Affine Models of Currency Pricing: Accounting for the Forward Premium Anomaly

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1 Carnegie Mellon University Research Showcase Tepper School of Business Affine Models of Currency Pricing: Accounting for the Forward Premium Anomaly David Backus New York University Silverio Foresi Salomon Smith Barney Chris I. Telmer Carnegie Mellon University, Recommended Citation Backus, David; Foresi, Silverio; and Telmer, Chris I., "Affine Models of Currency Pricing: Accounting for the Forward Premium Anomaly" (1998). Tepper School of Business. Paper This Article is brought to you for free and open access by Research Showcase. It has been accepted for inclusion in Tepper School of Business by an authorized administrator of Research Showcase. For more information, please contact

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9 _æ) B ; ƒ ; ƒ Ú ƒ { ŒŽ;Ṽ (eµ5 ) ½Ṽ )ƒ5 M _ > µº» ÀH µº»"µjº<» #µ\ 5Ž) ƒˆt j Œ M B H J Š j Œ M ñ ; ~ 6ƒ {å ) 3 ) ƒ ;ƒ@ Œ ƒ e _ J ¹ 'Ž; ' ; 5 ƒ5 c ) ) V B 3 Q 5 ;š@ƒˆ5 5 Œ M «I µjº<»5µj µº» µ; 5 ;š µº» µ ƒ ) M _Å\ _ Œ _ 2 š@ž) ;š) j v ½ j ;š2 B 5 2 ; _ƒ ; Ž; _ šÿ = ƒˆ+ ) 3ƒ V ) B Y Œ»ÇƒD ƒv Œ ƒ5 V ) 3 _æv M Œ Œ ) Ÿ J V B Q 5 Ž) 3Ž; ) š@ƒˆš Œ M ) Œ MṼ ) B ) _ K ~kƒ[ { Q å ¾Ž@ m m _æ) ) Œ šš [ c Œ Q 5 ) Œ M _ gƒ c Œ M ) BŽ) Q m ; ) ƒ ; J J Œ ƒ 5 ;š V ) åš@ B ) V Ṽ ¹ j Œ ƒ 2 Q 5 ÁÀ& Œ Q j g ; š» * V ) 3 W» ƒš ) ¹Ṽ ) 2 B V ) _ ¹ Q ) V Œ B v ¹ m Œ@ˆŠˆŠ B V ƒ5 c ) 3 ) Bƒ VT D B W» B B 2 ) b Œ»ÇƒŠ _Ž) V B ;Ṽ {å ) ½ B ; _ 3ƒ5 ) ) ƒ Dƒv Œ ƒ 2 M g ; 5» 3 B 5 m»y H) ÇṼ )ƒ@ƒv Œ 3 5 L ; 5 Y j Œ M ñ ; ~ 6ƒ 5 ;š ~ `ƒ žž) ) ;ƒv Œ µg ; Œ V šuµ{ V ; 5 j Œ M ñ ; ~ 6ƒ µ )Ž) š@ B ; 5 Q = ƒˆì~ 5 _ 5 B ƒ M ~ µº»3 µ ƒ À~ µjº<»? µº» ƒ N3O;PRQ S Ë ž5 ; _ 2» T B 5 Æ B š@ƒ5 J M 5 Š B Œ Å};ƒ5»½ ƒ2 ;ƒž) ;š) µ{ 5 ;še [ M _ T B _ )µ\ ¹ b B Vƒ ˆŽ; Œ 5 ¹ W ` Á«µT µº» Í µº» À Áµ µº» ~ µº» Gµ ƒ Í µjº<»! À Á«µP~ µº»ílµº» ƒ À Áµ µº» ~ µ Gµº» ƒ Ílµjº<»! À Á«µT µº» N O;PRQ S Í µº» Á«µT µº» NVU OPWQ#SÍlµº» =ƒ { H J ) ` ' B Ž) ; =Í j ;š2í ÞY B T Ž; T j B V ƒ µ5» Ç B j T 5 Œ M = V ) Ç ) Vƒ ;ƒv W Ṽ )ƒvƒ@ ) Šš[ JÅ\ B =ƒ _ 2 ) Œ MṼ ) 2 B ) _ <X µjº<» ÀY µjº<» _æä ~ M µº» ƒ M ) ` ƒ[ˆ ) Y ) ƒ Dƒv Œ ƒ M g 3 ;ƒ@ Œ ƒ Šƒ Š )Ž) _ ; W ) b ;ƒ5» B c ; 5 Œ Œ Y )ƒž) [ ) V ŒŽ)ˆŠ Á = Œ M _ Œ Q š@ ¹~Œ ŒƒˆŠ ƒ [ Œ B Q Bµ ;Ṽ Ž;š[ ) Š _Ž) V B ;Ṽ µ5 ù j ¾Ž; H J ƒ3 ƒ[ )ˆŠ B v _ MṼ T _ƒv Œ Q ƒj F ) Š ƒ@ƒäš) c [ _ ƒv c Œ ù [š ƒš@ B ; 5 VŽ) = ƒˆ )Ž) QṼ ; ) ;ƒ5» B Y ; 5 Œ Œ ~0ŒYƒj J ; _ Mš& 5 ;šn ' ) ; H kµ Ü 6 ` 6ƒ 5 ;š )ƒv Œ ¹Ṽ e )Ž) ³ Ṽ ; ) T Dƒ5»Ç B ; 5 Œ )ƒ5 Mš) Y _æ; _ Œ Å~0Ž 5 ) 5 ;šòš{ ) B \µ Ü 6 8 6ƒ ~ `ƒ î ï[z \K] }V^T~U}6ù&_e~D 6 ;z2~ô*ù`_åókz9a ò }6 bóñü b z À& Y B 5 b )ƒm» _ M 5 ) g Œ M Œ ) V Bˆ Ž)ˆ š@ ( ; ) š v Ú 5ˆT ' ƒ ) ƒ ; B V Œ ƒ5 ; ) { Œ» ƒ ) Œ MṼ ) B ) _ M B Šgƒ ; Mš@ B Ÿ =ƒ»y 5 Qš Q _ 3 Œ ; Ṽ J = ) & 5 š) 5 V 2 ' ) Š _æ; ; 5 ) [ º j e Ü ƒ5 ƒ ) ;ƒ[ž) ;šæ 5 ;š0cªµàö _æä ª~0 µ ƒ š@ƒ5 J M 5 Q µ\» & V ) =ƒ»y 5 _š2 Q 5 V BcªµY Œ B 5 3š) 5 š 3 ) )ƒ Q j Œ ƒ Ž) Œ Q M T Q [ _ Œ D Ṽ k ; e ) B Šš@ƒ5 J M 5 T B };ƒm» 5 Šš) 5 V ¹ Ü ƒ5 cªµb¼dµº»h ž5 ; _ b ' )ƒš ; H@ˆŠ B v _ Y 5 Yš) 5 e _µ) ) Œ MṼ ) 2 _ M 5 Œ ƒ ˆ~ Aƒ ³ÀÈÁ«µfeg µº» ~ cªµb¼$µº» ƒh Ë ' Mš[ ) j ;š2 5 ) z Vƒ ;ƒv W ƒ[ Ü µ@» l ; ;š ~ c µ µ ƒ Á µ ~ µjº<» ƒ ÀÛÁ µ ~ µº» µº» µ ƒ ÀÛÁ µ ~ µº» ƒ Ë

10 À ) =ƒ»y 5 QšŸ ) Bˆ Ž)ˆ¼ M µb¼ˆ µ À ƒ Áµ µjº<» ¼ ƒ Áµ µjº<»&ë M ¾[Ž; 5 Œ ƒ & 5 ;š*š@ ( Œ ƒ ; ƒ5 { ) Š Œ )ƒ V Y Q 5 eÿ ¾[Ž; 5 Œ ƒ ˆ~ `ƒ =ƒ ½š@ƒ[ˆŠ Œ Œ M b Q 5 5 ;š 5 5 ; H ƒ ƒ[ž; 3 _ M 5 Œ ƒ =ƒ ) Ÿ =ƒ _ Q 5 h µá 5 Ž; 2 µ ¼ )µeà ½)µ ¼ ½ µ µ ) Ÿ jˆ J M 5 _ƒ5 B B Œ Y _ 5 3 ; 5 Œ Œ2 _ƒ ;š[ Œ ƒ \ 'ƒ5» _ƒ ; W ¹š@ B Ÿ ) _ƒ[ˆš ;ƒ ) Q bƒ5 ½ V ) Š =ƒ»y 5 Qš$ ) Bˆ Ž)ˆ* ˆ{ ) 2 _æ) ; _ š _ 5 Šƒ5 š@ B ) Ṽ M 5 Œ ƒ M Bµ@ = ƒˆ ~ 8ƒ µ Ñ(µ Ô Á«µ µº» ¼É )µ ÀÈÁ«µH ƒ[ j µº» ¼ˆÁ«µ ƒ k µº»&ë * Œ B * V ; 5 Š ) ; Q Šƒ5 Ú 5ˆT _ƒˆš ;ƒ[ ) B v Q ¹ Ÿ ) eš[ Å\ B B ; _ _ƒ ;š[ Œ ƒ ; H ˆŠ 5 ; åƒ5 ù V ) ƒ[ v 5 Œ )ˆT åƒ5 ù V ) 3 ) Œ MṼ ) 2 [ B ) _ M B X{å ) 3 Œ M Œ 2 ) Bˆ Ž)ˆ¼ ¹ µ@ ` Vƒˆ ~ ß µ Ü ƒ µ ÏAµ À ƒ Áµ µº» ¼ÉÁ«µH ƒ[ j µº» ¼ ~= ƒ XÁ«µ µº» ¼ˆÁµH ƒ k µº» ƒ Ø ) ½š[ JÅ\ B B ; _ 3 D B W» B B ) 2ìV ƒ bƒ5 \ ) Y _æ) ; _ Q j Œ ƒ í 5 ;šš V ) 2ì_ _æ) ; _ Q 5 ƒ[ Tƒ5 \ ) å ƒ[ Pí ƒ5 c ) 3 ) Œ MṼ ) 2 B ) _ M l 5 ;š5 e š)š[ Œ ƒ ; H { Œ Ž; _ Ž) V 3»Ç B 5 2 ; ˆŠƒ[ Œ ; Ṽ o Š j ;ƒž) Y V ) 3 k _ ƒ Q å ; 5 ½ HÅ\ _ ) 2 Œ M Œ ) Bˆ Ž)ˆ* Î j v& Dƒ )Ž@ M 5 ˆŠƒÄš@ _ M ƒj œ Dƒ ;š 5 ;š _Ž) B ; _ ) ¹ _ µc ;Ṽ Ž;š[ ) ) 2 HÂT ) 2ˆŠƒ)š@ _ M» T _æ; 5ˆ ) * Œ )ƒ[ Œ µ{ Œ Q j» _ƒ[ ;š[ ƒ[ ; H J " ƒ ³= )ƒ ˆ H Y ) Œ MṼ ) B ) _ M ù ƒ[ m µjº<» 5 ;šÿ ƒ k µº» 5 _ƒ ;š[ Œ ƒ ; H J * )ƒ[ ˆT H U» ˆ~W V ƒ ˆŸ 5 ; l~n» µ Ø no» µ ƒ 5 ;š5 5 Œ M 5 ; _ y~nb µø n µ ƒ cà M Œ Ž; _ Ž) V µvƒ[ ) B³= ; B Œ ƒ)š* Dƒ ;š2 ) ¹ _ 5 5 ;š ) b Œ M Œ ) Bˆ Ž)ˆ M Á«µ µº» À _æ) e~nb» µ <nb µ ß8ƒ Á«µ µº» À _æ) e~n» µ <n µ ß8ƒ ~ Ü ƒ ~ ÜÜ&ƒ ~ Ü ß`ƒ ÏAµ À ~n µ ¼pnB µ ƒ ß Ë ~ Ü Û`ƒ Ú jˆt A _ƒ ;š[ Œ ƒ ; & V ¾Ž@ µb ¹ B Œ µ ~= ƒ ) B v 5 Œ _ƒ[ _ M 5 Œ ƒ D B W» B B š[ JÅF B V³ B ; _ _ƒ ;š[ Œ ƒ ; H ˆŠ 5 ; 2 5 ;š _ƒ[ ;š[ ƒ[ ; H 5 5 Œ M 5 ; _ 2ƒj º V ) Œ» ƒ ) Œ MṼ ) B V ) _ ¹ 5 ;š ~= J ƒ 5 V B Ç5 5 Œ M 5 Œ ƒ 2ƒ ) B³= ; m c ) 3š[ JÅF B V B ; _ 3 2 ) 3 _ƒ ;š[ Œ ƒ ; H 5 5 Œ M 5 ; _ B gà& ) B šuµý e Œ )ƒ HµÄ º 5 Yš@ H ƒj ù5 5 Œ M 5 Œ ƒ e _ƒ ;š[ Œ ƒ ; H 5 5 Œ M 5 ; _ B à ) & _ƒ ;š[ Œ ƒ ; H š[ M Œ )Ž) ƒ[ ; *ƒj 3 ƒ[ j j ;š ƒ 5 * )ƒ[ T )ƒ VˆT H kµy ) e Œ M Œ ) Bˆ Ž)ˆ H M Œƒ š@ B ; B ;š) ƒ[ ˆŠƒˆŸ B v Q ºƒ5 œƒ[ Qš@ B T V ) B 5 ) B Ú ƒ T 5 Q j š[ M Œ Œ )Ž) Œ ƒ \µu ¾[Ž; 5 Œ ƒ ~ ÜÜ&ƒ _ J ¹ 'Ž; y~w 5 v H ƒ V ; 5 * V ) 3ˆŠ 5 ; HÅ\ _ Y ) _æ) ; _ V š Q 5 V Yƒ5 ùš@ B ) Ṽ M 5 ƒ[ \ X{ ) Œ M Œ Š ) V Bˆ Ž)ˆ+ M 5 B \µ[ 2 B ) B Q H kµ@ v ~ Ü ß`ƒ µ[ )Ž) g c H J Fƒj ) _ƒ ;š[ Œ ƒ ; H cˆšƒˆÿ B v Q gƒ5 ƒ j µjº<» _æ@ M Œ µý ƒ XÁ«µT µjº<»3 B j 2 ; _æ) ; 5 ;š@ še ƒ XÁ µ µº» Àrq s tvu»jw t µ xy Ø ~ Ü Aƒ

11 w w w s q z w s q ~ w w { U w w w s q w U»Y ) B t µu M g ) jx@ _Ž)ˆ Ž@ M g `ƒ[ c ) œ _ƒ[ ;š[ ƒ[ ; H š[ ¹ Œ )Ž) Œ ƒ 2ƒ5 U ƒ µº»5 {¾[Ž; 5 Œ ƒ ~ Ü ƒ M Y j 2 _æä ; 5 ; W ƒ[ 2ƒ5 ù V ) _Ž)ˆ Ž@ M Y B ) B _ 5 Œ ) =Ž) ; _ Œ ƒ ˆ~k V ) Y ƒ v j Œ )ˆ ƒ5 V ) 3ˆŠƒ³ ˆŠ c B ) B Q 5 ) `Ž) ; _ ƒ[ ƒ Bm m Ž; j št j cƒ ) çv Œ B µj `ƒ[ c _æý µdž Ž; j { 5 ;š Y Qšv~ Ü 6 ` µ Ṽ ; Û µ Aƒ ³Š{Ž)ˆŽ@ ¹ j v Q 3 j Ṽ ƒv Œ _ & V _ ¹ j š ƒ2ˆšƒˆš Q BµU» Š Œ B b ` Vƒˆ ) Y ; Q Œ =ƒž)» µ*à@nb» µ µ µ=à@nb µ µ µ=à@n µwµ\ j ;š µ*à@n µ¼ Û ~nb µ ƒ e{ ) )ƒ _ 5 Œ ƒ 2 M 3 Œ _ 5 ;š) 5 QšUµ» nb» µcš@ B )ƒ Œ ) Š ) _ƒ[ ;š[ ƒ[ ; H wz ˆŠ 5 ƒ5 \ ƒ w{ µº» 5 ;š n t µqµ[ =ƒ Kx(} Ü µäš@ B )ƒ[ Œ ) Š ) x@ Æ _ Q H Y _ƒ ;š[ Œ ƒ ; H YˆŠƒˆŸ B v Ú ƒ b ) T )ƒ[ ˆT H Yš[ ¹ Œ )Ž) Œ ƒ \µ _Ž)ˆ Ž@ M Q 5 Ÿ B B ƒ H = B ) N ; _ Œ Š Œ» ƒ;µc Œƒ& ¾[Ž; 5 Œ ƒ ~ Ü Aƒ 5 Ž; e»y H&ƒ5 ¾Ž; Œ J = ) ) ˆŠ ; _ Šƒ5 š@ B ; 5 VŽ) ` ƒ[ˆ )ƒ ˆ H J Œ 2à ½ ) Ÿ `ƒ[ _ Æ [ B ) _ Y ; e ˆ J M 5 Š B ) V Œ B v _ 5 Œ ƒ \µ ) =ƒ»y 5 QšŸ ) Bˆ Ž)ˆ¼ ¹ 5 ;š ) b Œ M Œ ) Bˆ Ž)ˆ»Y ) B w U M»~ µ Ô µ>¼ˆ µ¾à t u w À& 3 _ = B Y B ) B ¹ B m ƒš ) ŒŽ)ˆ ÏAµÀ t µ ;xylø w U tvu» U»~ µ{ 5 ;š»~ µ ¼ t µ ¼ w U»~ µø t µ ƒ ;xylø U»~ µ Ô tvu Jw t µ xy Ë»~ µ ) B ³=ƒ Qš@ B _Ž)ˆ Ž@ M Q B ëí À ¾Ž; j Œ ƒ ; ~ Ü à`ƒ 5 ;š ~ ÜÜ4ƒ š@ _ ) Œ M Œ & ) Bˆ Ž)ˆT 5 ;š _æ) ; _ š Q j 3ƒ5 š@ B ) Ṽ M 5 Œ ƒ \µd» 3 ; H ŸØ eî;ä9 H+ 6 šçq [ ; 1-= M [ ; ± «-jê Œ Š ±N±c Œ ««"=5 Lê"-D [ -1/@«T±J +è[ _ -1/v YêŠ Œ -1/v«(-= c ªo _ çh M `èné5«_ ;«H± ê2ƒ ; 2>-1/v«p \ ö ê ;«(ç_«ê(ê _² çq D 1-= M ê{ B -1/v«B Q c [ W Ÿªo Œ«38 Ö ; ±J² M 'ªo±J²Ak EY ;«è -= j «ç_ Q Œ«H± #-= M :V«4-= c«_«½«œ«h ç_«êc M šç_ ; 1-= N ; ±[ «_ ê;2 n» µ ¼<nB» µ 2 ; 2 [ ½«H Œ«ç_«ê3 N i/@ kèv/v«8w Œ -jê2»~ µ ¼ w U».~ µ 2Ç D ˆA M E2è Œ«_ -=«[ Q N -= N * N -1/v«3±J --=«"5k D«+ç_«ê(ê [ Q² ; ³ê Š ç N«J->ç_ ; [ -= N 2 êå Ÿ ;«è -= j «eç_ 6 [ Q N ç_«:v«4-= c«_«¹ñ(µ¾à n» µ ¼0nB» µ½ D Z µb¼ˆ µ À n» µ ¼0nB» µ ¹ 2Ṽ ; 5 Q [ _ B Œ 5 Œ ƒ ƒj ) e Œ M Œ ) Bˆ Ž)ˆ# ŒŽ) Œ _ T B ) V B Q 5 Œ ƒ =ƒ 2 ) k H J Ž) V Tƒ5 3Þl «ŠXŒ'³ (ˆŠƒ)š@ _ ¹ M ˆŠƒ)š@ _ Ç ) Œ M Œ & ) V Bˆ Ž)ˆ [ =Ž) ; _ Œ ƒ ƒ5 Y ) _ƒ ;š[ Œ ƒ ; H Y5 5 Œ M 5 ; _ 2ƒ5 Y ) 2š@ B ) Ṽ M 5 Œ ƒ Q j ž Ž;š[ v Ž{ B 5 5 B ~ Ü 6 à8ƒ µ>žg Bḿ j B 5 ;šˆœ'ƒ)š@ Œ M ~ Ü 6 Û`ƒ µ\ 5 ;šˆ ƒˆšƒ5» Š 5 ;š Œ 5 v [ ƒˆ~ Ü 6 à`ƒ š@ƒä _Ž)ˆŸ B v Š Œ Vƒ ) 2 B Mš@ B ; _ ƒ5 { Œ ˆŠ B³=5 5 [ ) * _ƒ ;š[ Œ ƒ ; H cm 5 Œ M 5 ; _ ƒj Çš@ B ) Ṽ M 5 Œ ƒ e Q 5 µ; )Ž) ' J V Œ V ; 5 œ _ƒ[ ) ) _ Q ) * _ƒ ;š[ Œ ƒ ; m œ5 5 Œ M 5 ; _ * Vƒ& ) 2 Œ M Œ ) Bˆ Ž)ˆÄÏ\ Y ) * [ B» ƒ5 M k H J Ž) 2 M Ÿ ; 5 Þ- e «ŠXŒ'³ (ˆŠƒÄš@ _ M [ ƒ5 M 5 ƒž) Š Œ B ; Œ ƒ5 ½ Œ@ˆŠˆŠ B Š 5 e ; _ [ Œ Æ ) 2 _ƒ ;š[ Œ ƒ ; H m j Œ M 5 ; _ *ƒ5 ) š@ B ) Ṽ M 5 ƒ[ Q 5 V Š ; _ Š Œ M Œ ƒ Dƒ W ¹š@ ºƒ5 œ V ) 2ˆT 5 B Hµ{ 5 ;š ) B ; _ B j Œ )ƒ ) ŒŽ)ˆŠ ) ƒ[ 2 Hƒ[ {ƒ5 ƒ[ ) _Ž) B ; _ƒ ) 3ƒ ) B g YŽ) = Q 5ˆŸ B»Çƒ[ ;š[ M B { ) _ƒ ;š[ Œ ƒ ; m ù5 5 Œ M 5 ; _ ƒj ù ) š@ B ) V Ṽ ¹ j Œ ƒ e Q 5 ' M Ù µ ~0 µº» ¼É µ ƒ À U»~ µ ¼ w U».~ µ;5 Ù µ ~= ƒ µº» ¼e ƒ k µ ƒ Ø ~ Ü à`ƒ

12 ) 3 _ƒ ;š[ Œ ƒ ; H \m j Œ M 5 ; _ 3ƒ5 \ ) ½š[ JÅ\ B B ; _ 3 ; B Œ» B B ) Y 5 Œ )ˆT ƒ5 ) Y Œ» ƒ [ B ) _ M B { ) b Œ M Œ 2 ) Bˆ Ž)ˆ*µDƒ 2 ) bƒ ) B Y ; 5 ;šuµý M Y ; m { V ) š[ Å\ B B ; _ b * V ) _ƒ ;š[ Œ ƒ ; H cm j Œ ³ 5 ; _ leÿ ¾[Ž; 5 Œ ƒ ~ Ü Û`ƒFh 5 ;š [ ) B LjŸƒˆŠ Q eÿ ¾[Ž; 5 Œ ƒ ~ Ü à8ƒh MṼ T ) B š D 5 )ƒš Œ ; Ṽ o _ M 5 Œ ƒ 2 ƒ ) 3 _ƒ ;š[ Œ ƒ ; H 5 5 Œ M 5 ; _ 3ƒ5 ) š@ B ) Ṽ M 5 Œ ƒ 2 Q j gþ- e Š ŒY³ ˆŠƒ)š@ _ M Bµ; Vƒ )Ž) ' ½ µý `ƒ) _Ž; Yƒ[ * Šš[ JÅF B V B v ½ _ƒ[ ;š[ ƒ[ ; H ù5 5 Œ M 5 ; _ î ïjî Œ ŽÒ Gô* D}~ø½x ô* $ ] ù* Gø Ú Ž) V ) B 3 ) ƒ V ¾[Ž@ V 3ˆŠƒ V T Œ Ž; _ VŽ) À Š ƒ V T 5 Æ š) j ) Q 5 Œ ƒ e ƒ* _Ž) V B ;Ṽ ƒ5 c ) : Ž@ÂT 5 ;šnÿ3 j ˆ~ Ü b 6 `ƒ Ṽ M V ƒ5 { HÂT ) 3[ _ MšˆŠƒ)š@ _ M Bµ;»' )ƒv Œ 3 _ Bm j v Y ) Vƒ ; B 5 Š ŒŽ)ˆŸˆT 5 Œ B š$ ½ ) D B ;š[ æ Z{ ) J ) 5 Œ Œ&ƒ5 Ç V ) Œ ˆŠƒÄš@ _ M bˆt 5 [ ' b _ M 5 Œ _ ƒš [ Œ2 ƒš ƒ ) 3 J M B 5 Œ ƒ ; ƒ5 {š[ Å\ B 3 Œ Ž; _ Ž) V Y 5 ;š ; 5 Q 5ˆŸ B B Ym m Ž) ' =ƒ ) =ƒ»y 5 QšŸ ) Bˆ Ž)ˆ 5 )ƒˆt m ¹ Ṽ M ƒ5 mât ) _Ž) V B ; _ˆŠƒ)š@ _ M 2 Œ Q 5 _»å V _ ƒ[ ( ƒ5 Œ Q 5 m 5 ¹ =ƒ5 J ƒ5» ) ) M H» ƒ5 cˆšƒ Œ ƒ»y ) B š ƒ ; H \» M B H _ BˆŠ µº» À ~ :¼d ƒ ḑ j µ ḑ š~ µ ƒ» µº» µ œûỹã Y~0 AØ ƒ µ M Œ Q b» 2 ;ƒv W [ š[ M 5 ƒ ; m _ BˆŠ B v _ Bµo j ;š þ ž ~ ƒ À Ÿ'ž <K ž AË ~ Ü `ƒ M š[ M 5 ³ Ú Ž) V ) B _ƒ ;š[ Œ ƒ ; ºƒ Æ V ) T ; 5 _ 5ˆŠ B B Q [Ž; 5 Q B Š ; j ) 2 Œ Q 5 V ( 2 ) B B b H b ) B 5 ƒ eš@ ( ; ) š v2 )ƒ ) ) 5 Œ 5 H Ž) ƒ5 { ) bƒ5 M 5 Œ J J W =Ž) ; _ Œ ƒ ; eþ ž ço Œ B Y ½ ) D B ;š[ JæÒ =ƒ ½š@ B Q H J M B Þ' B ˆ )µý ) Œ MṼ ) 2 [ B ) _ M Y ; H ) 3 =ƒ ˆ 5 ;š ) š@ B ) Ṽ M 5 Œ ƒ Q 5 M ¼ ƒ[ m µjº<» À < µḑ Z~ µ ƒ» 7 µº» ¼ ƒ[ m µjº<» À < µ Z~ µ ƒ» 7 µº»&ø )µº»¼ˆ )µ À~ l¼< ƒ ~ ¼0 ƒ µ Î~ 2¼$ ƒ ~ µ ƒ» µjº<»&ë BµD ƒ B ) _ M 5 ;šš@ B ) Ṽ M 5 Œ ƒ Q 5 ' 5 Š _ƒ ;š[ Œ ƒ ; H J & )ƒ ˆ H» & _ƒ ;š[ Œ ƒ ; H ˆŠ 5 ; ' 5 ;š25 5 Œ M 5 ; _ ' ; 5 Y 5 J ) 5 ' ) Q 5 ) J M B 5 Œ ƒ ƒ5 ½ ¾[Ž; 5 Œ ƒ Û~ 8ƒ ƒj z ƒ ;ƒ@ Œ ƒ Ü _ƒˆš º» )ƒž) ƒv ºƒ5 ½ B ) B Q m M Ÿ B v[ ƒ )ˆŠ Û{ ) * ) V ŒŽ)ˆŠ ) Œ ƒ ƒ5 ) 2ˆŠƒ)š@ _ ½ M Ÿ ; 5 ) š[ M _ Q Æ j ;š Ž) )³ ) š[ M _ Q eˆšƒ5 BˆŠ Q œ " ƒ & ;ƒ[ ;š ) Œ M _ T 5 ;š š@ B ) V Ṽ ¹ j Œ ƒ Q Œ ; 5 ) ) š" v ) Œ Q 5 5 ;š ) ) )ƒ55 5 Œ ƒ ; š~ ƒ» Ú ƒˆ ¹ µ\ 5 v B ƒ[ Y ˆ~ `ƒ M 3 HÂT ) µu 5 ;š ~ Ü& 6ƒ ~ Ü `ƒ ~ Ü `ƒ Ü

13 À z Vƒ ;ƒv W ƒ[ B ) _ kµ Ü c ; Y 5 ¹ 0 ; b v j º m V B ; 5 Œ Y HÂT ) )ƒj ¹ _ 'ƒ5 ) `ƒ[ _ ) Œ MṼ ) ¼ ƒ dx µjº<» À ~ 4 ƒ ~F < ƒ µ Î~ ḑ ƒ ~ )µ ƒ» =ƒ Y ŒƒˆŠ 3 Q j Š )ƒ ) B B ƒšṽ )ƒ5 M _ 3ƒ5 *~ Ø Ø" ƒ M g¾ž; j Œ ƒ Å~ `ƒ BµD )ƒ5» B B µ@ ; 5 j ;š X ) Œ M _ Š H J ù V Q š@ š* [ Œ B Q V ) 5ˆŸ»Y H Ãk * ¹ 3 B ; Œ µ; V ) Œ» ƒš B ) _ M 5 ƒ ; Œ B Vm 5 Œ ƒ ; m ¾Ž@ 5 H B v µ) 5 ;šÿ ) B å ¹ g )ƒ ƒ@ cƒ5 \ B ) B _ H J Œ 2 5 ) z Vƒ ;ƒv W ƒ[ Ü VŽ) e )ƒm»ö ƒ ) ;ƒv J ŒÆƒj {Ž; ) *ˆŠƒ)š@ _ M M 3Ṽ M ƒ* [ B _ƒž) v =ƒ ) =ƒ»y 5 QšŸ ) Bˆ Ž)ˆ 5 )ƒˆt H µº»&ø Þ±w*w=seu p-qxp Ö s-rûqà2 Þ p2seãä lá BˆT j Ü Ž) Œ Q å ; 5 ' 3 Œ )ƒž@ Mš ; _ M 5 [ _ Œ2 ƒ2 _ƒ ; Œ V Ž; _ ½ _æ; ' ; 5 B³ ) ƒ)š@ž; _ Y ) ½ j )ƒˆt H» Y T 5 V Q 5 ) g =ƒ ùš[ JÅ\ B B ; _ Z ; _ Œ { 5 ;šš Œ _ƒ[ ;šˆšƒˆš Q ƒ5 { ) Œ MṼ ) * [ B ) _ M ƒšˆšƒ5 eƒ ) Dƒv Šš[ _ Œ ƒ ; B YŠ{ƒ[ ; Mš@ B ŠˆŠƒ)š@ _ c ) _ { 5 ;š Œ 5ˆ J ƒ B Y~ Ü 6 ƒ M ) T _ƒ ;š[ Œ ƒ ; H Yš[ M Œ Œ )Ž) Œ ƒ ; bƒ5 W» ƒ ) Œ MṼ ) * B ) _ M b H ³ B ; j ; B Œ» B B & Œ»ÇƒŸ ƒ ³= )ƒ VˆT H { B 5 ˆŠ ŠÃ= Y ) Šš[ JÅ\ B B ; _ Ÿ _ƒ ;š[ Œ ƒ ; H ˆŠ 5 ; ƒ5 ) ) Œ MṼ ) * B V ) _ ¹ ' ) B & B j ˆŸ Ü µ\ 5 ;š ƒ ) B³= ; H J Y ) š[ JÅ\ B B ; _ & _ƒ ;š[ Œ ƒ ; H m j Œ M 5 ; _ ' M ) B ' V B 5 ˆŠ ß µd 5 ;š25 5 Œ ˆŠƒ 3 V ; 5 * ) š[ JÅF B V B ; _ ˆŠ 5 ; BµD ) B ) 3ˆŠƒ)š@ _» J J c B ) ƒ)š@ž; _ ) 5 )ƒˆt H 5 V B ; H J B ) Ÿ M 3 ƒ* _ƒ ; Ž; _ ˆŠƒ)š@ _ Ç ; j 3ˆ ˆ M B V ) ) Vƒ ; B ƒ5 ½ _Ž) ³ B ; _ ) Œ M _ * 5 ;š" v V B Œ 2 Q 5 V ŠˆŠƒ[ * B ) B _ H J À& & 5 ) ) M ) Bˆ» HÂT ) ŸˆŠƒÄš@ _ M M ; H Š Œ B B Q m Ç š@m Q 5 [ M _ƒ[ v _æ) Ú Q Œ µá»ç ; H µ 3 ) ƒ5 = ƒ \µ ˆŠƒ Š V ; 5 Æ Œ» ƒ*š@ B š@ _æä D B Œ B ; _ *» HÂT ) ˆŠƒ)š@ _ ¹ ) Œ MṼ ) Å )æ) š ; _ƒˆš T _Ž) Œ Œ B 2 Ž;Ṽ eƒ5 M _æ) ; B Œ B ; _ 2 B 5 & D V Q 5 ; = B šeš[ _ Œ e ƒ2 _Ž) B ; _ ) Œ MṼ ) ; ž _ƒ ;šuµc _ƒ ;š[ Œ ƒ ; H YˆŠ 5 ; 5 ;še5 5 Œ M 5 ; _ bƒ5 ƒ v 5 V )ˆT bƒ5 Ç ) Œ MṼ ) & B V ) _ ¹ 5 å ) 5 g =Ž) ; _ Œ ƒ ; gƒ5 F _ ƒ gƒ5 F Q 5 m j Œ M B * 3 { ŒŽ@ µ[»ç B 5 Š J T _ƒˆÿ ; 5 ) _ 3 ) ƒ D B Œ 3 Vƒ Ú 5ˆT A å ) _ 5 e _ƒ ;š[ Œ ƒ ; =ƒ ) 3 =ƒ»y 5 _š2 ) Bˆ Ž)ˆ 5 )ƒ[ˆt H Ú ; H J µ½»» J B $ )ƒ Œ ; 5 ˆT ƒ5 ) ˆŠƒ)š@ _ ¹ ¹ 2Ṽ M V 2 5Ž) ƒˆt j Œ M B H J B ) B Q j Š ) T _ƒ[ v _ 5 *ˆŸƒm[ BˆŠ B v _ ) T _ƒ ;š[ Œ ƒ ; H YˆŠ j Æ 5 ;še5 5 Œ M 5 ; _ ƒ5 Y ) Œ MṼ ) B ) _ M ŒŽ) š v Ú jˆt A _ƒ ;š[ Œ ƒ ~= ƒ 2 ƒ [³= )ƒ ˆT H Œ B V Œ ) v B ª ïñð «7 ~b@ *øñ ðo Œ ^ ] ú¹üg}}6 Gô{`ýûú ] K ô*õª ;}z ] øñø _ ] zmz ƒ[ v [ ƒž; T Q 5 Œ ) M 2 W» ƒ³k _Ž) V B ; _ B Q ƒ ƒ5 ZŠ{ƒHæ\µ Ãk ) B Q ƒ5 J µ3 5 ;šû ƒ@ ~ Ü b à`ƒ YŽ) ½ B _ ƒ M ½ š) j ) šÿ ` Vƒˆ žž) B e~ Ü 6 ß`ƒ š[ M _ B B³= Œ ˆŠ _ 5 ; M 5 Œ ƒ \ ÜÜ

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15 YṼ M H ˆŠ š 5 Œ J B ; 5 Ž) Q H U _æä V B ; ƒ * ƒb Œ»Çƒ _Ž) B ;Ṽ å ¹ å ƒ ;ƒv Y 5 * 5 ; m ƒ[ ƒž; g ) Œ MṼ ) Š B ) _ \ =ƒ m m Ž@ ) b =ƒ _ )³k _Ž) B ; _ B Œ š};ƒ5»½ B { ) Y ) Œ MṼ ) Š B V ) _ =ƒ ~W V ƒ ;ƒ[ž) ;š) M g ; Œ š ƒ * Š _ƒ ;š* Œ _ 5 m 5 Œ M j ;šÿ `ƒ5 J ƒ5»½ ¼ ƒ[ m µjº<» À~ Ü ḑ ß8ƒ µgḑ "» µ µº»&ë { ) B ) 3 ;ƒž) ;š Œ )ƒ ' Q 5 ' M -½ µ ÀY µ{ 5 ;š ) =ƒ»y 5 QšŸ ) Bˆ Ž)ˆ¼ ¹ µb¼ˆ µ¾ày» µb¼< µë Ã= 3» Š ˆŠ Dƒv Œ ~k )Ž) _ `ƒ[ º _ƒ[ v B ; _ ƒ ) 2 ŒvˆŸˆŠ B & V Œ Œ M _ Œ ƒ» À Hµc» * B 5»Y Œ e ) _æä D _ š š@ B ) Ṽ M 5 Œ ƒ Ö Q 5 V NÑ(µ À Ü ḑ» ß ~» µ¼@ µ ƒ 5 ;š ) & Œ M Œ ) Bˆ Ž)ˆ ÏAµÀƼl~» ß`ƒ ~» µ6¼ µ ƒ { vž; g ) å ) 5 Œƒ5 \ ) 3 _ƒ ;š[ Œ ƒ ; H \ˆŠ ;š m j Œ M 5 ; _ * _ 5 ; M 5 Ÿ v ƒ$ `ƒ V»å j Qš& ) V Bˆ Ž)ˆ _ƒˆÿ ;ƒ ) Q ; j º j J ) j Š =Ž) ; _ Œ ƒ ; ƒ5 ) š[ JÅ\ B Œ M H ƒ» ¼< = *ƒ[ Y ˆŠ Dƒ Q j v M Y Ž; _ Ž) jž) ƒˆt 5 ¹ B m B ) B Q 5 V ) ) B v 5 [ T _ƒ _ M 5 ƒ[ Æ D B W» B B VÏ 5 ;š у5 Ú 5ˆT 3 _ƒ ;š[ Œ ƒ Î~= ƒ W ; _ 2 ¾[Ž; 5 Œ ƒ ~ ßß`ƒ J B Q _ M 5 Œ ƒ e D B W» B B ) _ƒ ;š[ Œ ƒ ; m {ˆŠ 5 j ;š2m j Œ M 5 ; _ ƒ5 ƒ µº»hµ 5 ;š ) Œ» ƒš ) Œ MṼ ) 2 B ) _ M 3 5 ;š@ B D B ;š@ B v µá ) š[ JÅ\ B B ; _ b & _ƒ ;š[ Œ ƒ ; H {ˆŠ 5 ; Ç ¹ v[ B Q Œ _ 2 _ M 5 š ƒ ) š[ JÅ\ B B ; _ 3 e _ƒ ;š[ Œ ƒ ; H cm 5 Œ M 5 ; _ ¹ ˆŠƒ)š@ _ T B 5 ) )ƒ µ )ƒm» B B Hµ 5 Œ M = Ú 5ˆ A * _ƒ[ ;š[ ƒ[ ±~= J ƒ ƒ B ) ƒ)š@ž; _ ) 5 )ƒˆ H ƒž; B V ƒ ƒ D Ã= Š» & B [ ) Æš@ B ) V Ṽ ¹ j Œ ƒ _ 5 eƒ ) e =ƒ»y 5 Qš ) Bˆ Ž)ˆ¼ M 'ˆŠƒÄš@ _ kµ) V ) ƒ D 3 M Ç À Ü ḑ» { ) ƒ ; ¹ Á )ƒ ;ƒ@ Œ µ 5 ;š3 V ) B _ `ƒ[ ; _ƒ ; M Œ V ) { 5 )ƒ[ˆt H µb _æý _ B š) ƒ ) µ) 5 ;šÿ M g ) B _ =ƒ ' ; _ƒ ; M Œ Y B B 2» ) Ú ƒ@ƒäš 5 ;šn ƒv :~ Ü 6 6 `ƒ B Mš@ B ; _ 3 =ƒ ) : = ß Ë ~ ß& Aƒ ª ï[z «7 ~b@ *øñ Z ¹ Gõ\~D 6óº> \ ~U@ ] }z À& 2 Ž) V Æ ) _æ) Š ƒ& B ) B Q H J 5 Œ ƒ ƒ5 ½ _æ; Ü ; j M Š B j ; *ƒ5 œ V 5 Œ M = ) & Dƒ ƒ5 Ú 5ˆ A c ) _ V 5 * _ƒ ;š[ Œ ƒ ; µ; )Ž) ½ j ; 5 ;š@ƒ ; ) 3 V Q š@ BˆT 5 V Š ;ƒv W B Œ ' Q 5 ƒ5 3 ) ˆŠgƒ æ)³=ãk ) [ B Q Œƒ5 J ³ ƒv ˆŸƒÄš@ _ k À& e H M Œƒ [š)š k _ ƒ Ÿ ; 5 M _ƒˆšˆšƒ ƒ& Dƒ _Ž) B ;Ṽ MṼ T H J ƒ5»½ Ž; c ƒ3 B =ƒ c )ƒ ) B B ƒ _ƒ V _ M 5 Œ ƒ Šƒ5 D v B V Œ c Q 5 c [ _ ƒv _Ž) B ;Ṽ b )Ž) Šš@ƒv )ƒ ƒ[ ) B» M Œ Š D 5 ƒ[ & ) T J J ŒÆƒ5 ) ŠˆŠƒ)š@ _ Ç Vƒ B 3 =ƒ ) 5 )ƒ[ˆt H Šgƒ ; Mš@ B $ W» ƒ³k _Ž) V B ; _Æ» ƒ ¹š" ; Œ š"ƒ ) V B ;š@ B D B ;š@ B v e Œ Q 5 V 2m 5 Œ M Bµ _ƒˆšˆÿƒ T Œ Q j m 5 Œ M "»½ j ;š ~W D _ `ƒ V ƒ _Ž) B ; _@³k Œ D Ṽ k o 3 Q 5 m j Œ M 5 ;š µ Ü Û

16 Ṽ `ƒj ƒ5» ) ~ ß ƒ z Œ MṼ ) B ) _ M å * ) š@ƒˆÿ Œ Œ M 5 ;šÿ =ƒ _ e _Ž) B ; _* 5 V» 7» ¼ ƒ j µjº<» À ~ Ü ḑ» ß`ƒ» µa Î~+¼ Ü ḑ» ß`ƒ» µ»» µ» µº»=ḑ»"» µ» µjº<» ¼ ƒ j µjº<»» 7» À ~ Ü ḑ» ß`ƒ» µa Î~+¼ Ü ḑ ß`ƒ µ»» µ» µº»=ḑ " µ µjº<» Ø» š ž µ ;š@ B ; B ;š@ œ Q 5 ;š) 5 Qšº )ƒ ˆT H U Q 5 ;š@ƒˆ+5 5 Œ M B { ) œš@ B ) V Ṽ ¹ j Œ ƒ 2 Q 5 å ¹ ) B _ =ƒ µº» ¼ˆ µ À ~+¼ Ü ḑ» ß`ƒ ~» µ ¼$ µ ƒ ḑ» ~»» µ» µº» ¼» 7 µ µº» ƒ Ø»Y ) B 3» 3 ; H 3 5 v H ˆŠ Dƒv Œ š2 V ) ŒvˆŸˆŠ B T _ƒ[ ;š[ ƒ[ \µo»«àh 5µ[ =ƒ Y 5 ; Œ M B ; _ {å ) 2 ) B»+ ) š[ B v _ T 5 V 2 ) * _ƒˆšˆšƒ[ & k _ ƒ 3»* 5 ;š ) * _ƒ@ _ Ṽ B v Q Ÿƒ5 ¼» 5 ;š ) Š ) Œ MṼ ) e B ) _ M B 2ž5 ; _ ) T _ƒˆÿˆšƒ [ _ ƒ» 5 ;š _ ' ) )ƒ55 5 Œ ƒ» HÅ\ _ ;ƒ[ Š ) Œ MṼ ) Š B ) _ M g ) 3 5ˆŠ '»å Hµ5 ) B ; H Y )ƒ _Å\ _ {ƒ[ T _Ž) B ; _Š ) ¹ _ gƒ v B V Œ š[ JÅ\ B B v ¹ m ¹ :{ ) B2 ) B _ =ƒ b ; H )ƒ2 _Å\ _ ƒ * ) ƒ ; Ÿ ; 5 Q 5ˆŠ B V B -ÇPb ; j ½ ; j Q _³ B Œ B g ) =ƒ»y 5 _š3 ) Bˆ Ž)ˆ 5 )ƒˆ H M{å ) ½ƒ V ) B { ; 5 ) [ µ )ƒ5» B B µ D 5 Q gš[ V _ Œ Šƒ ) ½ j )ƒˆt H *{ ) _ƒv _ Ṽ Q gƒ5 ~» Ø;»Ø ƒ 5 ;š Ç Œ )ƒ ³= V B B Œ g Q 5 ƒ5 ½µÀY» µ¼i» µc 5 ;šn½ µ ÀH» µa¼0 µ { ) =ƒ»y 5 Qšº ) Bˆ Ž)ˆ+ M l¼l~» µg¼ˆ µ ƒ 5 ;š _æ) ; _ V š š@ B ) Ṽ M 5 Œ ƒ M l~+¼ Ü» ß`ƒ ~» µ ¼ µ ƒ *{ ) 3 B [ ƒ e ƒ ; ¹ å ) B _ =ƒ Ç`«À Ü ¼$» ß Ø ~ ß6 MṼ 2 M ½ m»y H) c ' ; 5 2ƒ[ ) µ; 5 ;š ) B v 5 [ 3 =ƒ g ¹ j B )ƒ[ž) 2m H Ž) 'ƒ5 k»h À g ; H bˆšƒäš@ _ \ ; j å B j * B { =ƒ ) ' `ƒ[»y 5 QšŸ ) Bˆ Ž)ˆ 5 )ƒˆ H *{ ) _ƒv Œ g M ; j Ç» B 5 2 )ƒb ƒ ) B 'ˆT H v _ H * Œ Œ M _ Œ ;ƒv Œ v B V Œ Y Q 5 V B À ) B V ) B M M T e Œ B ƒ[ž; Tš[ J _Ž@ Œ `ƒ[ Š ) 2ˆŠƒ)š@ _ Y M M 5 V _ 5 Œ M B H ¹ V ŒŽ) * ; j» * š)š@ V M 5 M Š Œ _ Œ ƒ \ Ã= & Œˆ H J ½ ) ƒ ; J J Œ ƒ5 ½ ) B v 5 B Š Q 5 š) Ÿ ƒ& 5 HÂT ) ˆŠƒ)š@ _ ½ ; 5 M H J M Œ Œ M ƒ V ) B V Œ ; _ Q µc» 2ˆ v 5 M e Œˆ H J ' _ƒ@ Œ ; H Mš `ƒ[ Y ) _ƒ[ v B ; _ Šƒj c ) 5 Œ l Ž@ÂT 5 ;š ž5 ) 5 B ƒ ~ Ü 6 ` 6ƒ 5 ;š z 5 Q Œƒ e 5 ;š žž) Î~ Ü 6 & ƒ ˆT 5 T W ô M 5 5 Ž)ˆŠ Q ' _æä B ;š[ ) & V ) VŠ{ƒHæ)³=Ãk ) B _ Œƒ5 J ³ ƒv bˆšƒ)š@ _ ǃ5 ;ƒ[ ;š2 ) Œ MṼ ) ; ~ ßà`ƒ ª ïjî x ò } ] ] zgó 6ó ] ô æ; Ü 5 ;š ß J J Ž; Q 5 B ) B Q H U = 5 Ž) 'ƒ5 HÂT ) ˆŠƒÄš@ _ M ; [ Œ ššƒ[ Š ;š@ B ; B ;š@ v V B Œ ³= Q j c k _ ƒ _ B \à o» { Œ M _ cƒž) Q Œ _ Vƒ½ˆŠƒ)š@ _ M º `ƒ V _ [ º j ;š š@ƒ[ˆš Œ Œ M v V B Œ 3 Q 5 V ½š@ B D B ;šeƒ 2 ;š@ B D B ;š@ B v b k _ ƒ Q µo Œƒ ; 5 ) _ƒ[ ) ) _ Œ ƒ & ; B Œ» B B ) Bˆ M 2 & _ƒˆšˆšƒ[ k _ ƒ Š V ; 5 T HÅ\ _ Q Dƒ Q 5 V ) V 5ˆŠ *»Y Hµg ) B» B j ) )ƒ ˆŽ@ Q 5 ) BƒŽ; Š B =ƒ V ) å j )ƒˆt H j ;šˆ H v Q m Œ Œ M _ Œ Dƒv B Œ c _ 5 B Ü

17 Õ À T _ = B Š M [ B ) B Q H J 5 Œ ƒ ƒj œ _æ; ß 5 ;š@ B D B ;š@ B v k _ ƒ bˆšƒ)š@ _ 3 Ÿ Ö _æ; ß µ ) & Œ Q j e _ ƒ ; 2 V ) B ;š@ B D B ;š@ B v _ƒˆš ;ƒ[ ) B v Q µ½ )Ž) ) B» * H J ƒm» ) Bˆ1 Vƒ& ; _ ƒ Q ) * e _ ƒ[ (» ƒ5 _ƒˆšˆÿƒ [ _ ƒ Q b ; 5 HÅ\ _ v B V Œ Q 5 V 3 Dƒ _Ž) B ;Ṽ Ÿ ) * 5ˆŸ T»Y HÆ 5 ;š _ Vƒ Q» 5 ;šd ƒ5 œ _Ž) V B ; _v³k ; Ṽ o k _ ƒ Q à ù» 3 _æ) ) V ) _ƒˆš ;ƒ[ ) B v Q åƒ5 ù ; j Q 5ˆŠ B B _ Vƒ Q g» * ˆ J M 5 ŒŽ) ; _ ) _ Bµ ) ;š@ B D B ;š@ B v Ÿ [ _ ƒ Œ VŽ; _ Ž) Š» Š ; H ˆ M _ b ) Š Œ ¹ _ ƒ[ ; ƒ[ & ) B ) B Q m ù HÂT ) 3ˆŠƒ)š@ _ ƒ5 žž) ; Œ _ Œ ƒ Û Û ½ { ) ) B Y _ƒˆš Dƒ ) B v _ ƒ5 3 5 g ;š@ B ; B ;š@ k e M M 5 ƒ ; m ;» _ BˆŸ B v Q ž\ =ƒ ±¾ÀÈ AØ Ü Ø ß ½ { ) T _ƒˆšˆÿƒ _ Vƒ HÅ\ _ Q ;ƒ[ & ) Œ MṼ ) e B ) _ M 3 ) 5ˆŠ Š»Y H >» À` o f»«à@» ½ { ) * _Ž) B ; _@³k Œ ; Ṽ o ÀH ÀÛ Š 5 ;š» À@» ÀÛ )» 5 ;š k _ ƒ Q HÅ\ _ ) 2 ) Œ MṼ ) B ) _ ½ƒ5 ƒ ) * _Ž) B ; _ ) ˆ~ Ü b 6 `ƒ j ;šn ˆ 5 ;šn j ƒ5» ~ Ü 6 )Ü4ƒ _ƒ ; Mš@ B ˆ J M 5 3 Œ Ž; _ VŽ) B 3 ŒŽ@ bƒ5 M b Œ Ž; _ Ž) V µu ) Œ ŠˆŠƒ)š@ _ M ) 5ˆŠ B ; ƒ ; B Œ» B B & ) 5 )ƒˆ H 5 ;š Dƒv Œ b v V B Œ Y Q j g ; 5 Y» 3ƒ ; Œ B V šÿ * _æ; Ü 5 ;š ß )ähô* ÔoÏ Ð¹Ó Ð¹Ô\Õ@¾ AêB M [«l-1/v«š D«:çH± 4ê+ê½ çh v _ Œ«çH² H «±ëê½ [«êç _ T:V«Q : ² «@ -= N Aê A À Á 2ÀD2À  2À ÃEŠ c -1/(-1/@«3 M D «Œª)«; [«-j 6ç -= «ê.-= _ Pç -= v Œ«b «êç _ T:V«_ Ä:V 6 «95%6 ê `ç"/ H «± N YªU± N«êª) &ê 1-= j «i:v ; ²m N«±J &ê B Š ±N±{ [ Lê(ê (-1/v«ê"-= -=«¹ H _ M Ä: ±J«ê2>-1/v«1- ç_ ; D - è«d«œ -=«* D«0è[ -= H«¹ H ±J v«œ -1/v«êB±J _ªÄ«ª) Œ «4-=«H Ÿ>œ Œ Ö B _ c Œ ŠªU W«H Œ«0è[ Œ«ê(ê N Aê45 + ) ƒ@ƒ5 { M 3 j [ B & ˆ ) ; B ;š[ Jæ Ž½µÁ )Ž) ) Ž@ Œ ƒ `ƒj ƒ5»½ _æý Ü 5 ;š ß Z{ ) HÂT ) ˆŠƒ)š@ _ M 3 D B ˆ š z ƒ Dƒv Œ ƒ ß 5 b ; Œ šeƒ & Œ _ Œ M 3 V ; 5 5 bž) )³ ;ƒ[ž) ;š@ š &ƒ ) Šš[ _ Œ ƒ \ Ãk e Dƒ e _æý Bµ Œ _ Œ M ž V ŒŽ)ˆŠ Š H J { ;ƒv W [ m m Ž)»å V Dƒv Œ ) ƒ ; J Œ žž;ṽ $ Q Œ M 3 ; H b W» ƒš _Å\ _ Q 'ƒ ) Š Œ )ƒ Q 5 V µuƒ ) ƒ ; B Q j Œ ) 2 ) ƒž) e ) ˆŠ j ƒj Ç ) ) Œ MṼ ) * B V ) _ µá ) ƒ ) B 3 ) VƒŽ) e ) m j Œ M 5 ; _ š ½ $ ; _ V Œ & ) _ƒ ;š[ Œ ƒ ; H {ˆŠ 5 B ;š) ƒ2 Q H M Œ Ÿ ) Š Œ )ƒ 3 Q j 5 ; _ Œ º ) Š _ƒ ;š[ Œ ƒ ; H Ç5 5 Œ M 5 ; _ ƒ5» B Q å H Ã Ç ) ŠˆŸ 5 e _ÅF _ ' M M 5 [ B µ\ ' M ) NŠgƒ æ)³=ãk ) [ B Q Œƒ5 J ³ ƒv bˆšƒ)š@ _ kµc ) B ) T Œ )ƒ[ Q j b ¹ ;ƒž) ;š@ š j ;ƒ5 N{ ) 5 )ƒˆ H V ¾Ž@ b ; Œ V š& V ; 5 ) _Å\ _ ƒ5 Y ) m j Œ M 5 ; _ TˆŽ; Œ b ; Ÿ M 5 B µc 5 ; 5 å ; _ V Œ å e5 5 Œ M 5 ; _ D V ŒƒÄṼ M 5 V š2» eš@ _ Œ å * ) Œ )ƒ Y _ 5 *ŽgŽ) 3 ; _ ) Y _ƒ ;š[ Œ ƒ ; H ;5 5 Œ M 5 ; _ M ;ƒž) ;š@ š 5 Dƒm[ µ ) Y Œ )ƒ[ _ 5 {»å J U ; ) B v 5 Œ g =ƒ Á ¹ j B )ƒž) m H Ž) 'ƒ5 c ) Œ Q 5 V ½5 5 Œ M Ü à

18 À Ø ª ï1ª «7 *øñ îk ôá 6 ;}6ù= Gô*ù* Gô{A 0^Vó ÆÅ ô= \ ~U@ ] } æ; ß 5 ;š z ƒ Dƒv Œ ƒ ß ;š[ M B 5 V ; 5 {ƒ ) 3 5 ) ) ƒ@ Ÿ ƒ M ) ) 3 5 )ƒˆt m M 2 ƒ j ; 5 ;š@ƒ ) & ¾[Ž@ BˆŠ *ƒ5 Š Œ Œ M _ Œ ;ƒ@ Œ e v V B Œ 2 Q 5 V B )ƒ ) B M 2 ƒ B Qš@ B D B ;š@ B ; _ T D B Œ»Ç B B k _ ƒ _ Yš@ƒˆŠ Œ ¹ 5 ;š =ƒ _ v V B Œ Q 5 š@ B ; B ;š š[ JÅ\ B Y»Y ) ƒ 2 V ) 5ˆŠ Œ _ 5 m 5 Œ M ƒ ) B³N [ _ ƒ _æý Œ )ƒ5»½ g M ô [ v» ƒ Ú =Š{ƒ ; Mš@ B ½ bˆšƒ)š@ _ \ ; Œ šƒ 2 ) 5 Š Œ Q 5 V ½5 5 Œ M ; B[ ) Å~ ß ƒ» 2 ) Œ MṼ ) 2 B ) _ M» ¼ ƒ[ j µº» À ~ Ü ḑ» ß`ƒ» µa»» µ» µjº<» ¼ ƒ[ j µº»» 7 À ~ ß`ƒ» µ ḑ» µ» µº» Ë { ) ˆŠƒÄš@ _ ' ¹ º v V B Qš@ B ; B ;š@ V ) * Œ B ; Œ * V ; 5 (»2 måf _ _ ) 2 Œ» ƒ ) ¹Ṽ ) B V ) _ ¹ š[ JÅ\ B B v J ~ Ü Ø"» ƒ>ç ~ 8 Ø" ƒ \Ãk M B Œ ) ;µ5 Œ )ƒ \ _ 5 \ 5 V X½µÀ» µo 5 ;še½ µ À A» µœµ Œƒe ) Ÿ `ƒ[»y 5 Qše ) Bô Ž)ˆ M š µ ¼È µ À ~ Ü ¼ ƒ» µ ˆŽ{ƒ[ B Œ Ÿ Q 5 b 5 2 Œ Œ M _ Œ ;ƒ@ Œ 3 J A>}Î ) { ) š@ B ) Ṽ M 5 ƒ[ * Q 5 V ¹ )µº» ¼É )µ>àéè Ü ¼0 8= ~» ¼d» 7 ƒ ß9» µ ~»=¼d ƒ» µ» µº»ø ŒƒŠ _æ) ; _ V š*š@ B ) Ṽ M 5 Œ ƒ M Ñ(µ ÀËe Ü ¼0 8¾ ~» ¼ ƒ ß9h» µk *{ ) ƒ D ƒ5 c ) =ƒ»y 5 Qš ) Bˆ Ž)ˆ B V ƒ M Y ) B V _ `ƒ V ÇP«À Ü» ¼$ ß ~ Ü ¼0 A MṼ š[ JÅ\ B Q = ƒˆƒ ) J» ÀÌ Ç Ã 8ÒÀ Ü ) `ƒ[»y 5 Qš ) Bˆ Ž)ˆ( M Š B B ƒg 2 ) ˆŠƒ)š@ _ ù ; [ )ƒš =ƒ»y 5 Qš ~ ß` 6ƒ ) Bˆ Ž)ˆ 5 Y )ƒ =ƒ»y 5 _š ) Bˆ Ž)ˆ 5 )ƒˆt m Ú ƒ ½ƒ[ ) B m m Ž) µ) ) 3ˆŠƒ)š@ _ U 5 v[ B Q Œ _ M 5 Œ ƒ 2 ; B Œ» B B 2 ) ' `ƒ[»y 5 Qš ) Bô Ž)ˆ 5 ;š ) v V B Œ Šš[ JÅF B V B v Œ M H J ß ~ Ü ¼d ƒ j ;šd» ¼H ; H Šƒ ) Dƒv * ; 5 ;š ) Ÿ M 5 B ¹ M 5 B T 5 ; Œƒ5 Ž) 'm H Ž) = ½ ) N~ Ü 6 ` 6ƒ 5 ;š Ú Q Ṽ )ƒ =~ Ü 6 6 8ƒ š@ _ D 3 ˆ J M 5 _æý Y ˆŸ ª ï[í «7 ~b@ *øñ ªK ôá 6 ;}6ù= Gô*ù* Gô{A 0^Vó `Œ ^ ]H\ ~U@ ] }z À& B 5 * W _æä B ;š _æ; Û ƒ2 ˆŠƒ V H J M Œ Œ M b Œ» ƒ³n [ _ ƒ Y Œ B Œ ) ¹Ṽ e ) _ƒ V _ ¹ j Œ ƒ D B W» B B " `ƒ V _ [ 5 ;š š@ƒˆš Œ Œ B T Q j b M ˆŠ D B Œ = _ Š{ƒ ; Mš@ B 2 ˆŠƒ)š@ _ o ; šƒ W» ƒ3 Œ Q 5 V Ym 5 ¹ µf» 5 ;š µƒ D B ) Mš@ Œ M B H U ;š@ B ; B ;š@ ½ ¾[Ž; 5 ƒ@ƒ ) ƒ) _ Œ y~ ß ƒ µ) 5 ;š ) ¹Ṽ ) 2 B V ) _ ¹»» ¼ ƒ µº» À ~ Ü» ß`ƒ» µ ~F 8¾ ß`ƒ µḑ»» µ» µº»¾ ; µ µº» ¼ ƒ µº»»» À ~ ḑ ß`ƒ» µ Î~ Ü» ß`ƒ µ ḑ» µ» µº»» µ µº» Ë Ü

19 Ø Ž 5 ) o 5 ;š Š{ ) B ~ Ü 6 8 6ƒ µ& _ M Œ B 2 5 ;šÿžv 5³ ¾[Ž) žwƒ ~ œ Ü 6 [Û µb ) ³ Ü ƒ µ5 5 ;šÿžv 5³ ¾[Ž) žwƒ œ ~ Ü b & µ\ Ü& 6ƒ š@ V _ Œ ; W ô M 5 ˆŠƒ)š@ _ M B YŽ) Š B Q ƒ $ ¹ Ÿ ŒvˆŸˆŠ B Œ M b ) 2 Œ B ; Œ ; 5 ) ŠŽ) ; _ƒ[ ;š[ ƒ[ ; H åš[ M Œ )Ž) ƒ[ ; ƒ5 Ç V ) Š Œ»Çƒ ) Œ MṼ ) e B ) _ M 5 V Š ) Š 5ˆŠ µá )Ž) B ³ š@ B ; B ;š@ * ) Œ B ; Œ b ; 5 Y ) Œ Q 5 V ½5 5 Œ M 5 ;š ;ƒ Œ M H J HÅ\ _ Y V ) 3 W» ƒ B ) _ M å š[ JÅ\ B B v '»å H) B Šgƒ ; Mš@ B Y ) M B 5 ƒ[ ; ' `ƒ ) 5 )ƒˆt m åž )ƒ Y Q M YˆŸƒÄš@ _ ù j { ) =ƒ»y 5 QšŸ ) Bˆ Ž)ˆ*µ 5 ;š2š@ B ) Ṽ M 5 ƒ[ _ 5 µ ½ µ À» µ µ ½ µ À A» µ µë µb¼é )µ>àû½µb¼ˆ½ µ À~ Ü ¼0 A ƒ ~» µ<¼< µ ƒ Ë µjº<» ¼ˆ )µ ÀÎÈ Ü ¼0 A¾ ~» ¼$ ƒ ß9 ~» µ¼ µ ƒ ~»=¼$ ƒ ~ b B V ƒ W ƒ[ ; ƒj Ç À Ü» ¼d ß ~ Ü ¼p 8 ƒ»» µ» µº» ¼<» µ µº» ƒ Ø b B ; j ǃj F ¾[Ž; 5 Œ ƒ ~ ß` bƒ œ T _æ; Û µ@ 5 ) ) ƒ ) ¹ j œṽ )ƒ5 M _ 3ƒ5 ; j Q 5ˆŠ B B _ { H J ƒ5»½ Ž; 3 Vƒ2 B ) B Q 5 2 ) B v 5 [ Šm H Ž) N{ ) T _ ¹ B m Ç = 5 Ž) M 3 5 Qš M Bµ 5 v H \µ ; 5 Œ Q j ½5 5 Œ M 3 HÅ\ _ ) Œ» ƒ [ B ) _ M ½š[ JÅ\ B Œ à _æý B Qš@ B D B ;š@ B ; _ ½ Q j ' ; 5 ¹ _Ž@ M 5 Š Œ V Œ ) =ƒ ˆ* žž) ) ;ƒv Œ y~k» )³ ƒž) ƒv ƒ5 ; B ) B Q m Œ ƒ ; 5 K A Ú Ü Ú ƒˆ V ) å )ƒ c Q 5 V Ç ¾[Ž; 5 Œ ƒ ; µ» ˆ v { V b ; 5» M 3 V ) ì š@ƒ5 J ¹ j _ Vƒ µ í ; _ Š 3 ; 3 [ 5 B _Å\ _ 3ƒ e ) Šš@ƒ5 J ¹ j Œ )ƒ V 3 Q 5 b ; 5 5 Ú ƒ ½ ˆ J M 5 3 [ Œƒ ; '»Ç 3ô [ v _ = B ½ ƒ [ ) DƒŽ) ;š [ _ ƒ ŽgŽ) ½ ) 5 )ƒˆt m ~= Ÿ _ Hµ 5 v5 H Ž) 3ƒ5 DÇ`g g ; 5 Šƒ[ ) ƒ J l }Ï» µ5 [ ) T ; j ) )ƒ55 5 Œ ƒ ; ) Nì_ ;ƒž) ;š k _ ƒ (í ; H b 5 V B `};Ž) B ; _ Šƒ * V ) š@ƒ5 J M 5 3 B ) _ ; 5 š@ƒÿ ) )ƒ5m 5 Œ ƒ ; e ) š@ƒ5 J M 5 k _ ƒ H {à J ~k VƒTŽ; Œ T _ƒ[ ; _ B _æ; ƒ žtˆšƒ[ ) B2 ƒ5»y 2 ; š M 5 B å `};Ž) B ; _ ; j vžg Œ Œ M Œ ˆŠƒ ) B Q 5 VŠ ;ƒ5 J M _2ƒ *š@ƒ5 J M B Œ ' Q 5 Bµ@ )Ž) ½ Œˆ H J B `};Ž) B ; _ ƒ * ) š@ƒj M 5 ) Œ MṼ ) T [ B ) _ k ª ï1ð «zh 6ób ~D 6 ;z ]ÒÑ«7 ~b@ *øñ ;z Z ~ô*ù ª æ; ß µ Û µ 5 ;š ŒŽ) [ Œ 3 ; 5 3 V ) T Œ B 3ƒ5 ½ HÂT ) Š _Ž) V B ; _&ˆŠƒ)š@ _ ¹ ; 5 5 V T _ƒ )³ M Œ e ) b `ƒ V»å j Qš ) Bˆ Ž)ˆ 5 )ƒˆ H 2 M ;ƒ V B v Œ M H J 2 M 5 V Ãk M 3 Œ _ Œ ƒ \µu» B Dƒ 3 Œ Œ ˆT j Yƒj Ç _æ; ß 5 ;š 5 ;še _ƒˆšˆš 3ƒ e ) _ J J W ƒ [ B _ƒž) v =ƒ ;ƒ[ 2 ) j )ƒˆt H 2 5 ;šÿ ` j Ž) ƒ5 { _Ž) B ;Ṽ 5 B Œ ' Q 5 * B ) B _ H k Ü&

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