[
6Oûûv2O;JF>4?254F>MO+Y;!'7;H;>+.1E6O=?û63Fg@5'*6Z2´ú›ûW Æ47WH= F>MOûX6OûvLûv;>;H'*WH[L'*)YLKC),'*F>+,476C;J;G4FHMC'RFF>MCû
W>ûv;GKO).F>+,6O1'7;H;G+,176C=ûg63FÁ+Y;Á17KC'7WH'76EFHûûv2F>4ü›ûû 3KO+tFN'*üO),û$F>4P'*),)jF>MOû?úO)Y'Š[7ûgWH; ÆúOWH4RþQ+,2Oûg2
F>MC'*FF>MCû[ Æ47),).4 Jûg2íF>MCû'72Oþ3+YLû }Ti9:F+,;ûÿO'7LF>),[(FHMO+Y;L4E=?úOK5F>+,6O10ü›4525[ F>MC'*F Jû´û658
þ3+Y;>+.4E6 'E;F>MOû0;>KOú›ûWHKC;GûgWg@ü›ûgLg'*KC;>û Dû J47KC),2ÇKO).F>+,=?'*F>ûg).[Ç).+,-7û/F>4 3KC'763F>+ Æ[ '*),)!F>MCû
L47=?úOKOFH'RFH+.4E6´FHMC'RFFH'7-7ûv;DúC),'ELûÁ+.6F>MOûLg'*-7ûX25+,þQ+,;>+.4E6ºúOWH45Lûv;>;gTQ9b64EWH25ûgWmFH4L476Z;<FHW>KCLF
'*6í'7úOúOWH47úOWH+Y'RF>û$25+.þQ+Y;G+,476@ZFHMOû?;GKOú›ûWHKC;>ûWÁ='Š[/WHû 3KOûv;<FXKC;>ûWN; FH4LK5FúO+.ûvLûv;¹+,63F>4WH'*8
F>+,4E;FHMC'RFF>MOû/;GKOú›ûWHKC;>ûW”='Š[ ;Gú›ûgL+ Æ[ETjI'7;>ûg2 4E6çF>MOû´+,6 Æ4EW>='RFH+.4E6ç).ûv'*WH6Oûg2 ÆWH47= '
63KC=ü›ûWÁ4 ¾;GKZLNM(LK5FN;@ZF>MCû$;>KOúZûgW>KZ;GûgW¯=KZ;<FÁ6O4 %=?'7-7û'76('*úCúOW>4EúOWH+,'*F>û”'7;H;>+.1E6O=?û63F
4 °úZ4EWGFH+.4E6C;@Z;GKCLNM/FHMC'RF¯ûv'7LNM/KC;>ûW +Y; L4E63F>û63FvT ;>+.=?úO),ûûÿO'*=?úO),û !+,).)i+.),).KZ;<FHWH'*F>ûXF>MCû
úOW>45Lûg;H;TUSQKOúOú›4E;>ûF>MZ'RF¯F J4´KC;>ûWN; !+Y;GM0F>4º;>MC'*WHûFHMOû$Lg'*-7ûET MOû;GKOú›ûWHKC;>ûWÁL'*60'E;G476Oû
4 iFHMOû”KC;>ûWN;JF>4´LK5F F>MCûû63F>+,W>û”Lg'*-EûÁ+,63F>4?F J4û 3KC'7)£úC'*W>FH;gT MOû”;>KOú›ûWHKC;GûgW 6O4 '7;>-Q;JFHMOû4*FHMOûW!KZ;GûgW!F>4?ûþR'7).KC'*F>ûXFHMOûXF D4?WHûg;>KO).F>+,6O1?úC'*W>FH;gT MOû”;>ûgL4E6C2/KC;>ûW!+Y;JF>MOûg6
'7;H;G+,176Oûv2PFHMOû?úC'*W>F¹FHMC'RF;>MOûMC'72íMO+,17MOûgWXþŠ'7).KCû Æ4EWg@£'76C20FHMOû CWN;<FKC;>ûWX17ûFH;ÁFHMOû?W>û8
=?'7+.6C+.6O1úC'7WGFvT MO+,; Jû),)-Q6O4 !6í2O+.þQ+Y;G+,476 ;>LNMOûg=?û7@;>47=?ûFH+.=?ûg;¹FHûWH=ûv2 >9¯LKOFg@[E47K
LNMO4Q4E;>û O@3L),ûg'7W>),[$),ûg'ŠþEûg;müZ47F>MºKZ;GûgWH;DüZûg).+,ûþQ+,6O1”FHMOû[MZ'Šþ7û¯'*FJ),ûg'E;<FJMC'*) F>MCûÁLg'*-7ûE@E'76C2
+tFJ+,;mF>MQKC;J'”;>KCLLûg;H; ÆKO) œ'*+,WD2O+.þQ+Y;G+,476º'7).1E47WH+tFHMO=T OWH47=FHMO+,;DûÿO'7=úC).û Jû¹;>ûû F>MC'*FD476Cû
!"$#
&%
('
*)
+
-,
.)
/)
#
('
1)
435
('
0+
2+
6)
7)
98 :6;
=<1>
"$?
$@
A)
B'
+
DC
F
E
9)
1'
G+
H
&@
1)
JI
K
,
LK5F!;GK Lûg;mF>4úZûgW Æ4EW>= œ'7+.W25+,þ3+Y;>+.4E6 Æ47WDFD4$KC;>ûWN;T 6º+,63F>ûgW>ûv;<FH+.6O1 3KOûg;GF>+,476FH4'E;G,+ ; !MC'*Fm+,;F>MOû =?+,6O+,=KO=6QKO=ü›ûW¾4
ULK5FH;mW>û 3KO+.WHûg2F>4ú›ûWÆ47WH=' œ'7+.WD25+.þQ+Y;G+,476 !MOûg6
F>MOûgW>û'*WHû KZ;GûgWH;gT
MOûL'7-7û8:25+,þQ+,;>+,476úOWH47üO),û= MC'7;¯üZûgû60ûÿQF>û6Z;G+,þ7ûg).[;<FHKC25+,ûg2P+,6PFHMOû”),+tFHûWN'RF>KCW>û C@
@ C@ C@ @ AT CW>4E= 'XL47=?úOKOFH'RFH+.4E6C'*)5ú›47+,63F¾4›þ3+,û@
Dû '*63F°F>4X=?+.6O+,=?+gû!F>MCû
63KC=ü›ûW4 !LKOFH;6Oûgûg25ûv2£@;>+.6ZLûF>MO+Y;),ûg'E2O;ÁF>40';>=?'7).),ûW6QKO=$üZûgW4 !L4E=úCK5FH'*F>+,476C'7)
;<FHûúC;ú›ûW Æ47WH=?ûg2üQ[”FHMOû '*),174EW>+.F>MO=T*&P43;<F¾
4 ZFHMOû¯'7).1E47WH+tFHMO=;°úOW>4EúZ43;Gûv2+,6F>MOû¯).+.F>ûgWH'*8
F>KOWHû WHû 3KO+,W>
û LK5FN; Æ4EW KC;>ûWN; Ã;Gûgû Æ47WmûÿO'*=?úO),û ),174EW>+.F>MC= @QSQûvL}FH+.4E6 5T }@
!MO+.),ûFHMOû´ü›ûg;GF”-36C4 !6çLg'*-Eû8bLK5F>F>+,6O1P'*),1747WH+.F>MO=@ !MO+YLNMç+,;üC'7;>ûg2 4E6ç'P2O+.þQ+Y25û8b'*6C258
L476 EKCûW¾úOWH45Lûv25KOWHû7@7KZ;Gûv; ),471 LKOFH; œ;>ûû Æ4EWmûÿO'7=úC).û ¯).1E47WH+tFHMO= º@QS5ûgL}FH+.4E6
5T }Ti&P47WHûûÿO'*=?úO),ûg;$L'76 ü›û Æ4EKO6C2ç+,6 Z@ AT9:F+,;6O4*F$-36C4 !6 !MCûF>MCûW4E6Oû´L'76
254üZûFGFHûW¹F>MC'76 ),471 TC9b6 œ'EL}Fg@Z+tF¹+,; L476 <ûvL}FHKOW>ûv2/F>MC'*F F>MCûWHû+,;¯6O4´'*),174EW>+.F>MO=
F>MC'*FÁKC;>ûg; %).4E1 ¹LK5FN;¹+,60FHMOû D4EWH;GF¹L'E;GûET MCû$úOWH47üC).ûg= 4 m25ûF>ûWH=?+.6C+.6O1 !MC'*F
F>MOû¹=+,6O+,=KO= 6QKO=$üZûgWm
4 LK5FN;mWHû 3KO+,W>ûv2F>4”1EKC'*WN'*63FHûû ' œ'7+.WJL'7-7û8b25+,þQ+,;>+.4E6;Gûgû=;FH4
üZû”'þ7ûgW>[ºMC'*WN2º4E6Oû7T û 3KO4*FHû ÆW>4E
= !47ü›ûW>FH;>476'*6Z2 ûüCü Z@ZBDMC'*úOF>ûW OT MOûúCW>4EüO).ûg= 4 25ûF>ûgW>=?+,6O+.6C1P+.6ý1Eû6OûgWH'7)°F>MOû Æû Dûv;<F”6QKO=$üZûgW”4 !LKOFH;”WHû8
3KO+.WHûg2 Æ4EW œ'*+,Wm25+,þ3+Y;>+.4E6;>ûûg=?;F>4XüZû¹'¹þEûWH[”MC'7WH2$476OûETOTTgT û!MC'Šþ7û),4E;GFüZûFH;
üZû Æ47WHû7@EüOK5F+ Jû JûWHû¯'7;>-7ûv2FH4”1E' û +,63F>4FHMOû¹LW>[5;GFH'7)CüC'7).)A
@ Jû J47KO)Y2?úO)Y'7Lû
47KOW=?4E6Oû[ '71E'7+.6C;GF C6C25+,6O1¸'ç;GKCüC;<FN'*63F>+Y'*)+,=?úOW>4RþEû=?û63F?476 F>MCû %),471
üZ4EKO6C2£T
iL4EKOWH;>û7@Q' Dûg).)U-Q6O4 !6L4763F>+,6QKO47KZ;múOWH4*FH45L47)ZF>MZ'RF!KC;>ûg; XLK5FN;J+,;DF>MCûÁ=?4RþQ+,6O1
-36C+ ÆûJ'*),1747WH+.F>MO= œ;>ûûDSQûvL}FH+.4E6 5T }TŠBDûW>FH'*+,6O),[ LK5FH;iL'*6C6O4*Fü›ûmü›ûg'*F>ûg6@MO4 JûþEûWv@
;GKCLNML4E6EFH+.6QKO4EKC;j'*),1747WH+.F>MO=;'7W>ûDûÿOL),KC25ûv2 ÆWH47= 4EKOWiúCW>ûv;Gûg6EF°25+Y;>LKC;>;>+,476T KOW°W>ûv;GKC)tFN;
'*úOúO),[´4E6O).[ºF>425+Y;>LW>ûF>ûXúOWH4*FH4QL47)Y;JûÿOLûgú5F !MOû6ûÿQúC).+YL+.F>),[º;GFH'RFHûg2/4*FHMOûW !+Y;GûET
KOWº='*+,6ÂWHûg;>KO).F+Y;´FHMC'RF;G4EWGFH+.6O1ÇL'*6 üZû W>ûv25KCLûg2 F>4 L'7-7û8bLKOFGF>+,6O
1 œ'7+.W
L'*-Eû8bLK5F>F>+,6O1'7).1E47WH+tFHMO= L'76(ü›ûL476Qþ7ûgWGFHûg2FH4/'760û 3KO+,þR'*),û63FÁ4E6Oû$F>MC'*FXLg'*6í;>!47W>FÁ'76
'*WHüO+tFHWH'7W>[$;Gû EKCû6CLû 4 25+Y;GF>+,6CL}FJúZ43;G+.F>+,þ7û +,63F>ûg17ûWN;gT OKOW>F>MCûWv@*F>MC+,;D6Oû Ý'7).1E47WH+tFHMO= KC;>ûg;
6O4=?47WHû¯LK5FH; Æ4EWD'*6Q[;>ûFm
4 KC;>ûWN; jFHMC'*6´F>MOûÁ47WH+.1E+.6Z'*)O4E6Oû¯25+Y2£T MOûWHû Æ4EW>ûE@7L'7-7û8
LK5F>F>+,6O1í;>MO47KC),2çü›û'*F).ûv'7;GF$'7;MC'*WN2ý'7;$;G4EWGFH+.6C1CT MOûMOûg'7WGF$4 F>MO+Y;$W>ûv25KCL}FH+.4E6ý).+,ûg;
+.6 '0=ûvLNMC'*6C+,;>= Æ47W)Y'*ü›û),+,6O1PF>MCûºúO+,ûgLûg;$4 F>MOûL'7-7ûETjBD4763F>+,6QKO+,6O1C@ Dû/25û C6Cû´F>MCû
L)Y'7;H;m
4 " #%$'&)(*+" ,-." (0/1&" &)2L'7-7û8bLKOFGF>+,6O1'*),1747WH+.F>MO=;J'7;mF>MO43;Gû Æ47W !MO+YLNM´FHMOûXûÿQF>WN'L4E;GF
4 ¾)Y'*ü›û),+.6O1º+,;¯).+,6Oûg'7W¯+,6PF>MCû6QKO=ü›ûW¹4 ¾LKOFH;g4T 3D;>;>û63F>+Y'*),),[7@5FHMOû$L476Qþ7ûgWGFHûg2'*),174EW>+.F>MO=
+,;¹'7;!5û L+.ûg63FÁ'7;!F>MOû”4EW>+,17+,6C'7)476OûET C47W!FHMOû$L),'E;>;!
4 6" #%$&(1*7" ,)-8" (0/1&1" &2´'*),174EW>+.F>MC=?;g@ Jû
47ü5FN'*+,6 '76 9 %),471 ¯),4 JûWXüZ4EKO6C2í476íF>MOûg+.W”L47=?úOK5FN'RFH+.4E6C'*)L4E=?úO).ûÿ5+tF<[ET 447KCW
-36C4 !).ûv2517ûE@Q'7).)›FHMOûX-36C4 !6 œ'7+.W!L'7-7û8:LK5FGFH+.6O1?'*),174EW>+.F>MC=?; OF +,63F>4$F>MO+Y;17ûg6OûWN'*)£L)Y'7;H;g@
!MO+,LNM ).ûv'72O;KZ;”FH4(L4E6 <ûgLF>KOWHûF>MZ'RF$ûgþ7ûgW>[ œ'*+,WLg'*-7û8:LK5FGFH+.6C10'*),1747WH+.F>MO= +,; " #%$&(1*7" ," (0/1&1" &)2Z@'L4E6 <ûgLF>KOWHûF>MC'*
F DûMC'ŠþEû$6C4*F[7ûF;GûFGF>),ûg2T OWH47= FHMOûúOWN'7LF>+YL'*)°ú›47+,63F”4 þ3+,û @CF>MOûL4E=úCK5FH'*F>+,476C'7)ú›4 DûgW 4 FHMOû$;>KOú›ûWHKC;GûgW¯L'76PüZû'),+.=?+.FH'RFH+.4E6@U'*6C20;>4 Jû
+.63F>WH4525KCLû$FHMOû´L)Y'7;H;Á4 !'*),174EW>+.F>MO=;¹F>MZ'RF”'*),).4 F>MOû´;>KOú›ûWKC;>ûW”'/üOKC2O17ûFv@+,6(FHûWH=?;
4 L47=?úOKOFH'RFH+.4E6@ Æ4EW´ûþEûWH[ LK5FFHMC'RF+,;='E25û7T MQKC;g@FHMOû0L4E=úCK5FH'*F>+,476 F>MC'*F´F>MCû
;GKOú›ûWHKC;>ûWÁúZûgW Æ4EW>=;¹L'*6í476O),[17WH4 ),+,6Oûg'7W>),[ !+tFHM0F>MCû$6QKO=$üZûgW¹
4 DLK5FN;¯ú›ûW Æ47WH=?ûg2£T
SQKCLNM '7).1E47WH+tFHMO=; JûíF>ûWH;
= :=<?>A@B(1*C# D<?$)-8/1<E0$'2F&)2ZT ¯).)XFHMOûç-36C4 !6 '*),174EW>+.F>MO=;/'*WHû
:=<>@'(*G# D.<$-./1<?EF$B2F&)2ZT*9 +,6'72C25+tFH+.4E6F>4$üZûg+.6C
1 " #%$'&)(*+" ,-8" (0/1&1" &)2Z@*FHMOûX'*),1747WH+.F>MO=+Y;D'7),;>4
:=<>@'(*G# D.<$-./1<?EF$B2F&)2Z@RF>MOûg6 Jû¹4Eü5FH'7+.6'*
6 9 ),471 ¾),4 JûWmü›47KC6C2´4E6F>MOûÁ6QKO=ü›ûW
4 LK5FN;!W>û 3KO+.WHûg2+,6F>MOû J47WN;<F Lg'7;>û7T MQKC;FHMOûL4E6 <ûgLF>KOWHûX4 H!47ü›ûW>FH;>476'*6Z2 ûüCü
@
1
%
!
F
!
,
7'%
G+
%
2
+
4'
7'%
%
+
B@
'
!
7'%
% +
'%
%
+
B@
!
+
E
E
!
I
E
1)
(%
%
K
%
'
+
%
,
'
%
+
*)
2,
7'%
%
+
)
,
@
7'%
%
+
E
+,;¹F>WHKOû !+tFHMO+,60F>MCûL),'E;>;¹4 " #%$'&)(*7" ,)-8" (0/1&1" &2 :=<?>A@B(1*C# D<?$)-8/1<E0$'2F&)2º'*),1747WH+.F>MO=;gTi4
47KOW-36C4 !).ûv2517ûE@¾F>MC+,;/L)Y'7;H;´+,6CL),KC25ûv;'*),) F>MCûí-Q6O4 !6Â'7).1E47WH+tFHMO=;@ !MO+,LNM =?'7-7ûv;´+.F
'0þ7ûgW>[í+.63FHûWHûg;GF>+,6O1í'76C2ç6C'RFHKOWN'*)L)Y'7;H;”4¯Lg'*-Eû8bLK5F>F>+,6O10'*),174EW>+.F>MO=;gT MOûv;Gû/'*WHûF>MCû
CWH;GF >MC'*WN256Oûv;>; W>ûv;GKC)tFN; Æ47W'P17ûg6OûWN'*)DL)Y'7;H;”4 Lg'*-7û8:LK5FGFH+.6C1('*),174EW>+.F>MO=;XFHMC'RF?'*WHû
'*úOúO),+YL'*üC).ûÁF>4´'1Eû6OûgWH'7)›6QKO=$üZûgW!4 °KC;>ûWN;T
íû´'7),;>4PúOWH4Rþ3+Y25û?),4 DûgWüZ4EKO6C2O; Æ47W;>47=?û?F<[QúZûv;4 Lg'*-Eû8b25+.þQ+Y;G+,476T
L'*-Eû8b25+,þ3+Y;>+.4E6+,;Jû6QþQ[38 ÆWHûû¹+ jûg'ELNM´KC;>ûWJüZûg).+,ûþEûg;;GMCû¹MC'E;D'*FJ),ûg'E;<F!'7;D)Y'*WH17û¹'úZ4EWGFH+.4E6
Æ+,6MOûgWD4EúO+,6O+.4E6 D'7;Dûþ7ûgW>[?47F>MOûgWJKZ;GûgWg@3+ÃT û7T,@Q6O4KC;GûgWD+Y;Jû6QþQ+.4EKC;D4 i'76O4*FHMOûWKC;>ûWvT MCû
FD4íúZûgWH;>476 œ'7+.W25+,þQ+,;>+,476 ;HLNMOû=?û/úOWHûg;>û63F>ûv2ýûg'7W>),+.ûgW+Y;?'*)Y;G4 '*6 ûg6Qþ3[38 ÆW>ûgûº25+,þQ+,;>+.4E6
;>LNMOûg=?û7T FHMOûW”ûg6Qþ3[38 ÆW>ûgû'*),1747WH+.F>MO=; Æ4EW”=?47WHûKZ;GûgWH;”Lg'*6çü›û Æ47KO6Z2ç+.6 O@ Z@ O@ E@
:T39:FD+Y;m-Q6O4 !6FHMC'RF Æ47W'*6Q[?;GûFD
4 K5F>+,),+tF<[ ÆKO6ZL}F>+,476Z;¾FHMOûWHû¹'7W>û¹û6QþQ[E8 ÆWHûû¯;>47),K5F>+,476Z;
:T ¯4 Dûgþ7ûgWg@7F>MOûgW>ûX'*WHû¹4E6O),[´' Æû Âû6QþQ[38 ÆWHûûX'*),174EW>+.F>MO=;D-Q6O4 !6´+,6ºFHMOûX).+.F>ûgWH'*F>KOWHû
Æ47W "KZ;GûgWH; :T !ûg=?'7W>-R'7üO).[E@£'*),)°F>MOûv;Gû'*),174EW>+.F>MC=?;Á'*WHû @£+,6(FHMOû´;>û6C;>û
F>MC'*FºF>MCûWHû(ûÿ5+Y;<F/K5F>+,),+tF<[ ÆKO6ZL}F>+,476Z; Æ4EW !MO+YLNMÝFHMOû(6QKO=$üZûgW
4 LK5FN;+Y; C6O+.F>û7@JüOK5F
'*WHüO+tFHWH'7W>+,),[$)Y'*WH17ûET ¯1E'*+,6@Q6O4).4 JûWJü›47KO6C2C;476´FHMOûÁ63KC=ü›ûW!LK5FN;W>û 3KO+.WHûg2 Æ47Wû6QþQ[38
ÆW>ûgûX2O+.þQ+Y;G+,476ûÿ5+Y;<FvT íû1E+.þEûÁF>MOû CWN;GF!;>KCLNM/).4 JûWü›47KO6Z2O; Æ47WF J4?þR'*WH+,'*F>+,476C;J4 jF>MCû
û6QþQ[E8 ÆWHûû°úOWH47üO),û=@'76C2X47KOW£ü›47KC6C2O;'7W>û¾'7úOúO),+,Lg'*üO),ûjF>4 ü›4*FHM”25+Y;>LW>ûF>û¾'*6Z2ÁL4763F>+,6QKO47KZ;
'*),1747WH+.F>MO=;gT 25+.þQ+Y;G+,476+Y;
@*+ ›ûv'7LNMKC;>ûWü›û),+.ûgþ7ûg;m;GMOûMC'E; L'*-Eû
F>MC'76íFHMOû4*FHMOûWXKC;>ûWN;g@£+ÃT û7T,@ûg'ELNMíKZ;G)ûgWÁü›û),+,ûþ7ûv;ÁF>MOû47F>MOûgWKC;>ûWN; !+.),)¾ü›ûûg6Qþ3+,47KZ;X4 MOûWvT û;GMO4 FHMC'RF 9 LK5FH;'*WHûºWHû 3KO+,W>ûv2ç+.6 F>MOû J47WN;<F$Lg'7;>û´FH4(17KZ'*WN'*63F>ûgû´'
;<FHW>4E6O1Pû6QþQ[38 ÆWHûû25+,þQ+,;>+.4E6 !MOû6ý+.Fûÿ5+Y;<FN;T ä25+,þQ+,;>+.4E6ç+,;
@+ !ûþ7ûgW>[
KC;GûgWüZûg).+,ûþEûg;?FHMC'RF´ûgþ7ûgW>[¸47F>MOûgWKC;>ûW´MC'E;'RF´=?4E;GFº' œ'*+,Wº;> MC'*WHû4 )ÁF>MOû0Lg'*-7û Ã;Gûgû
Æ47W?ûÿO'*=?úO),û O@ AT ûP;GMO4 FHMC'R
F 9 LK5FN;?'*WHûWHû 3KO+,W>ûv2¸+,6 FHMOû D4EWH;GF?Lg'7;>û
F>417KZ'*WN'*63F>ûgûÁ;>KOú›ûW!û6QþQ[38 ÆWHûû25+,þQ+,;>+,476 !MOû6+.F ûÿ5+,;GFH;gT MOûv;GûX),4 DûgW!üZ4EKO6C2O; 17+,þ7ûX'
CWH;GFûÿQúC),'76C'RFH+.4E6 4 !M3[íF>MCû´úOWH47üO),û= 4 !û6QþQ[38 ÆWHûû´Lg'*-7û8:2O+.þQ+Y;G+,476 +,;MC'*WN25ûgWF>MC'76
œ'*+,W L'*-Eû8b25+,þ3+Y;>+.4E6 Æ47W!1Eû6OûgWH'7) ýT
MOû”)Y'7;GF¹L)Y'7;H; 4 mL'*-Eû8bLK5F>F>+,6O1´'*),174EW>+.F>MC=?;!F>MC'*F JûL4E6C;G+Y25ûgW¹'*WHû”L'7).),ûg2
'*),1747WH+.F>MO=;gTO9b60úOMC'E;Gûv2'*),1747WH+.F>MO=;g@5F>MOû$ûÿ5ûgLK5F>+,476P
4 °F>MOû'*),1747WH+.F>MO= +,;¯úC'*W>F>+.F>+,
476Oûv2
+.63F>4¯úOMC'7;>ûg;gT JFjûg'ELNMÁúCMC'7;>ûm'*),)*FHMOû H'7LF>+,þ7û JKC;>ûWN;='7-7û¾' LK5FgT JFFHMOûmûg6C2X4 C'!úCMC'7;>û
KC;GûgWH;”=?'Š[íüZû'7;H;G+,176Oûv2 úZ4EWGFH+.4E6C;@+.6 !MO+YLNM¸L'E;GûFHMOû[ üZûvL4E=û G+,6C'7LF>+,þ7û Æ4EW”F>MCû
W>ûg=?'7+.6Z25ûW
4 5F>MOûJ'*),174EW>+.F>MO=T&('*6Q[¹-Q6O4 !6”Lg'*-Eû8bLK5F>F>+,6O1 '*),174EW>+.F>MO=;'7W>ûúCMC'7;>ûg2£T û
;GMO4 FHMC'RFFHMOûWHûD'7W>ûKOF>+,).+.F<[ ÆKO6CL}FH+.4E6C; Æ47W !MC+,LNM úOMC'7;>ûg2Lg'*-Eû8bLK5F>F>+,6O1 '*),174EW>+.F>MO=
W>û EKC+.WHûg; 9 %).4E1 ¾LK5FH;mF>4$17KC'7WH'763F>ûû!ûgþ7ûgW>[$KC;G?ûgWD'úZ4EWGFH+.4E6?F>MOûg[ü›û),+,ûþ7û¯F>4$üZû¹4 úZ43;G+.F>+,þ7ûþR'*),KOû Ã'=KCLNM Jûg'7-7ûWL476C2O+tFH+.4E6¹FHMC'*6 œ'7+.W }T O47Wi;GKCLNM'7).1E47WH+tFHMO=;@'E;>;>+,176O+,6O1
úZ43;G+.F>+,þ7ûÁúZ4EWGFH+.4E6C;J'*),476Oû¹+,;JMC'7WH2£@5;>4WHû 3KO+,W>+,6O1F>MOûÁúZ4EWGFH+.4E6C;DF>4?'*)Y;G4$üZû œ'*+,W47WJû6QþQ[38
ÆW>ûgûÁLg'*6º4E6O),[=?'7-7û¹F>MOûÁúOWH47üO),û= MZ'*WN25ûWvTQ9b6ºúC'7WGFH+,LKO),'7Wg@ ),174EW>+.F>MC= Ã;GûgûXS5ûgL}FH+.4E6
5T }@' Jû),)-Q6O4 !6ç25+.þQ+Y25û´'*6Z2íL476 3KOûgW”'*),1747WH+.F>MO= +Y;XúOMC'E;Gûv2£@'76C2(4Eü5FH'7+.6Z;' œ'7+.W
25+.þQ+Y;G+,476(KC;G+,6O1 %),471 ¹LKOFH;gT MOûgW>û Æ47WHûF>MC+,;X'*),174EW>+.F>MC= +Y;¯4Eú5F>+,='*)°'*=?476C1´F>MCû
L)Y'7;H;4 iúCMC'7;>ûg2/'*),174EW>+.F>MO=; + JûL47=?úC'7W>û¹F>4´'7).1E47WH+tFHMO=;DF>MC'*F=?ûgW>ûg).[º'E;>;>+,176
úZ43;G+.F>+,þ7ûþR'*),KOûú›47W>F>+,476C;gT MOû$+Y;H;GKOû4 J25ûFHûWH=+,6O+,6O1F>MOû='Rÿ5+.=$KO=þR'*),KOûFHMC'RFL'76
üZû”1EKC'*WN'*63FHûûg2´F>4ûgþ7ûWH[´KC;>ûW !+.F>M LK5FH; MC'7;ü›ûûg60;<FHKC25+,ûg2+,6FHMOû),+tFHûWN'RF>KCW>û Z@
BDMC'*ú5FHûW :T û¯MZ'Šþ7û!FHMC'RF Æ47WDúOMC'7;>ûg2º'*),1747WH+.F>MO=;g@*F>MC+,;D='Rÿ5+.=$KO=þR'*),KOû¯+Y; gûWH4 Æ4EW
%),471 }T
MOûD4EK5F>),+,6OûD
4 5F>MOûWHû='*+,6C25ûgWi
4 5F>MOûúC'7úZûgWi+Y;°'7; Æ47),).4 ;gTv9b6”F>MCûJ6CûÿQF°;>ûgLF>+,476@ Jû
úOW>ûv;Gûg63FJFHMOû Æ47WH='*)25û C6O+.F>+,476C; 4 jF>MOû”Lg'*-7û8:2O+.þQ+Y;G+,476=4525ûg)£F>MZ'RF JûÁKZ;GûE@O'*6C2 !MC'*F
)
I
K
E
& 8 : '
@
2+
!
!
!
%
!
@
)
E
9)
G@
;: 1*2 8 :
DE
1'%
G+
: @
!
E
7'%
&:
G+
*2 8 : '
)
=%
$*
@
I
K
G@
I
K
E
1'%
%
+
B'
;+ ,
@
+
'
&
7'%
%
+
G
!
>
E
'%
%
+
)
L476Z;<FH+tFHK5F>ûv;'!L'7-7û8:LK5FGFH+.6O1!'7).1E47WH+tFHMO=@ Æ 47),).4 J ûg2¹üQ[¹;>47=?ûûÿO'7=úC).û¾'7).1E47WH+tFHMO=;T¯ûÿQFg@
Dû”úCW>ûv;Gûg6EF¯F>MOû$).4 JûW!ü›47KO6Z2O;T›9b6íSQûvL}FH+.4E6 Dû+.63F>WH4525KCLû”úOMC'E;Gûv2P'*),1747WH+.F>MO=; '76C2
17+,þ7ûº),4 J ûWü›47KC6C2O; Æ 47WF>MCû6QKO=$üZûgW4
¯ LK5FN;6Oûûv25ûg2£TmS5ûgL}FH+.4E6H!ç25+,;HLKZ;>;>ûg;$),'7üZûg).ûv2
'*),1747WH+.F>MO=;m'76C2?FHMOûÁL476O6CûgL}FH+.4E6F>4;G4EWGFH+.6C1CT39b6SQûgLF>+,476 J û¯17+,þ7û F>MOûÁ).4 J ûWDüZ4EKO6C2O;
Æ47W!û6QþQ[38 Æ WHûû25+,þQ+,;>+,476@O'76C2 )C6C'*),),[7@J û=?'7-7û;>47=?ûL476ZL),KC25+,6O1?W>ûg=?'7W>-5;J+,6PS5ûgL}FH+.4E6
ûWHûÆ ûW¯F>4FHMOû'ELL4E=?úC'*6Q[Q+.6C1?F>ûgLNMC6O+,Lg'*)WHûú›47W>F "
T¹KOûFH4;>úC'7Lû”L4E6C;<FHWH'7+.63FN;@ J
Æ47W!=?4E;GF 4i F>MOûúOWH4Q4œ ;gT
íó Gø øGñ °óCø
!#"$#%&#'(
íû”25ûg6O4*FHûXF>MOû”Lg'*-EûÁ'E;F>MOû+,63F>ûgW>þR'*)
:T 4iF>MOû”Lg'*-EûÁ+Y; '763[º+.63F>ûgW>þR'7)
:@
E@ !MOûgW>û °+Y;F>MOû).ûåF¯û6C2/ú›47+,63F¯'*6C2 $F>MOû”WH+,17M3F!û6C2ú›47+,63F
4 ?T MOû 4 ä+,; A G@U'76C2 Jû$FH'*-Eû”FHMOû !+,2QFHMí4
¾F>MCû$ûg=úOF<[(;GûF ´F>4/ü›û
ûWH4CT
'*6C2
D'*WHû
+ F>MOû !+,25F>Mý4 +Y; O@
4*F>MCûW !+,;>û Jû;>'Š[ºF>MC'*F '76C2 T + *TC9 '76C2
'7W>ûX;>ûúC'7WH'*F>ûg2@QF>MOûg6 Jû”;H'Š[?F>MC'*F ¹+Y;!),û åF 4 + T MOû
4j F>MOû XúO+,ûgLûg; ”+Y;JF>MOûúC+.ûvLû :T
+,;j'!6O4E658Aûg=?ú5F<[;GûFi4 C;>ûúZ'*WN'RF>ûv2XúO+,ûgLûv;
E@ 7T
4*FHûÁF>MC'*F¯'$ú›47W>F>+,476='Š[ºL4E6C;G+Y;GF
4 iúO+,ûgLûg; !MO+YLNM'*WHû¹6O47F '72 G'ELû 63F Æ+AT û7TC'$úZ4EWGFH+.4E6
=+,17M3Fü›û'XL47),).ûvL}F>+,476$4 >LWHKO=$üC; ÆWH47= 25+ ›ûgW>ûg63F¾úC'*W>FH;j4 ZF>MOû!Lg'*-7û }T J4¹ú›47W>F>+,476Z;
'76C2 '*WHû
+ ¾ûþEûWH[úO+,ûgLû”+,6
+,;¹;GûgúC'*WN'RFHûg2 ÆWH47= ûþEûWH[úO+,ûgLû+,6
T 6 4 ZF>MOû Lg'*-7û+Y;'XL47),),ûgL}FH+.4E6$
4 ›;>ûúC'7WH'*F>ûv2”ú›47W>F>+,476C;
!MO4E;>ûXKO6O+,476+,;JFHMOûû63FH+.WHûL'*-Eû CT
SQKOúOú›4E;>û?F>MC'*FF>MOû KZ;GûgWH;
!+,;>M F>40;>MC'*WHûF>MOûL'*-Eû7T 3D'7LNM KC;GûgW
MC'7;¾' 7
@ !MC+,LNM´25ûF>ûgW>=?+,6Oûg;mMO4 ÇKZ;GûgW þŠ'7).KCûg;FHMOû úO+,ûgLû A@
!MOûWHû
ET 3m'ELNM0KC;>ûW D-Q6O4 ;Á4E6O).[(+tFN;X4 !6(K5FH+.),+tF<[ ÆKO6CL}FH+.4E6
}@'76C2
MC'7;!6C4+,6 Æ4EW>='RFH+.4E6W>ûg1E'*WN25+,6O1$F>MOûK5FH+.),+.F<[ ÆKO6ZL}F>+,476Z;!4 °4*FHMOûW!KC;>ûWN;gT MOû ÆKO6CLF>+,476C;
'*WHû¹=?476C4*F>4E6O+YL'*),),[6O47658b25ûvLWHûg'7;>+,6O1 !+.F>M
$'76C2 7@ Æ4EWûþ7ûgW>[
KC;GûgW GT íû?WHû 3KO+,W>ûF>MC'*FÁFHMOû?þR'*),KOû$
4 J'úZ4EWGFH+.4E6(+Y;¹F>MOû;>KO= 4 mF>MOû?þR'*),KOûg;Á
4 mF>MCû
+.6C2O+.þQ+Y25KC'*)úO+,ûgLûg;$+.6ÇF>MZ'RF?úZ4EWGFH+.4E6 7T MQKC;g@iFHMOû/þŠ'7).KCû
4 úO+.ûvLû F>4 KC;>ûW ¹+,;
6
}@°'*6C2 Æ47W$'76Q[íú›47W>F>+,476
3@
}T
MOû$1E4E'7)4 JL'*-Eû8b25+,þ3+Y;>+.4E6P+,;¹F>4/úC'7WGFH+tFH+.4E60F>MCû$ûg6EFH+.WHû?L'*-Eû /+,6EFH4 ;GûgúC'*WN'RFHûg2
úZ4EWGFH+.4E6C;@°'7;H;>+.1E6O+.6C1(ûg'ELNM¸KC;>ûW$F>4ç'0ú›47W>F>+,476T C47WH=?'7).),[7@°'
+Y;?'*6 8
úC'*W>F>+.F>+,476
4 UL'7-7û C@ !+.F>M'76'E;>;>+.1E6O=?û63F4 ›úZ4EWGFH+.4E6 ›F>4XKC;>ûW <@ Æ4EW
'*),) ýT D4ºLg'*-Eû8b25+.þQ+Y;G+,476Z;
'76C2
'*WHû
+
Æ4EWJ'7).) Z@Q+ÃT û7T,@Qûþ7ûgW>[?KC;>ûWJ17ûFH;mF>MOûX;H'*=?û¹úZ'*W>FD4 jL'*-Eû¯+,6
üZ47F>MP25+,þ3+Y;>+.4E6C; ÆüOKOF úZûgW>MC'7úC; 25+,þQ+,2Oûg2+.63F>4´2O+ UûWHû63F!úO+,ûgLûv; T
MOûÁLg'*-Eû8b25+.þQ+Y;G+,476º+,;
47W
+ ý@ Æ47W!'*),) ý@
+ÃT û7T,@*ûg'ELNM$KZ;GûgW 1EûFH; !MZ'RF¾;GMCû L 476Z;G +Y25ûWN;iF>4ü›û 'RF),ûg'7;GF 4 CFHMOû L'7-7û!'7LgL47WN25+,6O1
F>4MOûgW 4 !6KOF>+,).+.F<[ ÆKC6CL}FH+.4E6 T û47ü5FN'*+,6FHMOû Æ4E).),4 !+.6C1+,63F>ûgW>ûv;<FH+.6O1?þR'*WH+Y'RF>+,476Z;4 ·¾°y3y3]Hopr£`<] opr£_¹_¾^5nNevevck3d3c­$eged3f£sxw!nH`<c”k3c¹_v­7¶3]ra<op]Hr¾n>yEd3d3ea¾opn}]}_g»Rs*k3_oprb®vrb_k3spc]NdR^7aa<ota<egedZ_Á²u£^5`Gev_gkEnHdQa<op­n}_egspf£spwRn}€_a<ªŠyE]v]H² `<]jnNegk3st­ ¶5]jrboxa<kQ_a<otegd3r
E
<1>
)
"$?
$@
0
* ?+ &"-,.*/,0+1,
2*
3+
4)
65 4)
7+ 8*
29
:)<; >
*#
; ?+=;
>)
>
* ?+
)/;@?A)
"
&: 7)/;
B)
C)
)<;
C)/;
*:;3 $)/; & $ )
ED
)
F)<;
<)
<*#;FGH*
0 0
EIKJ
7L * ?M=; ? M=
; ?NM ? M ?MPO ?PQQPQ? MSRUT;G?+ V
* ?+
@ &:;
W
>XLS)<;?) ?P
Q QQ?)<YZV =[!\
>
'
I
W
AW
;
W
@
%
G+
]W
$: &:;
%
3 8 *Ee c 'gf0+
1"],ifj,
e c'gf +
a`c =E
K
;
/W
a`$;G?PQQQ?` ^
b`dc
h`c
"$?f
2`dc
e c'gf +
e c '"+ >J"
e c' + >
k
+ > e c'g++
e c ' Y * ?+ 7
n cpo:; e c '):c +
e c'#*+
8W
>mL&)/;G?N)
lWjc
AWX; t ?QPQQ?NWX^ t
sW0;G?PQQPQ?W
^

%
/`dc
Nu
35&
+
-8 :
: &:; 3
e c $E
„
l`c
e c 'W +6>
%
;
.<
'
/` c
*? +
?QPQQ)<YZV
6<
-,
1W0;?QQPQ?NW ^
l,rqsJ
, %
<vlwyx{z|2}) c >~vwyx{z|€}  ) c
; ?QPQQ?W_^
<
e c '#W
c +‚\ Sƒ*%
Sƒ*%
a,jqC,
%
œ'*+,W°Lg'*-Eû8b25+.þQ+Y;G+,476@+<@R+.6?'72O2O+tFH+.4E6”F>4 œ '*+,Wv@ JûJ+.=?ú›4E;>ûÆKOW>F>MCûW°W>ûv;<FHW>+YL}FH+.4E6C;i47W=8 :; ;
$;: 2 476F>MOûWHû)Y'RFH+.4E6C;>MO+.ú/ü›ûFJûû6/FHMOû”'7;H;G+,176Cûg2´ú›47W>F>+,476Z;
(d"d= e c'#Wjc+b\ e c'#W
+ Æ 4EW'*),) q?{ ;: *2) 8 : + e c'#Wjc+bJ e c'#W
+
Æ 47W '7).)$q>_ ZT
U (d"d= e c 'W
+ , S ƒ Æ 47WÇ'*),)€q>  ;: &: & 8 : +
ƒ Æ 4EW '*),)q>8
ZT
e c'#Wjc+‚G S
MOûg;>û25û*)C6C+tFH+.4E6C; '*WHû;<FN'*6C2C'*WN2º'*6Z2 Æ 4EKO6C2/+,6 !
A T
#(!'= #"$
%
íû06C4 =?4Rþ7û4E6 F>4¸25û C6O+,6O1 'ýL'7-7û8:LK5FGFH+.6O1çúOWH4*FH45L47)&%R'7).1E47WH+tFHMO=T°9b=?'717+,6OûF>MCû
ûÿ5+,;GF>ûg6CLû4
°;>47=?û'72O=+,6O+Y;<FHWH'*F>4EWJ4EW¯;>KOúZûgW>KZ;GûgW !MC4+,;!WHûg;>ú›476C;>+.üC).û Æ47WFHMOû”L'7-7û8
25+.þQ+Y;G+,476T
MOû ;>KOúZûgW>KZ;GûgW çMZ'7;°),+.=?+.F>ûg2L47=?úOK5FH+.6C1úZ4 JûWv@R6C'*=?ûg).[;>MOû Lg'*6?úZûgW Æ4EW>=
üC'7;>+,L 47ú›ûWN'RF>+,476Z;¾;GKZLNMº'7;DL47=?úC'7W>+Y;>476C;g@*'72O2O+tFH+.4E6C;D'76C2?=KC)tFH+.úO),+YL'RFH+.4E6C;gT û¹'E;>;>KO=?û
F>MC'*F ûg'7LNM;>KCLNMüZ'7;>+,LÁ47ú›ûWN'RFH+.4E6WHû 3KO+,WHûg;J476OûÁFH+.=?û”;GF>ûúT
SQKOú›ûWHKC;GûgW L'76 'E;G- F>MCû KZ;GûgWH;ºF>4 LK5FPúO+,ûgLûg;/4 F>MOûýL'7-7ûí+.6 47WN25ûWF>4 17ûF
+.6 Æ4EW>='*F>+,476´WHû13'*WN25+.6C1XF>MOûg+.WJK5F>+,),+tF<[ ÆKO6ZL}F>+,476Z;T LK5F+,;JL4E=?úZ43;Gûv24 £FHMOû Æ4E).),4 !+,6O1
;<FHûúC; 7;>KOúZûgW>KZ;GûgW ;Gú›ûgL+ Zûg;°FH4KC;GûgW 'XúO+,ûgLû ›'*6Z2'XWN'RFH+.(4 ' !+tFHM )' F>MOûPKC;>ûWFHMOû6 WHûF>KCW>6C;FHMOûPú›47+,6E!F * +.6 ¹;>KCLNMÇF>MC'*F * +'$T
M3KZ;@C'?LK5F¯L'76/ü›ûWHûúOWHûg;>û63F>ûv2ºüQ[FHMOû Æ4EKOWG8AF>KCúO).-û , .' *0/}T û”L'7).) * F>MCû
4 ¾F>MCû?LK5FgT£9:F+Y;XúZ43;>;>+,üO).û$F>MZ'RF”'LK5F”L4EKO),2í[Q+.ûg),2(=KO).F>+,úO),ûLK5Fú›4E;>+tFH+.4E6C;@
+ÃT û7T !MOû6¸;>47=?ûWHû17+,476 4 FHMOûºL'7-7û?ûþR'7).KC'*F>ûv;XF>4 gûWH4 +,6ý;GKZLNM¸'PL'7;>û JûW>û EKC+.WHû
F>MC'*FÁFHMOû?LK5Fú›4E;>+tFH+.4E6(WHûF>KCW>6Oûv20+Y;¹F>MOû?),û åFG8:=?4E;GFgTU9b6çL'*-Eû8bLK5F>F>+,6O1'7).1E47WH+tFHMO=;@ZF>MCû
û6C25ú›47+,63FH;¯4 °F>MOû$úO+,ûgLû”F>4´ü›ûLKOF¹=KZ;<F¯ü›ûûg+tFHMOûW O@ 7@O4EW¹LKOF¯úZ43;G+.F>+,476Z;!F>MZ'RF¯MC'ŠþEû
üZûgû6 úOW>4525KZLûg2 üQ[¸ûg'7W>),+.ûgWLK5FH;gTmSQ4 Æ47W?ûÿO'7=úC).ûE@iFHMOû CWN;<F´LKOF?MZ'7;$F>4 üZû
4 ¯F>MCû
Æ47WH+
= , 21 .' * /}T MCû”;GûvL476Z2/LK5F¹L47KO)Y2F>MOûg6/ü›û”='72Oû476 A@ * 4EW
* :T OWH47= 6C4 ûþEûWH[PúO+.ûvLû !+,).)¾ü›û?4 DF>MO+Y; Æ47WH=T íû´'E;>;>KO=?ûFHMC'RF”'/KC;>ûWL'76
L476Z;<FHW>KCLFX'/LKOFX+,6çL476Z;<FN'*63F¯FH+.=?û QT L'*-Eû8bLK5F>F>+,6O1'*),1747WH+.F>MO= Æ+,=?úO),û=?û63F>ûv2(üQ[
F>MOû;>KOú›ûWHKC;>ûW +,;¯'´;Gû 3KOû6CLû4 ¾LKOFH;!FHMC'RF L476Z;<FHW>KCLFH;!+,6P47WN25ûgW!F>44EK5F>úOKOF¯F>MCû
25ûg;>+.WHûg2/L'7-7û8:25+,þQ+,;>+,476T
E
)
C
C
E
C
@
-C
A)
h`dc
* ?+
* ?+
#`c
e c ' * ?
* ?+
"l,
+Nƒ e c' * ?+ +
$E
$
,
>
"
)
g` c
s;?
;
"$?
;
"&?
=,
"$?
;
=E
kk
.C +
!3<(: #'(
54y 9b6OúOKOF 9 K5FHúOK5F =
BD47=?úOKOFH'RFH+.4E6>9 @
'
BC
6 #(!'= "$87
& %
3 7 8 0$:e ;'#f0+*?QQPQ? e ^ 'gf + 8 : & : `$;G?PQQPQ?` ^<;
* 8 & **: 8 :; ; $;: 2 ;
&/3 :; 4 Nu
&0B 8 2:@? > hQPQQ ; = *: 9 <?:
&B
&:;
*:.: u
&;;. *: `dcBA $: 8 : 6*
-( *DC?+6C <5 : ' CFE ,g` c A * C ? + C .' C * C / ;G : 2 5 & F: $B;
&*:;
: 1
$:93 0
$ 5 *: 7 $ 8 : & 07 33 0:*
*
; = ;35 B&5
G6 &1;
$: :7 &B 8 8 : 5
5
&. $6;
&*:;
:
35 &*: 7 ( ; * &:;& ;
„„
©­E`<op®*evotcÇ­Eopd3a<y3¬]°_”nNeg^3cop]N^3nN]¯k7aG¶R_wa<opev_gd3dº_goxs7`b^5`G_eva<opopdRevad3eg_gf5sU®*`Gop_]Ha<·!ote$€a<opy3rop_”rc”d3ev_}d7w «Æab¶5`<]°ot®*_Dot_gr:s›ab`<nNevevdEc¬!^E_gkErbaGrb_kEa<copeg^EdQa<_gopevsZdCaG_g€grbf,egª5`€O]Hy3ÚEe}_g·°c]H®Š^E]Hsp]`
aboxa”`G_vot­7r”opa<_´opegr:dZaG² _gd3­3_`G­ _grbrbkEc^Ea<opevd(c”_v­7]$opd(a<y3]spoxa<]H`G_a<kE`<]v€i_gd3­írbeº·°]?nNegdRa<otd*kE]$·¾oxa<y(a<yE]
9 $**
&:;$70 (3 1
035+ 8 &63 :; ;
*
& 2 íû/;>'Š[íF>MC'*FFHMO+,;'*),174EW>+.F>MC= KC;>ûg; L KOFH;gT Lg'*6¸25ûgúZûg6C2¸4E6
&
03
'*6Z2 F>MOû/K5F>+,),+tF<[
ÆKO6CL}FH+.4E6C; e cGT@ÝL4EW>WHûgLFLg'*-Eû8b25+.þQ+Y;G+,476$=KC;GFFH'7-7û!+,63F>4'7LgL47KC6EFFHMOû!K5FH+.),+tF<[ ÆKO6CLF>+,476C;
4C '*),)EF>MOûDKC;GûgWH;g@vMO4 Dûgþ7ûgWg@}FHMOûD;>KOú›ûWHKC;>ûW°254Qûg;6C4*Fi-Q6O4 çFHMOûg;>ûmKOF>+,).+.F<[ ÆKO6CL}FH+.4E6C;gT MCû
;GKOú›ûWHKC;>ûW+.=?úO),+YL+.F>),[¸+.6 Æ ûWN;”FHMOû6OûgLûg;H;>'7W>[ +.6 Æ 47WH=?'*F>+,476 '7üZ4EK5F?ûg'7LNM KC;GûgW# ;K5F>+,),+tF<[
ÆKO6CL}FH+.4E6 Æ W>4E= FHMOûºLK5FH;='E25û7T MOû´MO+Y;<FH47WH[04 '7).)FHMOûºLK5FH;W>ûgúOW>ûv;Gûg63FH;ÁF>MCû´û63F>+,WHû
-36C4 ! ).ûv2517û¹F>MC'*F.CÝMC'7;WHû13'*WN25+.6C1”F>MCûK5F>+,).+.F<[ Æ KC6CL}FH+.4E6C;!4i F>MOûKZ;GûgWH;gTOIJ[º'?;GKO+.FH'7üO),û
LNMO47+YLû?4! LKOFH;g@=C F>MOûg6ç47K5FHúOK5FH;$'L47WHWHûgL}F”Lg'*-7û8:2O+.þQ+Y;G+,476T=@¯6ç'7).1E47WH+tFHMO= +Y;6C'7=ûv2
'7LL47WN25+,6O1”FH4FHMOû œ '*+,W>6Oûv;>;L476C;GF>WN'*+,63FmF>MCûXLg'*-Eû8b25+.þQ+Y;G+,476º=KC;GF;H'RFH+,; Æ [7T,C47WûÿO'*=?úO),û7@
+! FHMOûº4EK5F>úOKOF$+Y;œ '7+.W 'Æû6QþQ[38 Æ WHûûG+ÁF>MCû6ýFHMOû'7).1E47WH+tFHMO= +Y;Lg'*),).ûv2¸' 8 : & 8 : 3 :; T
@ LKOFj'7; D
ûDMC'Šþ7ûD25û*)C6Cûg2+.Fi+Y;û3KO+.þR'7).ûg6EFiF>4Á' L4E6C;<FN'*63F6QKO=$üZûgWi4
C L47=?úC'7W>+Y;>476C;gT
@¸6QKO=ü›ûWj4C
'E2O25+.F>+,476C'7)EWHû3KO+,WHû=?û63FH;iL'76”üZûDúO)Y'7Lûv2476”F>MOûD=4525ûg) Æ 47WiLg'*-Eû8bLK5F>F>+,6O1
17+,þ7û6Ç'*ü›4Rþ7û7T ,O4EWûÿO'7=úC).ûE@ ! MOûg6Ç'íLK5F+,;$='725ûE@°'(L47=?=?476Ç'7;H;GKO=?ú5FH+.4E6¸+,6¸F>MCû
).+.F>ûgWH'*F>KOWHû¯+Y;¾FHMC'RF G: KC;GûgWDûgþR'*),KC'RFHûg;FHMOûÁW>ûv;GKO).F>+,6O1FD 4$úO+.ûvLûv; Æ 4EWmFHMOûÁ;>KOú›ûWHKC;>ûWvT
BD47=?úOK5FN'RF>+,476Z'*),).[E@FHMO+,;j'7;H;>KO=?ûg;F>MC'*FiK5FH+.),+tF<[ Æ KC6CL}FH+.4E6ûþR'7).KC'*F>+,476”+Y;j' 6Oûg17),+.1E+.üO),ûmL4E;GF
47ú›ûWN'RF>+,476T0,C47W¹F>MOû?=?4E;GFÁúZ'*W>Fg@›47KOWX),4 D ûgW¯ü›47KO6C2C;Á2O46O47FÁWHû3KO+,WHû$;>KCLNMí'E2O25+.F>+,476C'7)
'7;H;GKO=?ú5FH+.4E6C;gT59b64EKOW 25+Y;>LKC;>;>+,476D û ! +,).)='7-7ûXL),ûg'*W ! MZ'RF Æ KOW>F>MOûgW¯'7;H;GKC=úOF>+,476C; J û
=?'7-7û ! MOûg6/6CûgLûv;>;H'*WH[7T
E
H%
F
' = "$
%
íûüOWH+,û C[0úCW>ûv;Gûg6EF;>47=?û Dûg).)-Q6O4 !6çL'7-7û8bLKOFGF>+,6O1'*),174EW>+.F>MO=;gT£&P47WHû2OûFH'7+.)Y;L'76
üZû Æ4EKO6C2/+.6 AT ¯).1E47WH+tFHMO=; '*6C2 '*WHû¹ü›4*FHMœ'*+,W¯L'7-7û8bLKOFGF>+,6O1?'*),174EW>+.F>MO=;gT
9b6´'*),1747WH+.F>MO= ”@Q'*),)OFHMOû¯KC;>ûWN;mLK5FD'*F 4UF>MCû !MO4E).û¯Lg'*-Eû7TMCû KC;>ûW!MC4$LKOF
F>MOûÁ;G='*),),ûg;GFDúO+,ûgLû¯+Y;m1E+.þEû6?F>MZ'RFDúC+.ûvLû7@Q'*6Z2F>MOûÁW>ûg='*+,6O+.6C1”KC;>ûWN;¾WHûgLKCWH;>+.þEû),[$25+,þQ+,2Oû
F>MOûWHû='*+,6C25ûgW4 FHMOûL'7-7û œ'*+,W>),[7T MOûXþR'*),KOûX4 iF>MOûWHû='7+.6C2OûW4 iF>MOû”Lg'*-7û¹F>4?ûv'7LNM
4 F>MCûWHû='*+,6O+,6O1´KC;>ûWN; +Y;¹'*F¹),ûg'E;<F ý@Z'76C20;>4F>MOûWHûg;>KO)tFH+.6C1º25+,þ3+Y;>+.4E60+,; œ'*+,WgT
MO+,;¯'*),1747WH+.F>MO= WHû 3KO+,W>ûv; LK5FH;gT
9b6'*),174EW>+.F>MC= ´@ Æ47W!;>+.=?úO),+YL+.F<[º'7;H;GKC=û¹F>MZ'RFF>MOûgW>ûX'*WHû KC;>ûWN; Ã'*).F>MO4EKO17MF>MCû
'*),1747WH+.F>MO= +,;$17ûg6OûWN'*) }T ¯).)DF>MCûºKC;>ûWN;”LKOFF>MCûL'7-7û´'*F 5T MOûKC;>ûWN; !MO40='72Oû
F>MOûº;>='*),).ûv;<F LK5FN;”WHûgLKCWH;>+.þEû),[(25+,þQ+,25û´F>MOû´),û åF GMC'7) 4 F>MOûºLg'*-EûKOúçF>40'76C2
+.6CL).KZ25+.6C1?F>MOû=?ûg2O+,'76LK5Fg@Z'*6C2F>MCûKC;GûgWH; !MC4?LK5F!F>4?FHMOûWH+.1EMEF!
4 iFHMOû=?ûg25+Y'*6PLKOF
W>ûvLKOWN;G+,þ7ûg).[25+.þQ+Y25ûFHMOûWH+.1EM3F GMC'7) ´4 °F>MOû$L'*-Eû7TZS5+.6CLû$'7).)£FHMOû),û åFÁKC;>ûWN;!þR'*),KOûF>MCû
).û åF¯úC'*W>F 4 jF>MCûL'7-7û”'RF 1'*6C2'7).)£FHMOû”WH+.1EM3F KC;GûgWH;þR'7).KOû”F>MOû”WH+,17M3F!úC'*W>F 4 °F>MCû
L'*-Eû'*F 5@›F>MOû´'7).1E47WH+tFHMO= úOWH4525KCLûv;' œ'*+,W”25+.þQ+Y;G+,476T MO+,;'7).1E47WH+tFHMO= WHû 3KO+,W>ûv;
Š),471 LK5FN;T
äú›ûW ÆûgL}FH).[ç),û1E+tFH+.='RFHûLg'*-7û8:LK5FGFH+.6C1('*),174EW>+.F>MO= F>MZ'RF2O43ûv;6C4*F CF !+.F>MO+,6¸FHMO+,;
ÆWH'7=û D4EW>-P+Y;FHMOû T MOû´;>KOú›ûWHKC;>ûW=?4Rþ7ûv;'
-36C+ Æû L4763FH+.6QKO4EKC;G),[ ÆW>4E= FHMOû ).û åFû6Z2Â4 FHMOûíLg'*-EûPF>
4 F>MOûíW>+,17M3FgT MOû CWH;GFKZ;GûgW
!+.F>MO4EK5F),4E;H;”
4 17ûg6OûWN'*),+tF<[
!MC4(+Y;MC'7úOúQ[ !+tFHMýF>MOû/úO+,ûgLû´F>4(F>MOû/),û åF?4 !F>MCû
LKOWHW>ûg63FúZ43;G+.F>+,476 4 !F>MCûº-Q6O+ Æû[Eû),),; >LKOF 0'76C2ý+Y;$;>KOüC;>û 3KOûg6EFH).[ç1E+.þEû6çF>MZ'RF$úC+.ûvLû7T
¯;>ûW D+,;mMC'*úCú3[ !+tFHM?F>MC'*FmúO+,ûgLû7@7'76C2F>MOû¯W>ûg=?'7+.6C+.6O1XKC;>ûWN; JûWHû!MC'*úCú3[F>41E+.þEû!KOú
F>MC'*F¹úO+,ûgLû7T M3KZ;!F>MCûWHû='*+,6O+,6O1´KC;>ûWN;!=KZ;<FÁüZû$MC'*úOúQ[ !+tFHM(' œ'7+.WÁ25+,þ3+Y;>+.4E6P4 F>MCû
E
!
$@
Sƒ*%
;
+
Sƒ*%
%H'%
G+
R
%€ƒ
I
I
b\
€\
%
%
Sƒ
^
/'
Sƒ
@
K
K
=ƒ
@
)
2 8 8 :
;J3 :;
)
`$;*+
'
I
h`$;
K
W>ûg=?'7+.6C+.6O1X
4 ZFHMOû L'7-7û7TMCû!úOW>45Lûg;H;°+,;°FHMOû6?WHûú›ûg'*F>ûg2 !+.F>MF>MCû!W>ûg=?'7+.6C+.6O1Lg'*-7û!'76C2
F>MOûW>ûg='*+,6O+.6C1 KZ;GûgWH;gT MC+,;Á'*),174EW>+.F>MO= ='*-Eûg; $LK5FH; !MO+YLNMíL'76O6O47F¹ü›û
+.=?úOWH4Rþ7ûv2?KOúZ4E6@5;G+,6CLû¹'RF),ûg'7;GF ÁLK5FN;D6Cûûg2F>4üZûÁ='725û¯F>417û6CûWN'RF>û úO+,ûgLûv;T
4 Jûþ7ûgWg@NFHMO+Y;'*),174EW>+.F>MC= 254Qûg;6O4*F CF !+.F>MO+,6XF>MOû ÆWH'7=û D4EW>- Dû¾MZ'Šþ7û25ûg;HLWH+,üZûv2£@g'76C2
+,;J'*6´ûÿO'*=?úO),û¯4 '
QF>MCûWHû¯+Y;m6O4 J'Š[$F>4;G+,=KC),'*F>û FHMOû¯=?4RþQ+,6O1
-36C+ Æû !+tFHM '76Q[;>û 3KOûg6CLû$4 D2O+,;HLWHûFHûL
K5FH;gT OKOW>F>MOûgWg@Uûv'7LNM(LK5FÁ+,60FHMO+Y;Á'7).1E47WH+tFHMO=+,;
6O4*F”û EKC+.þR'*),û63FXF>40'L476C;GFH'76EF6QKO=$üZûgW4 !L47=?úC'7W>+Y;>476C;g@ Æ47WûÿO'7=úC).ûF>MCû CWH;GFLKOF
L476QþEû[5;DF>MOû+,6 Æ47WH='RFH+.4E6+,6 9 !L4E=?úC'*WH+,;>476Z;T ûg6CLûE@C;>KCLNM/'76P'*),1747WH+.F>MO= +Y;!6O47F
4 =$KCLNM+,63F>ûgW>ûv;<F ÆW>4E=F>MOûXL4E=?úOK5FH'*F>+,476C'7)UúZ4E+.63F!4 þQ+,û T MOûÁF<[QúZûv;J4 i'7).1E47WH+tFHMO=;
F>MC'*Fj4EKOW ÆWN'*=?û J47WH-¹'E25=?+tFN;i'7W>ûDKC;>KC'*),).[¹F>ûgW>=?ûv2 4EW
'7).1E47WH+tFHMO=;Tv&P47WHû
25ûFN'*+,),;g@5+.6ZL),KC25+,6O1´'*),174EW>+.F>MO=; Æ47W!ûg6Qþ3[38 ÆW>ûgûL'*6/ü›û Æ47KO6C2/+,6 :T
”ô ó çômö¹ñ¯
õ Nô¾ó õ ¾ô¾óCø<ò íû´L476C;>+,2OûW”'/17ûg6OûWN'*)L)Y'7;H;X4 !L'7-7û8:LK5FGFH+.6O1'*),174EW>+.F>MC=?;g@UF>MZ'RF Jû?Lg'*),) GúOMZ'7;>ûg2 CT
íû C6C2'Á).4 JûWjü›47KO6C2$476$F>MCûJ6QKO=$üZûgW°4 ›LK5FH;°WHû 3KO+,WHûg2”üQ[úOMZ'7;>ûg2'7).1E47WH+tFHMO=;iF>MC'*F
17KC'7WH'76EFHûûXûþEûWH[ºKC;>ûW¹'?úZ43;G+.F>+,þ7û”þR'7).KOûv2/úZ4EWGFH+.4E6T L'7-7û8:LK5FGFH+.6O1'7).1E47WH+tFHMO=;
MC'Šþ7û¹F>MOû Æ4E).),4 !+,6O1?úOW>4EúZûgWGFH+.ûv;T
T
MOû”;GF>ûúZ;4 jF>MOû”'7).1E47WH+tFHMO=ä'*WHû25+.þQ+Y25ûg2/+,63F>4 9 b6Çûv'7LNMÇúOMC'7;>û7@°ûgþ7ûWH[
KZ;GûgW?LK5FH;'íúO+,ûgLû7@jF>MOûûg6C25ú›47+,6EFN;?4 !MC+,LNM '*WHû
25û Z6Oûg2?KC;>+,6O1LKOFH;='72Oû¯25KOWH+.6C1
úOMC'E;Gûv;476C).[ET*9b6?F>MOû CWH;GFmúOMZ'7;>û7@*ûv'7LNM
KC;>ûW LKOFH;FHMOû !MO47),ûL'7-7û7T 6CLû 'XKZ;GûgW¾+,;m'7;H;G+,176Oûv2$'Xú›47W>F>+,476@RF>MC'*F¾KC;>ûW¾ü›ûgL47=?ûg;+,6C'EL}F>+,þ7û Æ4EW°F>MOû¯W>ûg=?'7+.6O8
25ûWj4 CF>MOû'*),174EW>+.F>MO=T ¹;>;>+.1E6Oûg2”úZ4EWGFH+.4E6C;i'7W>ûD6O4*F°L4E6C;G+Y25ûgW>ûv2 Æ47WiF>MOûJWHû='*+,6C25ûgW
4 jF>MOû”'7).1E47WH+tFHMO=T
&0'*6Q[ýL'7-7û8bLKOFGF>+,6O1('7).1E47WH+tFHMO=; OF?+,6EFH40FHMOûL),'E;>;$4 úOMZ'7;>ûg2¸'7).1E47WH+tFHMO=;T m[QúO+YL'7)
ûÿO'*=?úO),ûg;´'7W>û ¯).1E47WH+tFHMO=; '*6Z2 ´T MCûWHû0'*)Y;G4çûÿ5+Y;<Fº'7).1E47WH+tFHMO=;?F>MZ'RFº'*WHûP6O47F
úOMC'7;>ûg2@ Æ47W!ûÿO'7=úC).ûS3FHû+,6OMC'7KC; 54EW>+,17+,6C'7)U'7).1E47WH+tFHMO=T
íû´;H'Š[PF>MZ'RF”F J4P'*),1747WH+.F>MO=;'*WHû
+ FHMOû[ KC;>û?F>MOû´;H'*=?û6QKO=ü›ûW4 LK5FN; Æ4EW'76Q[ ;>ûF?4 K5FH+.),+.F<[ ÆKO6CL}FH+.4E6C;g@°'76C2ýúOWH4525KCLûºû 3KO+,þR'*),û63FLg'*-Eû8b25+.þQ+Y;G+,476Z;T
úO+.ûvLû+,; + J+tF”254Qûv;¹6C4*FL4763FN'*+,6í'*6Q[0LK5FÁú›4E;>+.F>+,476C; 'º6O4E658b;G4E).+Y20úO+,ûgLû$+Y;ÁF>MCû
KO6O+,476ý4 F J4P47W”=?4EW>û´;>ûúC'7WH'*F>ûv2 ;>47),+Y2íúC+.ûvLûg;gT KCW CWN;<F4EüC;>ûWHþŠ'*F>+,476ç+Y;F>MZ'RF$'763[
LK5F!üQ[´'KC;GûgW476'$6O4E658:;>47),+Y2´úO+,ûgLû 17+,þ3+,6O1?LK5F!ú›4E;>+tFH+.4E6 * L'*6/ü›ûÁWHûúC),'ELûg2 !+tFHM
'LK5F”üQ[F>MOû;H'*=?û$KZ;GûgW476í'/;>47),+,2íúO+,ûgLûL4763FH'7+.6Oûv20+,6 ?@U[Q+,û)Y25+.6C1FHMOû LKOF
úZ43;G+.F>+,476T
%
%
%
/%
)
&&
&
3 :;
=,
7)
1'%
+
2 .
<Z
: !
H
E
I
E
)
$K
&G
&G;
*)
4)
0: '@
+
)
@
#
E
u*
3 *2
3 @
F
)
a)
)
$ $
&G & )
$ 0
8 &:
) ; ?QPQQ*?N) Y : 8 : [ \ : g
,
`
N
)
.
'
0
*
/
c
&. $ : &;1
9 &* : 8 :7;
3 &G ' t 0 *3 ) :. $ *
0: &* & 7
&G; * t > * ; :; $:: ' t 0
Q ? e c ') Y + ;
0Ee c '#) ; +;?QPQ
û=?='
3A *
&G; * ;
,g`
.' t *
c )
$0(&3
'
t
/
º '7).),4 ;KC;F>4(W>ûv;<FHW>+YL}F4EKOW'*FGF>ûg63F>+,476ýFH4(;G4E).+Y2çúO+,ûgLû´úOMC'E;Gûv2ý'*),1747WH+.F>MO=;gT
MOû Æ4E).),4 !+,6O1º),û=?='FHMOû6í17+,þ7ûg;¯F>MZ'RF'*60+,6O+.F>+Y'*),).[0;>47),+,2(úO+,ûgLûF>4/üZû?LKOFÁüQ[0;>47=?û
KC;GûgWH;='Š[´ü›û”LKOF +.6F>MOû”;H'*=?û;>úZ47F ü3[ºûg'7LNM/4j F>MCûg;>ûÁKZ;GûgWH;gT
$ $
$
: ? &G 3 :; :B &*: : 3 + 8 *& 8 : 5 33
5
5
*:
$1: / 6
$B &33 * 3 0 33=
D $4 &G; ;
íûX6O4 Â1E+.þEû¹4EKOW).4 JûWJü›47KO6C2 Æ47WúOMZ'7;>ûg2º'7).1E47WH+tFHMO=;@ !MO+YLNM/'7úOúO),+.ûv;DF>4'*6Q[´'*),17478
W>+.F>MO= F>MC'*F 17KC'7WH'763F>ûûv;mûv'7LNM/KC;>ûW 'úZ4EWGFH+.4E64
jú›4E;>+.F>+,þ7ûXþR'*),KOû7T
E
" '= $
4 ' C' ( {' "
"$ % 7 = ? $* 3 :; 8
*: &:; &G;G63 &
8 : ?7 8 3 7
% + *
9 $ 5 :; G ;
%&j@ 'S
%),471
MOû),4 DûgW ü›47KO6C204 9 %),471 ¯LK5FN; Æ4EW¯úOMZ'7;>ûg20'7).1E47WH+tFHMO=;@C2Oû=?476C;GF>WN'RFHûg; F>MC'*F
ûþ7ûg6FHMOû!úOWH47üO),û= 4›'E;>;>+,176O+,6O1ÁúZ43;G+.F>+,þ7û!ú›47W>F>+,476C;iFH4KC;GûgWH;j+Y;6O4E658ÃFHW>+,þQ+,'7)ÃT MO+Y;),4 DûgW
üZ4EKO6C2¸+,=?=?ûg25+Y'RFHû),[¸'*úOúO),+,ûg;$F>4 œ'*+,W?'76C2ýûg63þQ[38 ÆW>ûgû'*),174EW>+.F>MC=?;g@i;>+,6CLûF>MOûv;Gû'*),17478
W>+.F>MO=; 'E;>;>+,176ºú›4E;>+.F>+,þ7ûXúZ4EWGFH+.4E6C;JF>4KZ;GûgWH;gT
”ô ó çômö¹ñ¯
õ Nô¾ó õ ¾ômóCøbò íûúOW>ûv;Gûg63F'P),4 DûgW”ü›47KO6C2 476çFHMOûº6QKO=$üZûgW$
4 ¯LK5FN;WHû 3KO+,W>ûv2 Æ47W'P17ûg6OûWN'*)JL)Y'7;H;
4 œ'7+.W '7).1E47WH+tFHMO=;JF>MC'*F DûXWHû ÆûWFH4'7; G),+,6Oûg'7W>),[38A)Y'*ü›û),ûg2 L4E=?úC'*WH+,;>476O8Aü›47KO6Z25ûg2 CT
MOûúOW>4Q
4 œ;j'7W>ûDüQ[”W>ûv25KCL+.6O1X;>47W>F>+,6O1 FH4XLg'*-Eû8bLK5F>F>+,6O1CT j+.WN;GFg@ Dû!;>MO4 çF>MZ'RF¾'*6Q[”L'7-7û8
LK5F>F>+,6O1¯'*),174EW>+.F>MC= L'76üZûDL476QþEûW>F>ûg2¯F>4¹'
'7).1E47WH+tFHMO= !MO+YLNM)Y'*ü›û)Y;£ûþEûWH[¯úO+,ûgLû
+.6 F>MCû´L'*-Eû8b25+,þ3+Y;>+.4E6T MOû6@ü3[ '*úOúCW>4EúOW>+Y'RFHû),[0LNMO4Q4E;>+.6C1K5FH+.),+.F<[ ÆKO6ZL}F>+,476Z;@ Jû?KC;>û
F>MOû)Y'*ü›û)Y;4 jF>MOûúC+.ûvLûg;JFH4´;G4EWGF!'?17+,þ7ûg6;>û 3KOûg6CLûX4 °+,6EFHû1EûWN;T
i+,WN;<Fv@ Jû$25û C6Oû)Y'*ü›û),ûg2('*),1747WH+.F>MO=;¯'76C2FHMOû6(;>MO4 %MO4 '763[L'7-7û8:LK5FGFH+.6O1'*).8
1747WH+.F>MO= Lg'*6/üZûL476Qþ7ûgWGFHûg2FH4'$)Y'*ü›û),ûg2/4E6Oû7T
+Y;!'üO+,6C'*WH[F>WHûûX+,6
!MO+,LNM/ûþEûWH[´6O4525ûX+Y;!û+.F>MOûgW ').ûv' i4EWF>MOûúZ'*WHû63F!4 F J4?6O4525ûg;gT +Y;!'
ÆKO).)CüO+.6Z'*WH[XF>WHûû+.6 !MO+YLNM$ûgþ7ûgW>[),û åF¾ûv2517ûJMC'7;°)Y'*ü›û) X'76C2ûgþ7ûgW>[XWH+.1EMEFûv2517ûJMC'7;°)Y'*ü›û)
7T 3¾þ7ûgW>[).ûv' m+Y;¹),'7üZûg).ûv
2 !+tFHM0FHMOûüO+,6C'7W>[6QKO=ü›ûWÁ47üOFH'*+,6Oûv2PüQ[L476CLg'RFHû6C'*F>+,6O1F>MCû
),'7üZûg),;J4 ûgþ7ûgW>[?ûg2O17û¯4E6´FHMOû¹úZ'RF>M ÆW>4E=F>MOûÁW>4Q47FmF>4$F>MZ'RF).ûv' <T 6ûÿO'*=?úO),û¯)Y'*ü›û),+.6C1
F>WHûû!+Y;¾;GMC4 !6$+,6 j+.1EKOW>û ET ûF ü›ûF>MOû¯2Oûûú›ûg;GFmL4E=?=4E6'*6CLûg;GF>47W°
4 ›F J4X).ûv'Šþ7ûv; '*6C2 T59 üZûg).4E6O1E;DF>4$F>MCû).û åF!;>KOü5FHW>ûgûX4 ´'76C2 ü›û),476O13;DF>4F>MOûXWH+.1EM3F;>KOü5FHW>ûgû
4 Z@5FH MOû
6 +Y; 4 T
BD476C;>+,2OûW¯'76 P8AúC'7WGFH+t FH+.4E6
4 jFHMOûLg'*-7ûET MOû”úZ'*W>F>+.F>+,476+,; + F>MOû Æ4E).),4 !+.6C1MC47)Y2 +,6 F>MOû0úZ'*W>F>+.F>+,476 MC'7;º'
O4EWº;G4E=?ûP),'7üZûg).+,6O1ýFHW>ûgû7@¾ûgþ7ûWH[ Ã;GûgúC'*WN'RFHûg2 úC+.ûvLû
25+Y;<FH+.6CLF¯)Y'*ü›û) F>MC'*F¯+,;¯'?).ûv' °476/F>MO+Y;FHW>ûgû7@C'76C2ûþEûWH[´).ûv' °476/F>MC+,;FHW>ûgû),'7üZûg),;
;G4E=?ûÁúC+.ûvLû7T
+,;m).û åFD
4 ¯+,6?F>MOûÁL'*-Eû!+ '76C2?476O),[+ ),ûg' £+,;m).û åFD
4 U),ûg' . +.6FHMOû )Y'*ü›û),+.6C1
F>WHûûET
L'7-7û8:LK5FGFH+.6O1´'7).1E47WH+tFHMO= +,;
+ ¾+.FÁ'*) 'Š[Q;úCW>4525KCLûg;¹'*6 8:úC'7WGFH+tFH+.4E6FHMC'RFÁ+,;
),'7üZûg).ûv2£T 6ûÿO'*=?úO),ûJ
4 U'X)Y'*ü›û),ûg 2úC'7WGFH+tFH+.4E6?+,;¾;>MO4 !6+.6 j+,17KOWHû 7TR9b61Eû6OûgWH'7)Ã@vF>MCûWHû
'*WHû=?'76Q[ 'Š[5;F>4),'7üZûg)i'úC'7WGFH+tFH+.4E6@Z'76C2/F>MCû$'*),174EW>+.F>MC= 6Oûgûg2P4E6O).[/47KOF>úOK5FÁ476Oû4 F>MO43;Gû J'Š[5;gT ¯ûÿQFg@ JûX;GMO4 FHMC'RF '763[´Lg'*-Eû8bLK5F>F>+,6O1$'7).1E47WH+tFHMO= L'*6üZûL476Qþ7ûgWGFHûg2?FH4
'*6/û 3KO+,þŠ'7).ûg63F ),'7üZûg).ûv2'7).1E47WH+tFHMO=T
&-
&: 2 * 84%
8 0$: : u*
:; 97'%
7'%
%
+
b 2
H
E
7I
$K
,
35 35
,
)
$@
8 33 0:
:
$@
$"
35 3 : @
;
,
;
;
35 8 (%
BW0;G?PQQPQ?W
,
'
^
35 35
A) c
&+
c
):c
)
@
35 35
@
Z
c
%
,
Labeling Tree
Cake
label: 00
010
011
10
11
0
1
1
0
0
00
0
1
1
10
11
ÆÅ _vÈ
Åå¶QÈ
¨ 3¨ ÅÆ_ŠÈÛÇst_g¶5]Hst]N­?^Q_`ba<oxa<opevdC²›Åå¶QÈhjeg`b`<]Nrb^5egdQ­7otdE¬st_g¶5]Nspopd3¬Xab`<]N]g²
010
011
" '= $
*:
3 :; ;
*
3 :;
.Nu
35&D 3 *3 6*
íû?6O4 ;>MO4 FHMC'RF”'/)Y'*ü›û),ûg2(Lg'*-Eû8bLK5F>F>+,6O1/'7).1E47WH+tFHMO= L'76(ü›ûKC;>ûg2PFH4P;G4EWGF
úZ43;G+.F>+,þ7û25+Y;<FH+.6ZL}F”+,6EFHû1EûWN;
Ti4W>ûg),'*F>û?;G4EWGFH+.6O1F>4PLg'*-7û8:LK5FGFH+.6C1C@ Dû CWN;GF
25û C6Cû¯' G),ûg;H;°FHMC'*6 ”W>ûg),'*F>+,476 Æ47W¾úC+.ûvLûg;gT79 '76C2 '*WHû ;GûgúC'*WN'RFHûg2£@*F>MOûg6
+ ¯+Y;D4E6´FHMOû¹),û åF!
4 TCBD).ûv'*WH).[E@3F>MO+Y; ”WHû)Y'RFH+.4E6´+,=ú›4E;>ûg;'F>47FH'*)U4EWH25ûgWD4E6'763[ ;GûF
4 j;>ûúC'7WH'*F>ûv2´úO+,ûgLûg;gT KOW '7úOúOWH4E'7LNMº+,;JFH4?;>MO4 ÝFHMC'RF!1E+.þEû6 ú›4E;>+tFH+.þEûÁ2O+,;GF>+,6CL}F
+.63F>ûg17ûgWH;g@ Jû¹Lg'*6/L476Z;<FHW>KCLFDK5FH+.),+.F<[ ÆKO6CLF>+,476C;;>KCLNM´FHMC'RF!'*6Q[ œ'*+,WJ2O+.þQ+Y;G+,476 !+.),)£'*),).4 KC;°F>4”;>47W>F°F>MOû!+,63F>ûg17ûWN;
T ¹û Z6OûF>MOû¯K5F>+,).+.F<[ ÆKC6CL}FH+.4E6C; Ý=?+.6 }@
Æ47W KC;>ûW GTC9b
6 !MC'*F Æ47),).4 ;g@ !+.),)i'7) 'Š[5;W>û ÆûWFH4F>MOûK5F>+,).+.F<[ ÆKO6CL}FH+.4E6C;¯2Oû C6Oûv2
'*ü›4Rþ7û7T ûF T 6C).[PúO+,ûgLûg;ÁFHMC'RF4Rþ7ûgW>)Y'*ú ¾MC'ŠþEûú›4E;>+tFH+.þEûþR'7).KOû Æ4EW
KC;GûgW T
BD476C;>+,2OûW'*6Q[ 8AúC'7WGFH+tFH+.4E6
@m;>KCLNMÇF>MC'*F´ûg'ELNM MC'7;'ç6O4E658 ûWH4
þŠ'7).KCû Æ47WFHMOû(WHûg;>ú›ûgL}FH+.þEûPKC;>ûW T ûF '
üZû(F>MOû0WH+,17M3F>=?4E;GF´úO+,ûgLû04 F>MC'*FJ4RþEûWH),'7úC; :T MOû¹4EWH2OûWH+.6O1WHû)Y'RFH+.4E6476´úC+.ûvLûg;D6O4 Ý+,6C25KCLûg;J'*6´4EWH2OûWH+.6O14E6
úZ4EWGFH+.4E6C; + ¾'*6C2/4E6O).[+ ' '7T ûÿQFg@ Jû”;>MO4 ÂFHMC'RF FHMOû”4EWH25ûgW!4 °F>MCû
úZ4EWGFH+.4E6C; °+Y;!WHû)Y'RF>ûv2 !+.F>M/FHMOû47WN25ûW
4 iFHMOû+.63FHû17ûgWH; GT
E
%
f;?PQQQ?f ^
*)
I
1)
)/;
&K
<)<;
:)
-)
€)<;7G0)
1IG4K
(%
`c
Sƒ*%
c >
u
3 y *)
e c
x
x
e c '#f0+ >
' ?% f +
*)
"$? c
s` c
_
0W ; ?PQQPQ*?Wj^
U` c
c
0W
W
c
bW
c
c
"&? c
W_chGHW
sW_c
7chG
‚fc
$ $
W.;G?QPQQ?W ^
8 : ;
^
;
;
?
P
Q
Q
*
Q
?
9
f
/
c
_
G
@
f
8
e
e
$@:
&3 8sWaG.W_c ;
MOûä47WN25ûgW>+,6O1
8 :
3 7
&
8 0$
WHû)Y'RF>+,4764E6úZ4EWGFH+.4E6C; Lg'*6ü›û KC;>ûg2 FH4 ;>47W>F F>MOû 8AúZ'*W>F>+.F>+,476
@E+ÃT û7T,@ Z6C2F>MOûÁ;Gû 3KOû6CLû!4£+,6C25+YLûg;
@3;GKCLNMFHMC'RF D1
T ¯6 '7úOúO),+,Lg'RFH+.4E604 û=?='ºF>MOûg6(17+,þ7ûv;!FHMC'RF 21
@
F>MQKC;;>47W>F>+,6O1¯FHMOû!úC'7WGFH+tFH+.4E6+Y;°û 3KO+,þŠ'7).ûg63FjFH4;G4EWGFH+.6O1¹F>MCû!+.63F>ûg17ûgWH;gT íû6O4 ;GMO4 ¸F>MC'*F
+iF>MOûXúC'7WGFH+tFH+.4E6º+Y;D)Y'*ü›û),ûg2@ DûXL'76ºKC;>ûÁF>MOûÁ),'7üZûg),;JFH4;>47W>FJF>MOûXú›47W>F>+,476C; 3KO+YLN-3),[7@
!MO+,LNM+,6ºFHKOWH
6 !+,),)'*),).4 KC;F>4;>47W>FF>MOû+,63F>û1EûWN; 3KO+,LN-Q),[7T
W
; ?PQQPQ?Wj^
!"!"! G W c# 0@
%
)
Cq ; ?QPQQ*?q ^
4W
af c
J
GE
c
f c J
‚W
GjW c G
!$!"! J~f c%#
c .
$ $
5 $
: &:
= !
53 35
&
3 2
%
&
:; W ; P? QQPQ?Wj^ :. 6:; 8 0* $$:; ;
:
7' +
F :
ID[ ûg==' O@E;G4EWGFH+.6O1ÁFHMOû!úC'*W>F>+.F>+,476
Ý+Y;û EKC+.þR'*),û63FFH4 ÆWHûþ7ûgWH;>û i;>47W>F>+,6O1
F>MOû?+,6EFHû1EûWN;
T OWH47= û=?=' Z@ Jû-Q6O4 F>MC'*FÁ+mFHMOû œ'7+.WLg'*-7û8:2O+.þQ+Y;G+,476
+,;J)Y'*ü›û),ûg2£@QFHMOû6DûXL'76;>47W>FDFHMOûXúC'*W>F>+.F>+,476+.6 mF>+,=ûE@!MOûWHû +Y;DF>MOûX6QKO=ü›ûW
4 úO+,ûgLûg;D+.6ºF>MOûXúC'7WGFH+tFH+.4E6T M3KZ;@ Jû¯47üOFH'*+,6´FHMOû Æ47),).4 !+,6O1”FHMOû4EW>ûg=@!MO+YLNMºWHûg2OKCLûv;
;G4EWGFH+.6O1$F>4´Lg'*-Eû8bLK5F>F>+,6O1 -W
fd;?QPQQ?f ^ =,
; ?QPQQ*?NW_^
!
7'
+
'
+
" '= $ 4U 35 : 8 :/
fd;?QQPQ*?f ^
7' + #( ' y 6 #( 7 0 : 3 8 8
:4
3 + *&/e ;?QQPQ*? e ^ : 5 /
:; $B&
*:
;
'(0' %P'
MOû4EW>ûg= í;>MO4 Dûv2çF>MZ'RFûþEûWH[çLg'*-Eû8bLK5F>F>+,6O1í'7).1E47WH+tFHMO=L'*6ÇüZûPL476Qþ7ûgWGFHûg2çFH4
'*6 û 3KO+,þŠ'7).ûg63FX)Y'*ü›û),ûg2 L'7-7û8:LK5FGFH+.6O1P'7).1E47WH+tFHMO=T J+.=?ú›47W>FH'76CLû?+Y;ÁF>MOû´L47=?úO),ûÿ5+tF<[
4F>MC+,;/L4E63þEûWN;G+,476T íû ;>'Š[ F>MC'*F/'¸Lg'*-7û8:LK5FGFH+.6C1 '*),174EW>+.F>MO= F>MZ'RF4EK5F>úCK5FH;'
L'*-Eû8b25+,þ3+Y;>+.4E6 !+tFHM úO+.ûvLûv;D+Y;
+j+tF!L'76ºü›ûXL476Qþ7ûgWGFHûg2FH4'$),'7üZûg).ûv2
'*),1747WH+.F>MO= F>MC'*F°4EK5F>úCK5FH;¾'76$û 3KO+.þR'7).ûg6EF¾Lg'*-7û25+,þQ+,;>+.4E6 !+.F>M júO+,ûgLûv;°KC;>+.6O1'*F
=43;<HF ûÿ3FHWH' F>+,=?û7@Š+ÃT û7T,@Š+ Z+tF°L'*6$üZûJL4E63þEûW>F>ûv2ÁF>4X'*6”û EKZ'*),).[Xû=´L+.ûg6EF°'*),174EW>+.F>MO=
F>MC'*F47KOF>úOK5FN;ºûv;>;>û63FH+,'7).),[¸FHMOûí;H'*=?û(25+,þQ+,;>+,476T 4¸4EKOWº-Q6O4 !),ûg2O17û7@D'*),) F>MCû(-Q6O4 !6
L'*-Eû8bLK5F>F>+,6O1?'*),1747WH+.F>MO=;'*WHû¹),+,6Oûg'7W>),[38A)Y'*ü›û),ûg2£TQ9b6úC'7WGFH+,LKO),'7Wg@ ¯).1E47WH+tFHMO=; '76C2 L'*6ÇüZû/ûg'E;G+,),[¸L476QþEûW>F>ûg2ýF>4 ),'7üZûg).ûv2 '*),174EW>+.F>MC=?;$KC;>+.6C1 '*F=?4E;GF 'E2O25+.F>+,476C'7)
47ú›ûWN'RF>+,476Z; FH4/4EK5F>úCK5F”'*6 û 3KO+,þŠ'7).ûg63FXLg'*-7û8:2O+.þQ+Y;G+,476T S5+.6CLû;G4EWGFH+.6O1+,;XWHûg2OKCL+,üO),ûFH4
),'7üZûg).ûv2L'7-7û8:LK5FGFH+.6O1Z@g)Y'*ü›û),ûg2L'7-7û8:LK5FGFH+.6O1ÁL'76O6O4*FjüZû œ'E;<FHûWiF>MC'76;>47W>F>+,6O1CT ûDMC'ŠþEû
F>MOû Æ4E).),4 !+.6C1WHûg;>KO).FgT
E
7'
3 0:;3 35 35
t
7'
+
+
@
7'
+
E
" '= $
&4
# 4
@ 'S "$ % 7 3 :; : &*: : 3 7 8 5 33 : u*
: ;
C' ( '
'
: ? 3 0:;3 *& 8 : 5 %).4E1
OWH47= F>MOû$úOWH'EL}FH+,Lg'*)ú›47+,63F¯4¾þQ+,û%476Cû”=?+.1EMEFÁ).+,-7û”F>4º),+,=+.F¯FHMOû$'7=?47KO63F¯4
L47=?úOK58
FH'RFH+.4E6ºFHMOû;GKCúZûgW>KC;>ûWJ+Y;!'*),).4 Jûg2?FH4?KC;GûÁ+,64EWH25ûgWJF>4?25ûFHûWH=+,6Oû !MC'*F!LK5FH;'7W>û¹F>4?ü›û
=?'E25û7FT 3m'7LNM?;GF>ûú?+,6F>MOû '7).1E47WH+tFHMO= +,63þE47),þ7ûv;j'LK5Fg@E'*6C2?L4E=?úOK5FH'*F>+,476C;°6CûgLûv;>;H'*WH[ Æ4EW
úZûgW Æ4EW>=?+,6O1?F>MOû$LK5FvT ¯=4E6O1?F>MCûg;>ûL4E=úCK5FH'*F>+,476C;!=?+,17M3F¯ü›û$L47=?úC'*WH+Y;G4E6C;@5+AT û7T,@OF>MCû
;GKOú›ûWHKC;>ûW =?+,17M3F¹L47=?úC'*WHû”LKOF¹ú›4E;>+tFH+.4E6C;T JF¹;GF>ûú ? @C),ûF -C25ûg6O4*FHû”F>MCû”6QKO=ü›ûW¹4 L47=?úC'7W>+Y;>476C;múZûgW Æ4EW>=?ûg2T MCûÁ'7).1E47WH+tFHMO= +,; + C C
Æ47W'ýL476C;GFH'763F '76C2Ý'*),) T 3m;H;Gûg63F>+Y'*),).[E@F>MOû(63KC=ü›ûWº
4 ”L47=?úC'7W>+Y;>476C;+Y;´),+,6Oûg'7W
+.6ÝFHMOû06QKO=$üZûgWº4 LK5FH;gT MCû()Y'*ü›û),ûg2Ý'*),174EW>+.F>MC=?; '*WHû "'7W>ûPûv'7;>+.),[ ;GMO4 !6 FH4
üZû´L47=?úC'*WH+Y;G4E658Aü›47KC6C25ûg2T û?6O4 1E+.þEû$4EKOW),4 DûgWÁü›47KC6C2 476íF>MOû?6QKO=ü›ûW4 JLK5FH;
W>û EKC+.WHûg2 Æ47W!),+.6Cûg'*WH),[E8:)Y'*ü›û),ûg2ºL47=?úC'7W>+Y;G4E658:üZ4EKO6C25ûv2º'*),174EW>+.F>MC=?;gT
35 35
91'%
8 :
% +
*
&:;&
,
0@
0@
ng o:;
&:;2 0
,
0E
" '= $ 4 ' 4' ( {' '
$ = #%&'( 4' ( @'= "$ % 7
: 3 7 8 0$
: 3 :; &:;2 0 8
*
5 33 ;
:
%).4E1
ô óçômö¯ñ¹õ Hômó Pñ
!ó ¾ô¾óCø<ò íû 1E+.þEû).4 JûWü›47KO6Z2O;¾4E6$FHMOû 6QKO=$üZûgW¾4LKOFH;WHû 3KO+,W>ûv2 Æ47Wm;GF>WH476O1'76C2;GKCúZûgW¾û6QþQ[38
ÆW>ûgûD25+,þQ+,;>+.4E6@ !MOû6;>KCLNM2O+.þQ+Y;G+,476C;iûÿ5+Y;<FvT û;GMO4 FHMC'RFjF>MOûgW>ûDûÿ5+Y;<FjK5F>+,).+.F<[ ÆKO6CLF>+,476C;
F>MC'*F¯'725=?+.F¯'7LLûú5FN'*üO),û25+,þ3+Y;>+.4E6C; Æ47W !MO+YLNM 9 LK5FH;!'7W>ûX6Oûgûg25ûv2£T
?13 :;3 35 35 8 : 5 91'%
% +
>
$
H
E
F
E
1'%
" '= $ 4 ' C' ( {'r% S'(
3 7 8 0$ 8 : 5 +
1;: (d"d= *2) 8 : 6
" '= $ 4 ' 4' ( {' 2% 8 *& 8 : 5
+
g"$#%&#'( 7 9 $
: % +
9 '" Q "F
:Nu
: * 7
2
(d"d= :
#"$#%&#'(
7;
$: *2) 8 : 7;
: u
: ;
7 9 $
:
97'" Q %
+
;
; 3 *
;
í ôDñ¯÷ Gö¹õ¯ø>ñ °ó
MOûD=?43;<Fj17û6CûWN'*)3W>ûv;GKO).FH;j'*WHû¾FHMC'RF'*6Q[L'7-7û8:LK5FGFH+.6O1Á'*),174EW>+.F>MO=%L'76ü›ûJL476Qþ7ûgWGFHûg2ÁFH4
'!;G4E).+Y2XúO+,ûgLû¾'7).1E47WH+tFHMO=@'*6Z2¯FHMOû6”F>4 '!)Y'*ü›û),ûg2X'*),174EW>+.F>MC=/T íûFHMOû6”;>MO4 Jûg2¹F>MZ'RFi'763[
),'7üZûg).ûv2 œ'*+,W¯L'7-7û8bLKOFGF>+,6O1´'7).1E47WH+tFHMO= L'76üZû”KZ;Gûv2/F>4º;>47W>Fg@5FHMOûWHû Æ4EW>û'763[ œ'*+,W¯L'7-7û8
LK5F>F>+,6O1 '7).1E47WH+tFHMO=L'76¸üZû/KC;>ûg2¸F>4í;>47W>FgT MO+Y;úOW>4RþQ+Y25ûg2ýF>MOûL4E6O6OûgLF>+,476¸ü›ûF Jûûg6
;G4EWGFH+.6O1ç'*6Z2 L'7-7û8:LK5FGFH+.6O1ZT íû0'7),;>4(úCW>4RþQ+Y25ûg2Ç'*6 +,6C25ûgúZûg6C25ûg6EFº;GF>WH476C1(WHûg;>KO)tF Æ4EW
úOMC'7;>ûg2('*),1747WH+.F>MO=;g@O6C'*=?ûg).[/F>MZ'RF 9 %),471 LK5FH;Á'*WHû”6Oûgûg25ûv2F>417KC'7WH'76EFHûûûv'7LNM
KC;GûgW'¯ú›4E;>+tFH+.þEûþŠ'7).KCûg2”ú›47W>F>+,476@*'*6C2 Dû'*)Y;G4Á47üOFH'*+,6Oûv2 9 iüZ4EKO6C2O; Æ4EWiF J4¹F<[3ú›ûg;
4û6QþQ[38 ÆWHûû”25+,þQ+,;>+,476TZ9b=ú›47W>FH'763F¯47ú›û6 3KOûv;<FH+.4E6C;!WHû='*+,60'*6C2 Jû”WHû ÆûgW!F>MOûW>ûv'725ûgW
F>4?F>MCû¹FHûgLNMO6C+,Lg'*)WHûú›47W>F '*6C2FHMOû).+.F>ûgWH'*F>KOWHû Æ47W!=?47WHûX25ûFN'*+,),;gT
ó ñ¯÷
{ ²·¾7²oxa<jy?_]H`<d*¶Qa<_oxd3a<sp]N]Nsåc²]N
dRa<_grNc²]H«Æa<yE]Neg`<]Ha<opn_sp¬vÌeg,`<éoxa<t€yE"!c*rXË #fY!%eg$`#&*fY_g€ ox`{ !"_g!"d3#*­í² r:ab`<egd3¬vsxwPfY_gox`n}_gªŠ]­Eop®*oprbotegd
„ ²7, ²'ÍQ°Ì"_- `<¶Q, _èvd3è.]N-såt²O€ l*{ !"k3/*^5Ë ]H#+`U0%$]Nd*®*| w*€ «Æ{ f,!"`<]H!]°7²n}_gªv]­Eop®*oprbotegd_gd3­¹opdQ­7]N^5]Nd3­E]NdEnN]jefOc]}_grbk7`<]NrN²)(*Ì+,é
&7²¯lRºa<]NÌ®Š,é]N)d11E²2gÍ4i,`Gé*_g Îgc€ r {}|v_„ dQË ­!%$ ÛD{}~ spst€ _gd/{ !"\%!"#*² U_NwEspe`}²ÛDdº]Nd*®*w*«Æf,`<]H]Án}_ªŠ]”­Eop®*oprbotegd/^7`<ega<eRnNegsƲ , 3
0E²¯lRK¾a<ë>]NêL®Š"]N d5EE=g²ÍEi²°`G_h°c_cÁr£_g¶7d3`<o.­¹­7¬vÛm]!sps.³D_d¹d3op\¹®Š]H²`<Urb_NoxaAwEwspeu£`}`<²7]N6ZrbÌrN€38:‚J9]H·¸;Yƒiê<=egg`<Í.ª5>'€76)‚D8?+ƒÁ@€ { !"Ì%!"AŠ*²ëBCDEEYÍGF5HI9JYêÆè7Ãë
#*²¯lRºa<]NÌ^3,é3yEëL]Nd¯Ì+\E=]NO<cÌ"QªŠP7eD_gOd3ÆÌ"­XQ°P7y3Oœ]Në>e*Í.­7OGegë>`<ê<]¾€ uU{ EŲMJ„ È>opspË sÆ{ ²70GNi#R$*»R#kE~ opaG€›_ÀJ¶3spnH]¾a<ev­E¶5opr:]Hab` `<op{¶3! k7~ga<~ opev² dXef5opdQ­Eop®*oprbop¶3sp]ev¶*Ü:]Nn>a<rN²
7²S~ ²QË N¾{ $ ²C{ \/R€ kE{¶3!opd3r!{ ² _dQ­1N¾²)M¹²›l*^Q_gdEop]H`}²TMDe}·Ýa<enNk7a¯_$n}_ªŠ]Áfå_ox`<spwR² , UVÌ+,éV1gÍ4,é* Îg€
/*²vl*_gevnNspevegc¶Weg
JdQst\ rm_XN­E]Hop`sp]Nc_gd3c”­ý_7hj²_y3^¾opdE̬g”«Æa<ë>ePê!ÌgÛDÍ5spìa¶5]H`b`ba$O<gî?Í7_*T²YEOJNcJÉë<nHéEot]HÌ+d*;a$=8G_€ stspeR{ Å=n}&v_È>a<Ë op„vev„ d¸&$ eg„ f¯&"_[&7€ Z {^7! `<~o-XH!*]"² \:$[]!opdE¬
~ ²¯_hi^3«d^7e`<MJeŠ_g_vnG_y¹ªŠ]va<eJ€›îdE«œ²2^3st
¹_NwR²›]HqD`£_gfY_goxa<ox`byZ«Ã€Z­E_op®*dQot­ rbopeg© d²2^EN`<²Uev¶El7spkZ]N²TcjrN²Qot­3P7­7opOd3Ƭ$Ì")f,›eg` é4]N=d*OG®RëDw*Ì«ÆÍ5f,`<ìg]N]NfdE]Nërb hNrNÌ+ËZ8<Û ë>€v›^7`<e!eR_gnN^E]}­7^5kE]}`G__g`}s²
!7²g,Í]HFg`<XHêJw3lhSC]N,é3¬vk7ë a°, _”dQ­ÁëL8CÊý=O<ÌgopspÍmnRXQw7i dEÌrb,ª7é3oåëL²ZXÀJÌ^7E=a<O<otÌ"c”2_P7sE^3O_œëL`båa<Îoxa<€ opev{}dE| 03otdEÅ ¬{ È>egË „ fZ_„ $ c„ ]}+0_gErb€›k3l7_]H`<^E¶Ea<st]¾]Nc¹rb^3¶5_g]HnN` ]v²Q{ ! jk~v8?~ ² OGë<ëbì"B
{N| ²¯opî?r!_dEspegotªºa¯î?_^E_¬Šot]H­7nNev]XdEeg«œzÃf°rbc”n}_g_gªŠop]gså€U²”hj›eg]Nr:nGaGy3_gdErotnNj_gkEsrbqDn>yC]N€C^5_ged3`ba ­/|Šî„ « kE{ª7„ ªg€›_gqDo2]H]d3`<rbotrbrb]NyEst_gdQ]>_`ÁcuUeRegegsx`bw7a<a<yR]HwRn>² yEd3h°op_nXªŠzA]HdE«œr:nNa<kEoxaba<a<kEopa<dE]v¬ €
{g{ ²CNº`<spopÌer<FŠwR_?̀7nuU‚mYÍO]Hƒ a<ë>]H€3`<{ÛDrb„Reg{}^7d~g`<|op_gs €5d3„³­ |vlE|Š© „Û¯²²Q€ N„|v²›|Šl7„ kZ² ² © egkE`b«œ^5]H`<rbegd/]Nd*®Rw*«œf.`<]N]¯n>yEeg`<]­7ot®*oprbopevdC²UÌ+,é3ëLÌEEOHê
{}„ ²J]Xq `¾²ŠìqDÃ]Nëb¶EìJc”rHÎI_gdCKJ²QGMDsJe}g·çÍ3êLa<rGe¹ëL8=¬gFR]HëLa!8dtÅÆ_uavZspéE]}ë:_gr:ºa>ȰÌ_!,é3fåëL_op`¾Ì+rbEy3=O<_Ì"`< ]D, egê<f›êLa<yEOÆ]DÌnNE=_gªŠÍo]v²:wh YÍo, º”ëLÌ8C,é3=O<ëLÌg€^QÌ+_E=¬vO<]NÌ"r 7„vjp„ $G&'Á/Rê €
{ &7²d*v{ !'_gkEnG/+cÁª/!7¶5² qm]H`jev¶5egf]H`bnNa<k7rba<egrNdí²x_(*dQk­+ÊçJotè)spspkot_gvZc é3ë?Ê8G]NÎg¶E€¶Z/ ²´„ Å Ûm„ È>^3Ë &^E0 `<|e}$Ú7&+opc”0"0E_€ a<op{ d3!"¬$!"#*få_g² ox`X­Eop®*otrbopegd0·¾oxa<y(_?spopcopa<]N­
{ 0E²vÛ _g²*nG]Xª¯²QqmuUev]H¶5a<]>]>`b`<a<rNrb€3ev‚Jd__abdQa<­¯opn>ª5Êç€Qotî?spspotÛ¯_gc݀ { Ê!! ]H~ ¶3² ¶Z²VÌ%AŠëB<DEEYÍF , F'+8L,éGÁê>cDë6›Ìy8:zyha{.+mÌgÍ3²
{{ 7²#*²JM¯© ²*²3Nl*a<²E]Nl7opd3kCy3²›_gqmkE]NrNdR²aG°_gs5y3y3]!_^E`<`<cegeg¶3d*sp]NwOc Ë7l*e^5fU]Hfå`<_d3op`J]>`­E\ rjop®*st]Hoprbcopevc”dZ²_ `xopdO<gfå_Í.ox`J­7ëLop®7E8LopErbOGopevÌdC€ ²{ *Ë, {N|7ëL{ 8L$ ={}O<| Ìg0EÍo€ { !+Ì0 ,~é3²ëLXÌ=B
{ /*²5d*
JEOGkE]>ÌcÁ`<.yQ1¶5_]H`G` ­|Íe,Eé*fJ²O ÎnNÊk7€ a<{NeRrN| ]H²/*ˬvopzÃ!d3d}& ¬g| ]H`p$`}!²X0 8wÛm„>èE€ dºëb{ Ìg_g!Í^3!"^7!7P3`<² Î+e}JÚEopè*c”_êCya<*oteg~d´grbn>Í yE]N, c F']¹8Cf,eg,` éÁn}_ê ªŠ]Xq `k­7P ot®*, oprbtop€ev^3d´_g·¾¬g]Noxa<r y~ _”!%$stGopdE! ]}|7_{ ` €
„|v|v„ ²
0:
s
E
E
7'%
%
+
7'%
"
0 N d:
+