BANCO DE PORTUGAL Economics Research Department The Optimal Mix of Taxes on Money, Consumption and Income Fiorella De Fiore Pedro Teles WP 2-99 March 1999 The analyses, opinions and findings of this paper represent the views of the authors, they are not necessarily those of the Banco de Portugal Please address correspondence to Pedro Teles, Research Department, Banco de Portugal, Av. Almirante Reis, nº 71, 1150-012 Lisboa, Portugal: Tel.#351-1-3130000; Fax#351-1-3143841; e-mail:[email protected]. Ai T|4@* Lu A@ it L? L?i)c L?t4T|L? @?_ W?UL4i 6Lhi**@ #i 6Lhi ,hLTi@? N?iht|) W?t|||i i_hL Ai*it| @?UL _i Lh|}@* N?iht_@_i @|L*U@ Lh|}it@ }t| c bbH Devwudfw Zh vkrz wkdw wkh Iulhgpdq uxoh lv rswlpdo lq wkh vwdqgdug wudqvdf0 wlrqv whfkqrorj| prqhwdu| prgho zkhwkhu wkh dowhuqdwlyh vfdo lqvwux0 phqw lv d frqvxpswlrq wd{/ dq lqfrph wd{/ ru erwk/ dqg zkhwkhu wd{hv duh sdlg zlwk prqh| ru qrw1 Wkhvh uhvxowv duh dw rggv zlwk uhfhqw olw0 hudwxuh1 Zh vkrz wkdw dq lqfruuhfw vshflfdwlrq ri wkh wudqvdfwlrqv whfkqrorj| h{sodlqv wkh glyhujhqfh1 Nh| zrugv= Iulhgpdq uxoh> Lqdwlrq wd{> Wudqvdfwlrqv whfkqrorj|1 MHO fodvvlfdwlrq= H64> H74> H8;> H95 Zh wkdqn Lvdeho Fruuhld iru yhu| lqvljkwixo frpphqwv1 Uhpdlqlqj huuruv duh rxuv1 Whohv judwhixoo| dfnqrzohgjhv qdqfldo vxssruw e| SUD[LV [[L1 | Fruuhvsrqglqj dxwkru= Shgur Whohv/ GHH/ Edqfr gh Sruwxjdo/ U1 Iudqflvfr Ulehlur/ 4483 Olverd/ Sruwxjdo> Who1& 684040645;6<:> Id{&6840406476;74> spswhohvCesruwxjdo1sw W?|hL_U|L? +iUi?| *|ih@|hi L? |i LT|4@* ?@|L? |@ @t @h}i_ |@| | t LT|4@* ?L| |L |@ hi@* M@*@?Uitc @*tL ? @ tiUL?_ Mit| Lh*_ ihi L?*) _t|Lh|L?@h) |@ it U@? Mi h@ti_ |L ?@?Ui }Lih?4i?| i Ti?_|hit 5?Ui |i 4@h}?@* ThL_U|L? ULt| Lu 4L?i) t UL44L?*) @tt4i_ |L Mi 3ihLc hi@* M@*@?Uit tL*_ |i? Mi ThUi_ @| 3ihL At hiULiht |i LT|4@* TL*U) h*i Lu 3ihL ?L4?@* ?|ihit| h@|itc _ihi_ M) 6hi_4@? EbSb ? @ Lh*_ | *4T t4 |@ it W| t @*tL @| L__t | i*Tt Eb.c ihi | t @h}i_ |@| *^_|) tL*_ Mi |@ i_ @t @?) L|ih }LL_ Ai @h}4i?| uLh |i LT|4@*|) Lu |i 6hi_4@? h*i t |LuL*_ 6ht|c 4L?i) tL*_ ?L| Mi |@ i_ MiU@ti | t @? ?|ih4i_@|i }LL_c @t k4MhL} EbHS TL?|i_ L| OLiih |t @h}4i?| t L?*) @*_ u |i |iU?L*L}) t UL?t|@?| hi|h?t |L tU@*i Wu |i |h@?t@U|L?t |iU?L*L}) t ?L| UL?t|@?| hi|h?t |L tU@*ic @t ? |i U@ti Lu |i @4L*ALM? |iU?L*L}) c |i? | t LT|4@* ?L| |L |@ 4L?i) L?*) MiU@ti 4L?i) t @ uhii }LL_ At t tL? ? Lhhi@ @?_ Ai*it EbbS Wu 4L?i) @t ?L| @ uhii }LL_c |i LT|4@* |@ L? 4L?i) L*_ Mi @ _hiU| @TT*U@|L? Lu |i t|@?_@h_ LT|4@* |@ @|L? h*it ? |i M*U 6?@?Ui *|ih@|hic @t ? +@4ti) Eb2. @?_ #@4L?_ @?_ hh*iit Eb. `i? 4L?i) t 4L_i**i_ @t @ ?@* }LL_c | tL*_ Mi |@ i_c @t @?) L|ih }LL_ `i? ?t|i@_ 4L?i) t 4L_i**i_ @t @? ?|ih4i_@|i }LL_c | tL*_ ?L| Mi |@ i_ i? |i |iU?L*L}) t UL?t|@?| hi|h?t |L tU@*i OLiihc MiU@ti 4L?i) t @ uhii }LL_ | tL*_ ?L| Mi |@ i_ ?_ih }i?ih@* UL?_|L?t Ai ?||L? t |@| ii? u |i LT|4@* @_@*Lhi4 |@ h@|i L? @ ULt|*) }LL_ t TLt|ic |i LT|4@* ThUi t ? }i?ih@* 3ihLc @t |i ULt| @TThL@Uit 3ihL W? |i t|@?_@h_ |h@?t@U|L?t |iU?L*L}) 4L?i|@h) 4L_i*c @t ? k4 MhL} EbHSc B_L|| @?_ Vi} Ebb @?_ @hc ht|@?L @?_ ki Li EbbSc Lhhi@ @?_ Ai*it EbbS tL |@|c u |i }Lih?4i?| ULLtit |L ?@?Ui }Lih?4i?| i Ti?_|hit | i|ih |i ?@|L? |@ Lh @? ? UL4i |@ c |i? |i 6hi_4@? h*i t LT|4@*c uLh L4L}i?iLt |h@?t@U|L?t |iU?L*L}it Lu @?) _i}hii Wu |i @*|ih?@|i |@ |L ?@|L? t @ |@ L? UL?t4T|L?c |i UL?_ |L?t ?_ih U |i 6hi_4@? h*i t LT|4@* _iTi?_ L? i|ih |@ it @hi T@_ | 4L?i) Lhhi@ @?_ Ai*it Ebb. @?_ **}@? @?_ 5@*@@h|? 4 Y1 Edxpro +4<85, dqg Wrelq +4<89, 2 Ebb. tL |@|c i? |i UL?t4T|L? |@ it @hi ?L| T@_ | 4L?i)c |i 6hi_4@? h*i t @*tL LT|4@* uLh L4L}i?iLt |h@?t@U|L?t u?U|L?t Lu @?) _i}hii W? |t U@tic i|ih |i }Lih?4i?| tit ?UL4i Lh UL?t4T|L? |@ it _Lit ?L| @giU| |i LT|4@* ?@|L? |@ Ai |L |@ it @hi i^@*i?| `i? ?t|i@_ | t h}|*) @tt4i_ |@| |i UL?t4T|L? |@ it @hi T@_ | 4L?i)c |i i^@*i?Ui Mi|ii? |i ?UL4i |@ @?_ |i UL?t4T|L? |@ t *Lt| **}@? @?_ 5@*@@h|? Ebb.c ? *?i | B_L|| @?_ Vi} Ebbc @h}i |@|c ? |t U@tic L4L}i?i|) Lu |i |h@?t@U|L?t |iU?L*L}) t ?L| i?L} |L }@h@?|ii |i LT|4@*|) Lu |i 6hi_4@? h*i Ai 6hi_4@? h*i t LT|4@* L?*) u @__|L?@* hit|hU|i @tt4T|L?t @hi 4@_i L? |i |4i tTi?| L? |h@?t@U|L?t @| u** *^_|) UULh_?} |L **}@? @?_ 5@*@ @h|? Ebb.c |t ?_?} |h?t |i hit*| Lu LT|4@*|) Lu |i 6hi_4@? h*i uLh @** L4L}i?iLt u?U|L?t ?|L @ uh@}*i hit*| L| ? B_L|| Ebb @?_ **}@? @?_ 5@*@@h|? Ebb.c |i ?||L? uLh ) |i hit*|t ?_ih |i |L @*|ih?@|i |@ it _gih hi4@?t LMtUhi W? |t T@Tihc i tL |@| @t *L?} @t ?UL4i |@ it @hi @@*@M*ic |L}i|ih | UL?t4T|L? |@ itc |i hit|hU|i UL?_|L?t @hi ?L| ?iUitt@h) `i @*tL @h}i |@| |i hi@tL? uLh |i _gih?} hit*|t ?_ih |i |L @*|ih?@|i |@ it t |@| |i |h@?t@U|L?t |iU?L*L}) t ?L| i** tTiUi_ i? |ihi @hi UL?t4T|L? |@ it @?_ |@ it @hi T@_ | 4L?i) W?_ii_c ?_ih @ ULhhiU| tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L})c |i 6hi_4@? h*i t @}@? LT|4@*c uLh @** L4L}i?iLt u?U|L?t `i UL?U*_i |@| |i LT|4@*|) Lu |i 6hi_4@? h*i t ?_ii_ @ hLMt| hit*| Ai T@Tih ThLUii_t @t uL**LtG W? 5iU|L? 2c i _ihi |i UL?_|L?t ?_ih U |i 6hi_4@? h*i t LT|4@*c i? |i @@*@M*i |@ ?t|h4i?|t @hi |i ?@|L? |@ @?_ @ |@ L? UL?t4T|L?c @?_ |@ it 4t| Mi T@_ | 4L?i) `i ?_ |@| |iti UL?_|L?t @hi _gihi?| uLh4 |Lti _ihi_ M) B_L|| @?_ Vi} Ebb @?_ **}@? @?_ 5@*@@h|? Ebb. W? 5iU|L? i tL |@| |i UL?_|L?t uLh |i LT|4@*|) Lu |i 6hi_4@? h*ic @hi UL?_|L?t ?_ih U | t ?L| TLttM*i |L @giU| |4i ti_ uLh |h@?t@U|L?tc @?_ @t @ hit*|c | t @*tL ?L| TLttM*i |L @giU| ThL|t `i @*tL tL |@|c u 4L?i) @t ?L| @ uhii }LL_c | L*_ @*@)t Mi LT|4@* |L |@ hi@* M@*@?Uit W| t L?*) MiU@ti 4L?i) t @ uhii }LL_c |@| i LM|@? UL?_|L?t uLh LT|4@*|) Lu |i 6hi_4@? h*ic Liih hit|hU|i |i) 4@) Mi W? 5iU|L? ec i @**L uLh |i ti Lu ML| @*|ih?@|i |@ ?t|h4i?|tc UL?t4T|L? @?_ ?UL4i |@ itc @?_ ?_ |@| |i 6hi_4@? h*i t @}@? |i LT|4@* |@ L? 4L?i) uLh L4L}i?Lt |h@?t@U|L?t |iU?L*L}it Lu @?) _i}hii OLiihc |i LT|4@* |@ h*it uLh |i L|ih |L |@ it @hi _t|hM?}G Ai }Lih?4i?| tL*_ |@ ?UL4i @?_ u**) tMt_3i UL?t4T|L? ? Lh_ih |L hi_Ui |i @*i Lu |h@?t@U|L?t @?_ |ihiuLhi t@i L? hitLhUit tTi?| L? |h@?t@U|L?t Aiti hit*|t t}}it| @ 4tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L}) W? 5iU|L? Dc i tL |@| |i |h@?t@U|L?t |iU?L*L})c @t t tTiUi_ ? |i *|ih@|hic @t |i ?_ith@M*i ThLTih|) |@| | t TLttM*ic M) 4@?T *@|?} |i |@ L? UL?t4T|L?c |L hi_Ui |i |4i ti_ uLh |h@?t@U|L?t |L| @U|@**) hi_U?} i|ih |i hi@* ^@?||) Lu |i }LL_t |h@?t@U|i_c Lh |i ^@?||) Lu 4L?i) ?iUitt@h) |L ThU@ti |iti }LL_t At ThLT ih|) t hitTL?tM*i uLh |i @__|L?@* hit|hU|i UL?_|L?t uLh LT|4@*|) Lu |i 6hi_4@? h*ic i? |i UL?t4T|L? |@ t |i t?}*i @*|ih?@|i |@ |L ti}?Lh@}i W? u@U|c ? |@| U@tic |ihi t @ |h@_iLg }i?ih@|i_ M) |i ?Ui?|i |L t@i L? hitLhUit ti_ uLh |h@?t@U|L?tc tL |@| @ t*}|*) }ih ?@|L? |@ @?_ @ *Lih UL?t4T|L? |@ ** @**L |L t@i L? |Lti hitLhUit N?_ih @ ULhhiU| tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L})c |i 6hi_4@? h*i t LT|4@* uLh @** L4L}i?iLt |h@?t@U|L?t |iU?L*L}it 5iU|L? S UL?|@?t |i UL?U*tL?t 2 Ai T|4@* L4M?@|L? Lu |i W?@|L? A@ @?_ |i L?t4T|L? A@ Ai i?hL?4i?| t @ |h@?t@U|L?t |iU?L*L})c 4L?i|@h) 4L_i* @t ? @hc ht|@?L @?_ kiLi EbbSc Lhhi@ @?_ Ai*it Ebb. @?_ **}@? @?_ 5@*@@h|? Ebb. Ai 4L_i* t @ t*}| @h@|L? Lu |i 4L_i* ? k4 MhL} EbHSc B_L|| @?_ Vi} Ebb @?_ Lhhi@ @?_ Ai*it EbbS ? |@| |i |4?} Lu |i U@t ? @_@?Ui UL?t|h@?| t _gihi?| At _t|?U|L? t ?L| hi*i@?| uLh |i hit*|t `i ?L ThLUii_ |L UL4T|i |i LT|4@* tU@* TL*U)c i? |i @@*@M*i |@ ?t|h4i?|t @hi |i ?@|L? |@ @?_ @ |@ L? UL?t4T|L?c @?_ |@ it 4t| Mi T@_ | 4L?i) W? |t iUL?L4)c |ihi t @ *@h}i ?4Mih Lu _i?|U@* LtiL*_tc Lti Thiuihi?Uit @hi _i?i_ Lih @ UL?t4T|L? }LL_ @?_ *ithi ,@U Lti L*_ t i?_Li_ | L?i ?| Lu |4i |@| U@? Mi @**LU@|i_ |L *@MLhc *ithic Lh |h@?t@U|L?t Ai UL?t4T|L? }LL_ t ThL_Ui_ t?} @ *?i@h |iU?L* L}) | @ ?|@h) ULiUi?| Aihi @hi |L @tti|tc 4L?i) @?_ ?L4?@* e ML?_t Ai }Lih?4i?| 4t| ?@?Ui @ }i? UL?t|@?| *ii* Lu }Lih?4i?| i Ti?_|hit | hii?it uhL4 @ UL?t4T|L? |@ Lh uhL4 |i ?@|L? |@ W? |t iUL?L4)c |i LtiL*_t tii! |L 4@ 43i [" q L ES c c | | |'f E | ihi L t @? ?Uhi@t?} UL?U@i u?U|L?c S| @hi UL?t4T|L? }LL_t @?_ | t *ithi @| |4i | Ai LtiL*_t tTT*) *@MLh | r| c ihi r| t |4i tTi?| ? |h@?t@U|L?t Ah@?t@U|L?t @hi ULt|*) t?Ui |i) hi^hi |4i |@| UL*_ L|ihti Mi ti_ uLh ThL_U|L? Ai @4L?| Lu |4i _iL|i_ |L |h@?t@U|L?t ?Uhi@tit | UL?t4T|L? @?_ _iUhi@tit | hi@* 4L?i) M@*@?Uitc @UULh_?} |L |i uL**L?} |h@?t@U|L?t |iU?L*L})G | r| , e| c c | E2 ihi e| ' S| E n S| _i?L|it UL?t4T|L? i Ti?_|hitc }hLtt Lu |@ it | wi| 6| ' | `i @tt4i |@| |i u?U|L? , t L4L}i?iLt Lu _i}hii & @?_ tL | U@? Mi h||i? @t ,Eec 6 ' uE 6e e& u t U@h@U|ih3i_ M) |i uL**L?} UL?_|L?tG u G $ -n c -n ( u fc u E 6e ' fc i? 6 ' tT ( u f 6 t |i TL?| Lu u** *^_|)c ihi @? @__|L?@* e e ?| Lu hi@* M@*@?Uit _Lit ?L| hi_Ui |h@?t@U|L?t |4i L|Ui |@| | @ UL?t4T|L? |@ *Lih |@? c i Ti?_|hit UL*_ MiUL4i ?i}@|i 5?Ui |i ThLM*i4 t i** tTiUi_ L?*) i? i Ti?_|hit @hi TLt|ic i hit|hU| |i |@ L? UL?t4T|L? |L Mi S| W?Uhi@t?} hi|h?t U@??L| Mi |LL }c Lh |i ThLM*i4 ** ?L| Mi UL?U@i At 4T*it hit|hU|L?t L? |i 4?44 @*i Lu |i _i}hii Lu L4L}i?i|) Lu |i |h@?t@U|L?t |iU?L*L})c &c |@| _iTi?_ L? |i Uh@|hi Lu |i |*|) u?U|L? W? T@h|U*@hc i hit|hU| & fc MiU@ti L|ihti ,e L*_ Mi ?i}@|i @| u** *^_|)c uLh @ tMti| Lu |i U*@tt Lu |h@?t@U|L?t |iU?L*L}it2 W? i@U TihL_ |c |i LtiL*_t ULLti L*_?}t Lu 4L?i) | c |L Mi ti_ uLh |h@?t@U|L?t ? |@| t@4i TihL_c @?_ ?L4?@* ML?_ L*_?}t | Aiti ML?_t i?||*i |i LtiL*_t |L E n | | ?|t Lu 4L?i) ? TihL_ | n p 3 + , Vlqfh 5 Iurp wkh krprjhqhlw| dvvxpswlrq zh nqrz wkdw n4 + , h @ h 3 + , @ 3 dw ixoo oltxlglw|/ zkhq + , lv vwulfwo| srvlwlyh dw wkh wklv srlqw/ wkhq pxvw eh srvlwlyh iru h wr eh srvlwlyh1 O w o o Ow D h nO w O w n L?t4T|L? t |@ i_ @| @ h@|i S| Ai M_}i| UL?t|h@?|t uLh | f @hi }i? M) UL?_|L?t E n S| | S| n |n n |n | n E n | | n | E | r| c E f n f `f c |L}i|ih | @ ?LL?3 }@4it UL?_|L? 6Lh t4T*U|) i @tt4i |@| `f ' f Wu |i ?|@* ?L4?@* i@*| @t t|hU|*) TLt|i | L*_ Mi LT|4@* |L ti| |i ?|@* ?L4?@* ThUi *ii* |L @? @hM|h@h*) *@h}i ?4Mihc U L*_ u**) _i@*i |i ?|@* hi@* i@*| Ai Th@|i ThLM*i4 t _i?i_ M) |i 4@ 43@|L? Lu Ec tMiU| |L E2 @?_ |L EAi ht| Lh_ih UL?_|L?t ?U*_i LS E| ' E n S| E n ,e E| c L E| Ee ,6 E| ' | c ED L E| ' n o|n c qL E| n ES | Ai LT|4@* ULUi Lu hi@* M@*@?Uit hi^hit ihi n o|n E n |n |n |@| |i Th@|i 4@h}?@* @*i Lu t?} 4L?i)c ,6 c t i^@* |L |t LTTLh| ?|) ULt|c | Ai 4T*i4i?|@|L? Lu |i 6hi_4@? h*ic | ' fc 4T*it |@| ,6 ' f Ai }Lih?4i?| 4?43it |i i Uitt Mh_i? Lu |@ @|L? M) tL*?} @ +@4ti) ThLM*i4 Ai +@4ti) tL*|L? t @? @**LU@|L? @?_ @ ti| Lu ThUit @?_ TL*U) @h@M*it tU |@| i*u@hi t 4@ 43i_ @?_ |i @**LU@|L? U@? Mi _iUi?|h@*3i_ @t @ UL4Ti||i i^*Mh4 ? 4T*i4i?|@M*|) UL?_|L?c LM|@?i_ t?} |i ht| Lh_ih UL?_|L?t Lu |i Th@|i ThLM*i4 |L i Thitt |@ it @?_ ThUit ? |ih4t Lu ^@?||itc |L}i|ih | |i hitLhUit UL?t|h@?|tc }@h@?|iit |@| |i LT|4@* @**LU@ |L? U@? Mi _iUi?|h@*3i_ wi| _| ' Eno c | _f ' 5?Ui @| |i Eno| LT|44c *4 E_| 6| n _| | *R| ' fc |i ti| Lu M_}i| hit|hU|L?t U@? Mi | h||i? @t <" S " [ |'f _| E n S| S| n " [ |'f _| | 6| ' " [ |'f _| E | r| E. Nt?} |i L4L}i?i|) @tt4T|L? |L LM|@? , E| ,6 E| 6| ' ,e E| e| E& , E|c @?_ t?} |i ht| Lh_ih UL?_|L?t Eec ED @?_ ESc |L hiT*@Ui |@ it @?_ ThUit ? |i ?|ih|i4TLh@* M_}i| UL?t|h@?| E.c i U@? h|i |i 4T*i4i?|@M*|) UL?_|L? @t " [ |'f q | iLS E|S| L E| d | n E &, ES| E n S| c 6| oj ' f EH Ai hitLhUit UL?t|h@?|t @hi S| n }| | , ES| E n S| c 6| c Eb ihi S| @t ?L| Mii? u**) tMt|||i_ ? |i 4T*i4i?|@M*|) @?_ hitLhUi UL?t|h@?|tc uLh @?@*)|U@* UL?i?i?Ui Ee t @ UL?t|h@?| Lu |i +@4ti) ThLM*i4 t?Ui | 4T*U|*) _i?it |i UL?t4T|L? |@ @t @ u?U|L? Lu |i ^@?||itc S| ' S ES| c | c 6| Ai +@4ti) ThLM*i4 t |i ULUi Lu iS| c | c 6| j|'f |@| 4@ 43it Ec tMiU| |L EHc @?_ Ebc @?_ ihi |@ it @hi _i?i_ 4T*U|*) M) Ee wi| @?_ q | b| c | fc Mi |i 4*|T*iht @ttLU@|i_ | UL?_|L?t EH @?_ Eb hitTiU|i*) 5?Ui |i) 4i@thic hitTiU|i*)c |i i Uitt Mh_i? Lu |@ @|L? @?_ |i t@_L ThUi Lu hitLhUit ? |t iUL?L4)c |i) 4t| Mi TLt|i @| |i LT|44 6hL4 |i ht| Lh_ih UL?_|L? Lu |i Th@|i ThLM*i4 EDc i !?L |@| | ' f _iUi?|h@*3it @? @**LU@|L? ihi hi@* 4L?i) M@*@?Uit @hi @| u** *^_|) Oi?Uic i U@? @?@*)3i |i LT|4@*|) Lu |i 6hi_4@? h*i M) ihu)?} i|ih ,6 ' f t@|tit |i ht| Lh_ih UL?_|L?t Lu |i +@4ti) ThLM*i4 Ai 4@h}?@* UL?_|L? Lu |i +@4ti) ThLM*i4c uLh hi@* M@*@?Uitc t }i? M) % & YS| dL E| E& n b| o ,6 E| n ,e E| S| ' fc Ef Y6| ihic uhL4 UL?_|L? Eec " YS| E n S| ,e6 E| LS ,e6 E| ' ' E Y6| n ,e E| n E n S| S| ,ee E| SLS ,ee E| n L E n ,e E|2 At LT|44 4@h}?@* UL?_|L? t|it |i uL**L?} ThLTLt|L? . hLTLt|L? wi| |i }Lih?4i?| ?@?Ui i Ti?_|hit | @ UL?t4T|L? |@ @?_ @? ?@|L? |@ c @?_ *i| |i |h@?t@U|L?t |iU?L*L}) |@!i |i uLh4 ? E2 Ai?c i? i|ih ,e6 E| Lh ,e E| t 3ihL @| |i TL?| Lu u** *^_|)c | ' fc uLh @** |c t |i LT|4@* tL*|L? hLTLt|L? i |i?_t |i hit*|t ? |i *|ih@|hi B_L|| @?_ Vi} Ebb @?_ **}@? @?_ 5@*@@h|? Ebb. @h}i |@|c i? |h@?t@U|L?t |4i t @ u?U|L? Lu UL?t4T|L? }hLtt Lu |@ itc |i 6hi_4@? h*i L?*) L*_t u |i @__|L?@* @tt4T|L? t 4@_ic |@| ,e E| t 3ihL @| u** *^_|) 6Lh L4L}i?iLt u?U|L?t Lu _i}hii _gihi?| uhL4 3ihLc |t @4L?|t |L @tt4?} |@| |4i tTi?| L? |h@?t@U|L?t @| u** *^_|) t 3ihL W?t|i@_c hLTLt|L? t|@|it |@| ii? i? |4i tTi?| L? |h@?t@U|L?t t TLt|i @| u** *^_|)c |i 6hi_4@? h*i 4@) t|** Mi LT|4@*c ThL_i_ |@| ,e6 E| ' f Wu |@ it ihi ?L| T@_ | 4L?i)c |i? |i |h@?t@U|L?t |iU?L*L}) L*_ Mi | E2 r| ' , S| c | YS| ? |i ht| Lh_ih UL?_|L? Lu |i +@4ti) ThLM*i4 Ai |ih4 ,e E| S| Y6 | Ef L*_ _t@TTi@hc @?_ |i hi*i@?| 4@h}?@* UL?_|L? L*_ Mi dL E|E & b| o ,6 E| ' f E Ai tL*|L? U@? Mi _iUi?|h@*3i_ | | ' f @?_ | i|ih @ UL? t4T|L? |@ c Lh @*|ih?@|i*) @? ?UL4i |@ Ai i^@*i?| ?UL4i |@ t | ' nS| Wu 4L?i) @t ?L| ?ii_i_ |L T@) |@ itc |i 6hi_4@? h*i L*_ Mi LT |4@* uLh L4L}i?iLt u?U|L?t Lu @?) _i}hiic hhitTiU|i Lu U t |i @*|ih?@|i |@ ?t|h4i?| OLiihc *i | t hi@tL?@M*i |L @tt4i |@| ?UL4i |@ it _L ?L| @i |L Mi T@_ | 4L?i)c |@| t ?L| |i U@ti uLh UL?t4T|L? |@ it ?Ui i h}|*) @tt4i |@| UL?t4T|L? |@ it 4t| Mi T@_ | 4L?i)c |i i^@*i?Ui Lu |i |L @*|ih?@|i |@ ?t|h4i?|t t *Lt|c @?_ |i 6hi_4@? h*i t LT|4@* ?_ih |i @__|L?@* UL?_|L?t _ihi_ @MLi W? |i ?i | tiU|L?c @?_ |hL} |i i?_ Lu |i T@Tihc i ThL_i |i ?||L? uLh |iti hit*|t H N?_iht|@?_?} |i L?_|L?t uLh |i T |4@*|) Lu |i 6hi_4@? +*i W? |i *@t| tiU|L? i tLi_ |@|c i? |i }Lih?4i?| ULLtit |i LT|4@* UL4M?@|L? Lu |i ?@|L? |@ @?_ |i UL?t4T|L? |@ c UL?_|L?t L? |i _ih@|itc ,e @?_ ,e6 c Lu @? L4L}i?iLt |h@?t@U|L?t |iU?L*L})c r ' ,Eec 6c 4t| Mi t@|ti_ ? Lh_ih uLh |i 6hi_4@? h*i |L Mi LT|4@* W? Lh_ih |L ThL_i @ U*i@h ?||L? uLh |iti hit*|tc | t tiu* |L UL?t_ih @? i^@*i?| iUL?L4) |L |i 4L?i|@h) iUL?L4) ihi hi@* M@*@?Uit U@? Mi @ ULt|*) }LL_c @?_ ihi @** |i }LL_t @hi ThL_Ui_ M) h4tc tL |@| |i 4T*U| ThL|t ? |i ThL_U|L? Lu |h@?t@U|L?t @hi 4@_i i T*U| At t |i t|h@|i}) uL**Li_ ? Lhhi@ @?_ Ai*it EbbS 5?Ui |i u** _)?@4U ThLM*i4 t t|@|L?@h) c i ** UL?t_ih |@| |i i^@*i?| hi@* iUL?L4) t t|@|U Ai t|hU|hi Lu |t iUL?L4) t _iTU|i_ ? 6}hi hL_U|L? t|hU|hi ? @? i^@*i?| hi@* iUL?L4) L?t4T|L? t ThL_Ui_ t?} |4ic ? c @?_ |h@?t@U|L?tc neS c @UULh_ ?} |L @ wiL?|iu |iU?L*L})c S ' 4? neS c ? Ai ULiUi?| Lu |i ht| @h}4i?| ? |i wiL?|iu |iU?L*L}) t nS MiU@ti |h@?t@U|L?t |4i t @ 6 Wkh vwdwlrqdulw| ri wkh Udpvh| vroxwlrq lv qrw d uhvwulfwlrq exw udwkhu d uhvxow ri rswlpdolw|1 Lw dovr grhv qrw ghshqg rq wkh dvvxpswlrq wkdw lqlwldo wrwdo qrplqdo dvvhwv duh }hur1 Li wkhvh zhuh vwulfwo| srvlwlyh/ lw zrxog vwloo eh rswlpdo wr vhw wkh uhdo ydoxh ri wkrvh dvvhwv wr }hur/ dqg wkh vroxwlrq zrxog eh wkh vdph1 b u?U|L? Lu |h@?t@U|L?t }hLtt Lu |i UL?t4T|L? |@ c tL |@| r ' ,Eec 6c ihi e ' E n S S @hi i Ti?_|hit Ai ThL_U|L? Lu 4L?i) hi^hit *@MLhc ?2 c @UULh_?} |L @ *?i@h |iU?L*L}) | @ i_ ULiUi?|c 6 ' k?2 Ai |@ t|hU|hi ? |t iUL?L4) t hit|hU|i_ M) |i u@U| |@| |h@?t@U|L?t |4i @?_ *@MLh U@??L| Mi |@ i_ AihiuLhic hii?it U@? L?*) Mi h@ti_ |hL} @ |@ L? UL?t4T|L?c S c @?_ @? @_@*Lhi4 |@ L? 4L?i)c 6 6h4t 4@ 43i ThL|t uhL4 |i ThL_U|L? Lu UL?t4T|L?c |h@?t@U|L?tc @?_ 4L?i) hL|t @hi _t|hM|i_ |L |i LtiL*_tc U @hi @*tL |i L?iht Lu |i h4t Ai LtiL*_t 4@ 43i |*|)c tMiU| |L |i M_}i| UL?t|h@?| S E n S ? E n E n S Ee Oihi ? t |i UL44L? 4T*U| @}i ? @** |i @U||itc @?_ @hi ThL|t ? ?|t Lu |i UL?t4T|L? }LL_c LM|@?i_ uhL4 |i ThL_U|L? Lu |h@?t@U|L?tc U t |i L?*) @U||) |@| 4@) ?L| Mi UL?t|@?| hi|h?t |L tU@*i Ai LT|4@*|) UL?_|L?te hi^hi |@| ,6 ' n 6 k |h@?tuLh4i_ 6hi_4@? h*i L*_ ULhhitTL?_ ? |t UL?|i | |L 6 ' fc @?_ 6 L*_ Mi ThUi_ @| |i ULt| Lu ThL_U|L? k Nt?} |i ht| Lh_ih UL?_|L?t uhL4 |i ThL| 4@ 43@|L? Lu h4tc i U@? _ihi |i uL**L?} i ThittL? uLh c @t @ u?U|L? Lu Sc c @?_ 6G ' L E& , LS ED Ai Mi?iL*i?| }Lih?4i?| 4@ 43it |i LtiL*_t< |*|)c tMiU| |L |i 4T*i4i?|@M*|) UL?_|L? @?_ |i hitLhUit UL?t|h@?| Ai UL?t|h@?|t U@? Mi i Thitti_ hitTiU|i*) @t LS S L E LS ' fc @?_ S n } n , EE n S Sc 6 n n 6 ' f k ES E. 7 Vhh Dsshqgl{ D iru d ghulydwlrq ri wkh uvw0rughu frqglwlrqv/ wkh lpsohphqwdelolw| frqglwlrq/ dqg wkh surw ixqfwlrq1 f Ai 4@h}?@* UL?_|L? ? |i }Lih?4i?| ThLM*i4 uLh hi@* M@*@?Uit t % & YS LS 6 n b ,6 n ,e S ' f EH n Y6 k ihi @?_ % & L YS 6 ' E& ,6 n ,e S c LS Y6 YS E n S ,e6 ' Y6 n ,e n E n S S,ee Ai ht| |ih4 ? |i ht| Lh_ih UL?_|L? EH t |i 4@h}?@* 4T@U| Lu @ U@?}i ? hi@* M@*@?Uit L? ThL|tc *i |i tiUL?_ |ih4 t |i |L|@* 4@h}?@* 4T@U| Lu |i U@?}i ? hi@* M@*@?Uit L? hitLhUit At ?U*_it |i _hiU| S igiU| ,6 c |i ?_hiU| igiU| |hL} i Ti?_|hit ,e S Y Y6 c @?_ |i igiU| L? hitLhUit uhL4 |i ULt|*) ThL_U|L? Lu |i }LL_ k Ai igiU| |hL} S i Ti?_|hit ,e S Y Y6 hit*|t uhL4 |i 4T@U| |@| @ U@?}i ? hi@* M@*@?Uit U@? @i L? ML| |i ?@|L? @?_ |i UL?t4T|L? |@ Ai U@?}i ? |i UL?t4T|L? |@ ** ? |ih4 @giU| i Ti?_|hit U U@? @i @ 4@h}?@* 4T@U| L? |4i ti_ uLh |h@?t@U|L?t `i? |i 4@h}?@* ThL_U|L? ULt| Lu hi@* M@*@?Uit t 3ihLc tL |@| k ' fc |i? @| u** *^_|)c ihi ,6 ' fc |i 4@h}?@* 4T@U| ML| L? ThL|t @?_ YS S L? hitLhUit t @*tL 3ihL @t *L?} @t ,e ' fc Lh Y Y6 ' f Y6 ' fc i? ,e6 ' f L|Ui |@| |i ht| Lh_ih UL?_|L? EH U@? @*tL Mi h||i? @t % & YS dL E& n bo ,6 n ,e S n b ' fc Y6 k U t |i t@4i i ThittL? @t Efc i? k ' f 5L |i UL?_|L?t LM|@?i_ ? |i *@t| tiU|L?c uLh |i 6hi_4@? h*i |L Mi LT|4@* @hi UL?_|L?t L? |i 4@h}?@* 4T@U| L? ThL|t @?_ hitLhUit ?i U@ti ? U U*i@h*) |ihi U@? Mi ?L igiU|t L? |4i ti_ uLh |h@?t@U |L?tc t i? & 9' f @?_ ,e t 3ihLc @| u** *^_|) W? |t U@tic uhL4 ,*ih<t |iLhi4 r& ' ,e S E n S n ,6 6c | 4t| Mi |hi |@|c @| u** *^_|)c |i |4i tTi?| L? |h@?t@U|L?t t @*tL 3ihL 3ihL ?@|L? |@ t LT|4@* ? |t U@ti L?t_ih ?L |@| & ' fc @t | t |i U@ti i? |i |iU?L*L}) |@!it |i uLh4 t}}it|i_ M) |i @4L*ALM? 4L_i* Lu |i _i4@?_ uLh 4L?i) W| uL**Lt |@| ,e 4t| Mi 3ihL @| u** *^_|)c *i |h@?t@U|L?t |4i 4@) i** Mi TLt|i @| |@| TL?| Ai?c ii? |L} |h@?t@U|L?t @hi ULt|*) @| |i TL?| Lu u** *^_|)c @ 4@h}?@* U@?}i ? hi@* M@*@?Uit _Lit ?L| @giU| |4i ti_ uLh |h@?t@U|L?t Oi?Uic |i 6hi_4@? h*i t @*tL LT|4@* 5TTLti ?L |@| hi@* M@*@?Uit ihi ULt|*) |L ThL_Uic i k 9' f Ai? @ |h@?tuLh4i_ 6hi_4@? h*i L*_ ULhhitTL?_ |L @ 3ihL |@ L? |i ?|ih4i_@|i }LL_ 6c tL |@| |i ThUi Lu hi@* M@*@?Uit L*_ Mi |i ULt| Lu ThL_U|L?c ,6 ' k W? |t U@tic |i UL?_|L?t ,e ' f Lh ,e6 ' f L*_ ?L| Mi t@|ti_ @| |i TL?| ,6 ' k c tL |@| ? }i?ih@* |ihi L*_ Mi @? 4T@U| L? ThL|t @?_ L? hi@* hitLhUitc @?_ |ihiuLhi |i tiUL?_ Mit| L*_ ?L| Mi U@h@U|ih3i_ M) @ 3ihL |@ L? 6 Wu |i |h@?t@U|L?t |iU?L*L}) @t L4L}i?iLt Lu _i}hii c |i ThL|t L*_ Mi 3ihLc M| |i |ih4 Lu |i 4@h}?@* igiU| Lu hi@* M@*@?Uit L? hitLhUit L*_ t|** ?L| U@?Ui* L|c @?_ tLc @*tL ? |t U@tic | L*_ Mi LT|4@* |L |@ |i ?|ih4i_@|i }LL_ iU@ti Lu |i T@h|U*@h ThL_U|L? @?_ |@ t|hU|hi ? |t iUL?L4)c #@4L?_ @?_ hh*iit Eb. |@ @|L? h*it Lu ?|ih4i_@|i h*it U@??L| Mi @TT*i_ `i? |i ULt| Lu ThL_U?} |i ?|ih4i_@|i }LL_ @TThL@Uit 3ihLc | 4@) @*hi@_) Mi hi@tL?@M*i |L 4@!i |i @tt4T|L?t |@| 3ihL L| |i 4T@U| Lu U@?}it ? hi@* M@*@?Uit L? ThL|t Lh L? |i hitLhUit W? u@U| |i @tt4T|L? |@| ,e ' fc @t Mii? 4@_i ? |i *|ih@|hi EV k4MhL}c bHSc t?Ui | 4i@?t |@| |4i ti_ uLh |h@?t@U|L?t t 3ihL @| u** *^_|) EuLh _i}hii Lu L4L}i?i|) _gihi?| uhL4 3ihL *tLc i? u** *^_|) t @||@?i_ @| @? @hM|h@h*) *@h}i @*i Lu hi@* M@*@?Uitc |i? ,e6 ' fc i? ,6 ' f W? u@U|c @| u** *^_|)c ,e6 ' f 4T*it |@| ,66 ' fc @?_ |t 4t| Mi |hi u ,6 f ,6 f t L?i Lu Lh @tt4T|L?t L? |i |h@?t@U|L?t |iU?L*L}) W? @?) U@tic | t t|** TLttM*i |@| ,e E| @?_ ,e6 E| @hi ?L| 3ihL @| u** *^_|) 5?Uic i? |@| t tLc |i |L |@ it L? UL?t4T|L? @?_ L? ?UL4i @hi ?L| i^@*i?|c | t ?iUitt@h) |L UL4T|i |i LT|4@* ?@|L? |@ i? ML| |@ it U@? Mi ti_ |L}i|ih | |i ?@|L? |@ `i _L |t ? |i ?i | tiU|L? e A@ it L? L?i)c L?t4T|L? @?_ W?UL4i W? |t tiU|L? i @**L uLh ML| |i UL?t4T|L? @?_ |i ?UL4i |@ it |L Mi ti_ |L}i|ih | |i ?@|L? |@ `i tL |@| |i UL?_|L?t ?_ih U |i 6hi_4@? h*i t LT|4@* @hi |i }i?ih@* UL?_|L?t Lu L4L}i?i|) 2 Lu |i |h@?t@U|L?t u?U|L? @t LM|@?i_ ? Lhhi@ @?_ Ai*it EbbSc bb.c t?} L?*) ?UL4i |@ it @t |i @*|ih?@|i |L |i ?@|L? |@ `i @*tL tL |@| ?*itt ,e ' fc @| u** *^_|)c |i LT|4@* TL*U) UL4M?@|L? hi^hit |L u**) |@ ?UL4i @?_ tMt_3i UL?t4T|L? W? |@| Lh*_ ihi |i }Lih?4i?| L*_ Mi |_h@?} @** |i ?UL4i |L }i @ T@h| M@U! |L |i @}i?|t @t UL?t4T|L?c }hLtt i Ti?_|hit L*_ Mi 3ihL @?_ hitLhUit ti_ uLh |h@?t@U|L?t L*_ Mi 4?43i_ `i ThLUii_ |L tL |iti hit*|t Ai LtiL*_t ?L 4@ 43i Ec tMiU| |L E2 @?_ |L |i M_}i| UL? t|h@?|G | EnS| S| n|n n|n | E,| d | ,EE n S| S| c 6| on| nEn| | Eb f n f f | |i LT|44 |i uL**L?} 4@h}?@* UL?_|L?t 4t| Mi t@|ti_G % & LS E| ' E n S| n ,e E| c L E| E ,| | c ,| # $ L E| ,| ' E n o|n qL E| n ,|n ,6 E| ' E2f E2 E22 L|Ui |@| |ihi t @? ?_i|ih4?@U) Lu |i ThUit uhL4 |i Th@|i ThLM *i4 W? u@U|c E2f @?_ E2 @hi |L i^@|L?t ? |hii ?!?L?tG S| c ,| c @?_ | AihiuLhic | t L?*) TLttM*i |L i Thitt |L ThUit @t u?U|L?t Lu |i ^@?||it @?_ Lu |i hi4@??} ThUi `i ULLti |L i Thitt ,| c @?_ | @t @ u?U|L? Lu S| W? |t ti|T |i +@4ti) ThLM*i4 t _i?i_ M) |i 4@ 43@|L?c | hitTiU| |L |i ^@?||it @?_ |L |i *ii* Lu |i UL?t4T|L? |@ c Lu |i |*|) u?U|L?c tMiU| |L |i 4T*i4i?|@M*|) UL?_|L? @?_ |i hitLhUit UL?t|h@?| 5Mt|||?} i^@|L?t E2fE22 ?|L |i ?|ih|i4TLh@* M_}i| UL?t|h@?|c hi@hh@?}?}c @?_ t?} |i u@U| |@| , E| t L4L}i?iLt Lu _i}hii &c i LM|@? |i t@4i i ThittL? uLh |i 4T*i4i?|@M*|) UL?_|L? @t ? |i U@ti i? @ UL?t4T|L? |@ t |i L?*) @*|ih?@|i |@ |L ?@|L? `i hih|i | ihi uLh UL?i?i?UiG " | [ q iLS E|S| L E| dE | n E &, ES| E n S| c 6| oj ' f |'f E2 Ai hitLhUit UL?t|h@?|t @hi @*tL _i?|U@*c @?_ @hi }i? M) S| n }| | , ES| E n S| c 6| E2e L|Uic Liihc |@| ?L S| t @ ULUi @h@M*i uLh |i }Lih?4i?| wi| @?_ q | b| Mi |i 4*|T*iht Lu |i 4T*i4i?|@M*|) UL?_|L?t @?_ |i hitLhUit UL?_|L?tc hitTiU|i*) `i ** Mi t?} |i ht| Lh_ih UL?_|L?t Lu |i +@4ti) ThLM*i4c uLh *ithic hi@* M@*@?Uitc @?_ |i UL?t4T|L? |@ c |@| @hi }i? hitTiU|i*) M) L n iLS S| n L L d | n E& , E|oj ' b| E2D dL E& n b| o ,6 E| ' f E2S dL E& n b| o S| ,e E| ' f E2. hLTLt|L? 2 wi| |i }Lih?4i?| ?@?Ui i Ti?_|hit |hL} @? ?UL4i |@ c @ UL?t4T|L? |@ c Lh @? ?@|L? |@ c @?_ *i| |i |h@?t@U|L?t |iU?L* L}) |@!i |i uLh4 ? E2 Ai?c @? ?|ihLh tL*|L? Lu |i +@4ti) ThLM*i4 hi^hit |@| ,6 E| ' ,e E| ' f *tLc u ,e E| ' f @| u** *^_|)c uLh @?) e| c |i? |i LT|4@* tL*|L? t _iUi?|h@*3i_ M) | ' fc @?_ M) @ UL?|?4 Lu UL4M?@|L?t Lu S| @?_ ,| At t |i U@ti uLh |i @4L*ALM? |h@?t@U|L?t |iU?L*L})( u ,e E| : f @| u** *^_|)c uLh @?) e| c |i? |i LT|4@* tL*|L? t _iUi?|h@*3i_ M) | ' fc S| ' c @?_ ,| ' W? |t U@ti i Ti?_|hit @hi 3ihL @| |i LT|44 hLLu 6hL4 E2S @?_ E2.c u |i |ih4 ? t^@hi Mh@U!i|t t ?L| 3ihLc |i? | t U*i@h |@| @? ?|ihLh tL*|L? 4t| t@|tu) ,6 E| ' ,e E| ' f W? TTi?_ c i tL |@|c ?_ii_c |i |ih4 ? t^@hi Mh@U!i|t t t|hU|*) TLt|i `i ?L ThLUii_ |L tL @?_ e wi| ,e ' f @| u** *^_|)c uLh @?) e| ' S| EnS| Ai?c i^@|L? E2S t t@|ti_ M) ,6 E| ' fc @?_ i^@|L? E2. t t@|ti_ uLh @?) @*i Lu S| 6hL4 |i ht| Lh_ih UL?_|L? Lu |i Th@|i ThLM*i4 E2c |i LT|4@* tL*|L? t _iUi?|h@*3i_ M) | ' fc @?_ M) @?) UL4M?@|L? Lu S| @?_ ,| U t@|tit |i Th@|i ht| Lh_ih UL?_|L? E2f 6Lh |h@?t@U|L?t |iU?L*L}it | & ' fc ? T@h|U*@h uLh |i @4L*ALM?c ,e ' f @| u** *^_|)c uLh @?) e At t U*i@h t?Uic r& ' ,e e n,6 6c uhL4 ,*ih<t |iLhi4 wi| ,e : f @| u** *^_|)c uLh @?) e| t tL? ? TTi?_ c |i |ih4 ? t^@hi Mh@U!i|t ? E2. t ?L| 3ihL @?_ |ihiuLhic |ihi t ?L ?|ihLh tL*|L? `i ?L UiU! uLh @ ULh?ih tL*|L? Ai igiU| Lu @ 4@h}?@* U@?}i ? |i UL?t4T|L? |@ L? i*u@hi t }i? M) |i _ih@|i Lu |i w@}h@?}@? Lu |i +@4ti) ThLM*i4 | hitTiU| |L S| c U U@? Mi hih||i? @t Yu ' dL E& n b| o S| ,e E| E2H YS| 5?Ui ,e E| fc @?_ t?Ui |i |ih4 ? t^@hi Mh@U!i|t t TLt|i uLh Yu t @*@)t @?) _i}hii Lu L4L}i?i|) Lu |i |h@?t@U|L?t |iU?L*L})c Y S| ?i}@|i AihiuLhic | t @*@)t LT|4@* |L _iUhi@ti |i UL?t4T|L? |@ ? Lh_ih |L ?Uhi@ti i*u@hi Oi?Uic i UL?U*_i |@| i*u@hi t 4@ 43i_ @| S| ' i)L?_ |t TL?| i Ti?_|hit L*_ MiUL4i ?i}@|i @?_ |i ThLM*i4 L*_ ?L| Mi i** tTiUi_ 6hL4 |i ht| Lh_ih UL?_|L? Lu |i Th@|i ThLM*i4 E2fc hih||i? @t ,| ' L E| E n S| c LS E| L E| E n S| ,e E| | uL**Lt |@| |i LT|4@* @*i Lu |i ?UL4i |@ t ,| ' 5?Uic uhL4 E2S @| |i LT|44 ,6 E| ' fc |i 6hi_4@? h*ic | ' fc t @*@)t LT|4@* Ai ThLTLt|L? t|@|it |@|c i? i @**L uLh |i ti Lu ML| UL?t4T |L? @?_ ?UL4i |@ it @t @*|ih?@|i |@ ?t|h4i?|t |L ?@|L?c |i 6hi_ 4@? h*i t @*@)t LT|4@* Ai ?||L? t |@|c uLh @?) i_ *ii* Lu |i UL?t4T|L? |@ c | t @*@)t Thiuih@M*i |L ti| |i ?@|L? |@ |L 3ihL @?_ D |L h@ti |i ?iUitt@h) hii?it |hL} |i ?UL4i |@ At t |i t|@?_@h_ ThLM*i4 @?@*)3i_ M) Lhhi@ @?_ Ai*it EbbSc bb. i? |i) UL4T@hi |i ?@|L? |@ | @? ?UL4i |@ Ai UL?t4T|L? |@ t t| @ T@h@4i|ih ? |@| ThLM*i4 5L | t U*i@h |@| |i 6hi_4@? h*i t @*@)t LT|4@* Ai T@h|U*@h*) t|h!?} *ittL? uhL4 hLTLt|L? 2 t |@| i? ,e t ?iih 3ihL @| |i TL?| Lu u** *^_|)c Lh i? ,e t 3ihL L?*) i? e ' fc |i? |i LT|44 hi^hit |@| UL?t4T|L? t UL4T*i|i*) tMt_3i_ @?_ *@MLh t UL4T*i|i*) |@ i_ W? |@| tL*|L?c LtiL*_t @hi *iu| | ?L ?UL4ic @?_ UL?t4T|L? t uhii 5?Ui UL?t4T|L? t uhiic |ihi @hi ?L |h@?t@U|L?t @?_ |ihiuLhic hitLhUit tTi?| L? |h@?t@U|L?t @hi 4?43i_ W? T@h|U*@hc i? & : fc |h@?t@U|L?t |4i t 3ihL @| |i LT|44c ?L 4@||ih @| |i *ii* Lu UL?t4T|L? t At LMiU|i |L 4?43i hitLhUit ti_ uLh |h@?t@U|L?t @*tL i T*@?t |i hit|hU|i UL?_|L?t uLh |i LT|4@*|) Lu |i 6hi_4@? h*ic i? |i ULUi t Mi|ii? |i ?@|L? |@ @?_ |i UL?t4T|L? |@ *tL |ihic |ihi t @? ?Ui?|i |L hi_Ui |i |@ L? UL?t4T|L? ? Lh_ih |L t@i L? hitLhUit ti_ uLh |h@?t@U|L?t `i? |i ?UL4i |@ t @@*@M*i @t i**c | t |i? TLttM*i |L |@!i |t @h}4i?| |L |i *4|c @?_ @t @ hit*| i LM|@? |i i |hi4i TL*U) ThitUhT|L? |@| UL?t4T|L? tL*_ Mi u**) tMt_3i_ | |i i@h| Lu |t ThLM*i4c |ihi t @? ?ULhhiU| tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L}) L|Ui |@| ? |t iUL?L4) |4i ti_ uLh |h@?t@U |L?t t 4?43i_ i? |i }Lih?4i?| @t |L |_h@ @** |i hitLhUit ? UhU*@|L? @?_ |i? }i |i4 M@U! @t UL?t4T|L? |L |i @}i?|t `i ?L |h? |L |i _tUttL? Lu @? @*|ih?@|ic 4Lhi @TThLTh@|ic tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L}) D W4ThL?} L? |i 5TiUU@|L? Lu |i Ah@?t @U|L?t AiU?L*L}) Ai |h@?t@U|L?t |iU?L*L}) @t tL u@h Mii? hiThiti?|i_ M) | r| ' , S| E n S| c | At tTiUU@|L? @t @? ?_ith@M*i ThLTih|) |@| i T*@?t |i ?hi@tL?@M*i TL*U) ThitUhT|L?t LM|@?i_ MiuLhi W? u@U|c ?L|Ui |@|c uhL4 L4L}i?i|)c S |i u?U|L? U@? Mi h||i? @t # r| ' E n S| , S| c & | E n S| | $ E|U| ihi & t |i _i}hii Lu L4L}i?i|) L|Ui |@|c uLh & 9' fc | t TLttM*i |L U@?}i |4i ti_ uLh |h@?t@U|L?tc |L| U@?}?} |i hi@* ^@?||) Lu |h@?t@U|L?t 4i@thi_ ? ?|t Lu |i UL?t4T|L? }LL_c S| c @?_ |L| | U@?}?} |i hi@* ^@?||) Lu 4L?i) hi^hi_ |L M) |Lti }LL_tc En S| | At U@? Mi @Uii_ M) @TThLTh@|i*) U@?}?} |i |@ L? UL?t4T|L? | | @?_ | ? i |hi4i i @4T*i Lu |t t |@|c M) U@?}?} | |L hit|Lhi u** *^_|)c | t TLttM*i |L TU! S| ' t @ hit*| e| ' fc @?_ |i? |4i ti_ uLh |h@?t@U|L?t t @*tL 3ihLc r| ' f At t U*i@h*) @ i@!?itt Lu |i tTiUU@|L? `i ThLTLti ?L @ tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L}) |@| _Lit ?L| t@hi |t ThLTih|) uLh @?) _i}hii Lu L4L}i?i|) W?_ii_c | t @ }LL_ ThLTih|) Lu |i 4L_i* |@| i? |i hi@* ^@?||) Lu |i }LL_t _Lit ?L| U@?}i @?_ i? 4L?i) ?ii_i_ |L M) |iti }LL_t _Lit ?L| U@?}i @t i**c |i? |4i ti_ uLh |h@?t@U|L?t tL*_ ?L| U@?}i i|ih Ai ?i |h@?t@U|L?t |iU?L*L}) t _itUhMi_ M) # $ | h r| ' , S| c E2b E n S| | Ai |L tTiUU@|L?t @hi i^@*i?| i? & ' f W? |t U@tic @| u** *^_|)c ,e E| ' ,hS E| ' fc @?_ |ihiuLhi | t ?L| TLttM*i |L @giU| |i |4i ti_ uLh |h@?t@U|L?t N?_ih |i ?i tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L})c |i 6hi_4@? h*i t LT|4@* i? |i }Lih?4i?| ULLtit Mi|ii? |@ ?} UL?t4T|L? Lh 4L?i) `i ?L ThLUii_ |L tL |t `i }L M@U! |L |i 4L_i* iUL?L4) Lu 5iU|L? c ihi |i L?*) @*|ih?@|i |L ?@|L? t @ |@ L? UL?t4T|L? @?_ ihi |@ it @hi T@_ | 4L?i) Ai _gihi?Ui t |@| i @_LT| |i ?i tTiUU@|L? uLh |i |h@?t@U|L?t ULt| |iU?L*L})c @t _itUhMi_ M) E2b Ai LtiL*_t |i? 4@ 43i Ec tMiU| |L E2b @?_ |L |i M_}i| UL?t|h@?| Ec ihi `f ' f Ai ht| Lh_ih UL?_|L?t @hiG LS E| ' n S| n ,hS E| c L E| . Ef h,6 E| ' | E n S| c E L E| ' n o|n c qL E| n E2 | 5Mt|||?} i^@|L?t EfE2 ?|L |i i| ' En Lc _i?i 6 S| | ?|ih|i4TLh@* M_}i| UL?t|h@?| E.c @?_ t?} |i u@U| |@| h, E| t L4L}i ?iLt Lu _i}hii &c i LM|@? |i 4T*i4i?|@M*|) UL?_|L? " |q k lr [ i| ' f q LS E|S| L E| E | n E &h, ES| c 6 |'f E Ai hitLhUit UL?t|h@?|t @hi }i? M) i| S| n }| | h, ES| c 6 Ee i| t Ai 4@h}?@* UL?_|L? Lu |i +@4ti) ThLM*i4 uLh 6 d E& n b| o ,h6 h E| ' f ED ihi @?_ q | b| @hi |i 4*|T*iht Lu |i 4T*i4i?|@M*|) UL?_|L?t @?_ |i hitLhUit UL?_|L?tc hitTiU|i*) hLTLt|L? Ai +@4ti) @**LU@|L?c i? |i }Lih?4i?| U@? ?@?Ui i Ti?_|hit |hL} @ UL?t4T|L? |@ @?_ @? ?@|L? |@ c @?_ |i |h@?t @U|L?t |iU?L*L}) |@!it |i uLh4 ? E2bc t _iUi?|h@*3i_ M) | ' fc uLh @** | hLLu | u** *^_|)c ,h6 h E| ' f 6hL4 i^@|L? E | @TTi@ht |@| |i LT|4@* tL*|L? UL*_ Mi _iUi?|h@*3i_ M) i|ih | ' f @?_ S| : fc Lh M) S| ' @?_ | : f OLiihc ti||?} S| ' c L*_ 4T*) |@| |i hi*@|i ThUi Lu UL?t4T|L? L*_ Mi 3ihLc U L*_ ULhhitTL?_ |L t@|@|L? ? UL?t4T|L? W? u@U|c i U@? hih|i |i ht| Lh_ih UL?_|L? Lu |i Th@|i ThLM*i4c Efc @t LS E| h,S E| L E| ' n S| L E| `i? S| ' c | 4t| Mi |@| |i *iu| @?_ t_i Lu |i i^@|L? @MLi t ti| |L 3ihL At t |i U@ti i? LS E|,hS E| L E| ' fc i |i 4@h}?@* Mi?i| Lu UL?t4T|L?c ?i| Lu |i ULt| ? |ih4t Lu *ithi Lu }ih |h@?t@U|L?t |4ic H t 3ihL Ai ThUi Lu UL?t4T|L? MiUL4it tL *L |@| LtiL*_t @hi t@|@|i_ ? UL?t4T|L?D At t ?L| ui@tM*i N?_ih |i ?i tTiUU@|L?c | t ?L *L?}ih TLttM*ic @| u** *^_|)c |L hi_Ui |4i ti_ uLh |h@?t@U|L?t M) ?Uhi@t?} |i tMt_) L? UL?t4T|L? | Atc i| c ihi 6 i| ' En W? u@U|c ? |t U@ti &r| ' ,hS E|S| n ,h6 h E|6 S| | _iUhi@t?} |i |@ L? UL?t4T|L?c @| u** *^_|)c _Lit ?L| @giU| |i |4i ti_ uLh |h@?t@U|L?t Ai hit*|t ? |t tiU|L? @**L t |L UL?U*_i |@| |i 6hi_4@? h*i t |i LT|4@* TL*U) uLh @** L4L}i?iLt |h@?t@U|L?t |iU?L*L}it W| t |ihiuLhi @ }i?ih@* hit*| Ai L?*) hi4@??} @h}4i?| uLh uh@}*|) Lu |i LT|4@*|) Lu |i 6hi_4@? h*i t *@U! Lu L4L}i?i|) W? u@U| u |i |h@?t@U |L?t |iU?L*L}) t ?L| L4L}i?iLt |i 6hi_4@? h*i 4@) ?L| Mi LT|4@*S AiLhi|U@* Lh! L? |h@?t@U|L?t |iU?L*L}it tTTLh|t |i @tt4T|L? Lu L4L}i?i|) At t |i U@ti ? @4L* EbD2 @?_ ALM? EbDSc |i }i?ih@*3@|L? Lu @hhL Eb.Sc B_L|| EbHb Lh aL@?LU EbH2 W? @** |iti 4L_i*t |i |h@?t@U|L?t |iU?L*L}it @hi L4L}i?iLt Lu _i}hii 3ihL @ht@** Ebb2 ThLTLtit @?_ it|4@|it @ |h@?t@U|L?t |iU?L*L}) |@| t L4L}i?iLt Lu _i}hii L?i( @?_ h@? Ebbe it|4@|it |i _i}hii Lu L4L }i?i|) |L Mi bH OL4L}i?iLt u?U|L?t @i |i ThLTih|) |@| |i tU@*i i*@t|U|) Lu |i 4L?i) _i4@?_ t L?ic @| u** *^_|) W?_ii_c uLh @? L4L}i?iLt u?U|L? r ' ,Eec 6c i U@? h|i , ' uE 6e e& | u** *^_|)c i @i u E 6e ' fc tL |@| 6 ' kec ihi k t @ UL?t|@?| `*i |ihi t i4ThU@* i_i?Uic Lu|i? UL?|h@_U|Lh)c L? |i tU@*i i*@t|U|)c |ihi t h|@**) ?L i_i?Ui L? |i i*@t|U|) @| u** *^_|) Ai U*Ltit| i_i?Ui @hi |i hit*|t ? **}@? @?_ 5@*@@h|? EbbS |@| t}}it| |@| |i tU@*i i*@t|U|) Lu |i LtiL*_ _i4@?_ uLh 4L?i) @TThL@Uit L?i uLh ?|ihit| h@|it |@| @hi Mi*L |i Uhhi?| L?it W? @?) U@tic ? |i UL4T|@|L? Lu |i LT|4@* ?@|L? |@ c **}@? @?_ 5@*@@h|? Ebb. 4@!i |i @tt4T|L? Lu L4L}i?i|)c @?_ UL?Ui?|h@|i L? |i 4T@U| Lu |i hit|hU|L? |@| |@ it @hi T@_ | 4L?i) L? |i LT|4@* ?@|L? |@ L| thTht?}*) |i) UL?U*_i |@| |i LT|4@* ?@|L? |@ t ih) U*Lti |L |i 6hi_4@? h*i 8 Li wkhuh zhuh wd{hv rq lqfrph/ wkrvh wd{hv frxog xqgr wklv hhfw/ dqg lw frxog vwloo eh rswlpdo wr vhw fw @ 4/ dv lv wkh fdvh lq Vhfwlrq 61 9 Fruuhld dqg Whohv +4<<;,/ xvlqj d fdoleudwhg prgho zlwk XV gdwd rq wkh prqh| gh0 pdqg/ vkrz wkdw li wkh wudqvdfwlrqv whfkqrorj| lv qrw krprjhqhrxv/ vwloo wkh rswlpdo lqdwlrq wd{ lv yhu| forvh wr wkh Iulhgpdq uxoh1 b S Wt |i T|4@*|) Lu |i 6hi_4@? +*i @ +LMt| +it*|q L?U*_?} +i4@h!t W? |t T@Tihc i UL4T|i |i LT|4@* ?@|L? |@ ? @ t4T*i 4L?i|@h) 4L_i* ihi 4L?i) @?_ |4i @hi ti_ uLh |h@?t@U|L?t `i tL |@| |i 6hi_4@? h*i t |i LT|4@* tL*|L? i|ih |i tU@* ULUi t Mi|ii? @? ?UL4i |@ @?_ @? ?@|L? |@ c @ UL?t4T|L? |@ @?_ @? ?@|L? |@ Lh |i |hii |@ ?t|h4i?|tc @?_ i|ih |@ it @hi T@_ | Lh ?L| W? _L?} tLc i LMiU| |L |i U*@4 ? hiUi?| *|ih@|hi EV **}@? @?_ 5@*@@h|?c bb. |@|c i? |@ it 4t| Mi T@_ | 4L?i)c |i UL?_|L?t ?_ih U |i 6hi_4@? h*i t LT|4@* @hi hit|hU|i @?_ |@| |ihiuLhi |i LT|4@*|) Lu |i 6hi_4@? h*i t @ uh@}*i hit*| `i @h}i |@| @ 4tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L}) t |i hi@tL? uLh |i @TT@hi?| uh@}*|) Lu |i LT|4@*|) Lu |i 6hi_4@? h*ic i? UL?t4T|L? |@ it @hi ti_ `i? |i }Lih?4i?| u@Uit |i ThLM*i4 Lu ULLt?} |i UL4M?@|L? Lu |i ?UL4i @?_ |i ?@|L? |@ c |i LT|4@* tL*|L? t |L u**) ti |i ?UL4i |@ @?_ @Mt|@? uhL4 |@ ?} 4L?i)c uLh L4L}i?iLt |h@?t@U|L?t u?U|L?t Lu @?) _i}hii At t tL? ? Lhhi@ @?_ Ai*it EbbSc bb. Ai hi@tL? uLh |i }i?ih@* hit*| Lu LT|4@*|) Lu |i 6hi_4@? h*i t |i uhii }LL_ U@h@U|iht|U Lu 4L?i) W?_ii_c u 4L?i) @t ULt|*) |L ThL_Uic | L*_ L?*) Mi LT|4@* ?L| |L |@ 4L?i) uLh UL?t|@?| hi|h?t |L tU@*i |h@?t@U|L?t |iU?L*L}it Ai *|ih@|hi L? |i LT|4@* tU@* ULUi Mi|ii? |i ?@|L? |@ @?_ @ UL?t4T|L? |@ @t _i?|i_ @__|L?@* hit|hU|L?t uLh |i 6hi_4@? h*i |L Mi LT|4@*c i? |@ it @hi T@_ | 4L?i) `i tL |@| |iti hit|hU|L?t @hi ?L *L?}ih ?iUitt@h) i? ?UL4i |@ it @hi @*tL @@*@M*ic |L}i|ih | UL?t4T|L? |@ it `i @*tL tL |@| |i hi@tL? uLh |i @__|L?@* hit|hU|L?t t @ 4tTiUU@|L? Lu |i |h@?t@U|L?t |iU?L*L}) N?_ih @ 4Lhi hi@tL?@M*i tTiUU@|L? ihi |t ThLTih|) t ?L| Thiti?|c |i hit*| tL? M) Lhhi@ @?_ Ai*it EbbSc bb. |@| |i LT|4@*|) Lu |i 6hi_4@? h*i t @ hLMt| hit*| t u**) hiULihi_ Ai |h@?t@U|L?t |iU?L*L})c @t t tTiUi_ ? |@| *|ih@|hic @t |i ? _ith@M*i ThLTih|) |@| | t TLttM*i |L hi_Ui |i |4i ti_ uLh |h@?t@U|L?tc |L| U@?}?} hi@* UL?t4T|L? @?_ hi@* 4L?i) ti_ |L M) |c M) hi_U ?} |i |@ L? UL?t4T|L? W? T@h|U*@h u UL?t4T|L? t u**) tMt_3i_c |i? |4i ti_ uLh |h@?t@U|L?t U@? Mi ti| |L 3ihL 5?Ui ?UL4i |@ it @hi 2f @@*@M*ic | t ui@tM*ic @?_ 4@) Mi LT|4@*c |L u**) tMt_3i UL?t4T|L? M) u**) |@ ?} ?UL4i Ai t@4i 4iU@?t4 i T*@?t |i hit|hU|i UL?_ |L?t _i?|i_ ? |i *|ih@|hi uLh |i 6hi_4@? h*i |L Mi LT|4@*c i? |i }Lih?4i?| ULLtit |i LT|4@* UL4M?@|L? Lu |i ?@|L? |@ @?_ @ UL?t4T|L? |@ Ai LT|4@*|) Lu |i 6hi_4@? h*i t ?_ii_ @ hLMt| hit*| MiU@ti |i }i?ih@*|) Lu |i hi^hi_ UL?_|L?t Lu L4L}i?i|) U@? ?L| Mi uL?_ ? @?) L|ih ti|t Lu h*it ? |i M*U 6?@?Ui *|ih@|hi W| t |i uhii }LL_ U@h@U|iht|U Lu 4L?i) |@| i T*@?t |t hLMt|?itt Ai hi*i@?| ^it|L? @4L?|t |L @t!?}G `@| t |i LT|4@* ThUi U@h}i_ L? @ }LL_ |@| @t @ ih) *L ULt| Lu ThL_U|L?q ,i? u |i LT|4@* @_@*Lhi4 |@ t ih) }c t|** |i ThUi tL*_ ? }i?ih@* Mi ^|i *L At t |i hi@tL? uLh |i hLMt|?itt Lu |i 6hi_4@? h*i @t @? LT|4@* |@ @|L? h*i 2 +iuihi?Uit do @hhLc +LMih| ac W?|i}h@* L?t|h@?|t @?_ }}hi}@|L? ? @? W?i?|Lh) L_i* Lu L?i) #i4@?_c aLh?@* Lu 6?@?Ui Eb.Sc ..H. d2o @4L*c `**@4 ac Ai Ah@?t@U|L?t #i4@?_ uLh @tG ? W?i?|Lh) AiLhi|U TThL@Uc "@h|ih*) aLh?@* Lu ,UL?L4Ut SS EbD2c DeD DDS do h@?c ?|L?c ?L|ih ||i4T| |L "@?|u) |i i?i|t Lu +i_U?} W?@|L?c 6i_ih@* +itihi @?! Lu ??i@TL*t "@h|ih*) +ii 6@** Ebbec .2D deo @hc V Vc w@hi?Ui a ht|@?L @?_ @|hU! a kiLic T|4@*|) Lu |i 6hi_4@? +*i ? ,UL?L4it | #t|Lh|?} A@ itc aLh?@* Lu L?i|@h) ,UL?L4Ut . EbbSc 2f22 dDo Lhhi@c Wt@Mi* @?_ i_hL Ai*itc Wt |i 6hi_4@? +*i T|4@* i? L?i) t @? W?|ih4i_@|i BLL_qc aLh?@* Lu L?i|@h) ,UL?L4Ut H EbbSc 222ee dSo Lhhi@c Wt@Mi* @?_ i_hL Ai*itc Ai T|4@* W?@|L? A@ c W?t| ||i Lu ,4ThU@* @UhLiUL?L4Ut Lu |i 6i_ih@* +itihi @?! Lu ? ?i@TL*t #tUttL? @Tih 2 Ebb.c uLh|UL4?} +ii Lu ,UL?L4U #)?@4Ut d.o #@4L?_c i|ih @?_ a@4it hh*iitc T|4@* A@ @|L? @?_ M *U hL_U|L?c 4ihU@? ,UL?L4U +ii S Eb.c H2.c 2S2SH dHo 6hi_4@?c *|L?c Ai T|44 "@?||) Lu L?i) W? Ai T|44 "@?||) Lu L?i) @?_ L|ih ,tt@)t i_|i_ M) 6hi_4@?c TT Dfc *_?ic U@}Lc W*c bSb dbo B_L||c @M*L ,c , U@?}i +@|i #i|ih4?@|L?c W?|ihit| h@|it @?_ @? W?|i}h@|i TThL@U |L |i #i4@?_ uLh L?i)c aLh?@* Lu W?|ih?@ |L?@* L?i) @?_ 6?@?Ui H EbHbc 2beD dfo B_L||c @M*L , @?_ @h*Lt Vi}c Ai T|4@* W?@|L? A@ i? L?i) +i_Uit Ah@?t@U|L?t Lt|tc aLh?@* Lu L?i|@h) ,UL ?L4Ut Ebbc Hb2fD 22 do aL@?LUc L)@?c W?@|L? @?_ `i*u@hi ? |i 5|i@_) 5|@|ic aLh?@* Lu L*|U@* ,UL?L4) bf EbH2c DSD.. d2o k4MhL}c ki?| c Ai T|44 "@?||) Lu L?i) +*i ? |i AiLh) Lu M*U 6?@?Uic aLh?@* Lu L?i|@h) ,UL?L4Ut H EbHSc 2..2He do wU@tc +LMih| ,c Ai `i*u@hi Lt| Lu W?@|L?c 44iLc Ai N?ih t|) Lu U@}Lc bbe deo @ht@**c #@_ c W?@|L? @?_ tti| +i|h?t ? @ L?i|@h) ,UL? L4)c aLh?@* Lu 6?@?Ui e. Ebb2c De2 dDo **}@?c @ti) @?_ j@ih j 5@*@@h|?c _LT|L? Lu 6?@?U@* AiU?L*L}itG W4T*U@|L?t uLh L?i) #i4@?_ @?_ L?i|@h) L*U)c ,+ `Lh!?} @Tih 5ihit rDDfec @hU bbS dSo **}@?c @ti) @?_ j@ih j 5@*@@h|?c Ai T|44 "@? ||) Lu L?i)G AiLh) @?_ ,_i?Uic aLh?@* Lu L?i)c hi_|c @?_ @?!?} Ebb.c VL*2bc L ec SH..D d.o +@4ti)c 6h@?! c L?|hM|L? |L |i AiLh) Lu A@ @|L?c ,UL ?L4U aLh?@* . Eb2.c e.S dHo ALM?c a@4itc Ai W?|ihit| ,*@t|U|) Lu |i Ah@?t@U|L?t #i4@?_ uLh @tc +ii Lu ,UL?L4Ut @?_ 5|@|t|Ut H EbDSc 2e2e. 2 +it|hU|i UL?_|L?t uLh |i LT|4@*|) Lu |i 6hi_4@? h*i W? |i i^@*i?| hi@* iUL?L4) |L |i 4L?i|@h) iUL?L4)c **t|h@|i_ ? 6}hi c UL?t4T|L? t ThL_Ui_ t?} *@MLh ? c @?_ |h@?t@U|L?tc neS c @UULh_?} |L @ wiL?|iu |iU?L*L})c S ' 4? neS c ? Ai ThL_U|L? Lu |h@?t@U|L?t hi^hit |4ic rc @?_ 4L?i)c 6 L?i) @*tL hi^hit *@MLhc ?2 c @UULh_?} |L @ *?i@h |iU?L*L}) | @ i_ ULiUi?|c 6 ' k?2 5?Ui |h@?t@U|L?t |4i @?_ *@MLh U@??L| Mi |@ i_c hii?it U@? L?*) Mi h@ti_ |hL} @ |@ L? UL?t4T|L?c S c @?_ @? @_@*Lhi4 |@ L? 4L?i)c 6 Ai @}i uLh *@MLh ? @** |i @U||it 4t| Mi |i t@4i @?_ t _i?L|i_ M) ? c *i R t |i ThUi Lu }LL_ ? ?|t Lu |i UL?t4T|L? }LL_ @hi ThL|tc i Thitti_ ? ?|t Lu |i UL?t4T|L? }LL_c LM|@?i_ uhL4 |i ThL_U|L? Lu |h@?t@U|L?tc |@| t |i L?*) ThL_U|L? u?U|L? |@| t ?L| UL?t|@?| hi|h?t |L tU@*i OLtiL*_t< ThLM*i4 @%L ESc c r| S E n S ' ? E n E n S Ai ThLM*i4t Lu |i h4t @ S ' S t| S ' 4? ? ? Re ec n S e c ? n S ? r R6 E n 6 6 c @ e ' e E n S Re Re t| r ' , Eec 6 ? ?2 @ 6 ' 6 c E n S R6 r| 6 ' k?2 6ht| Lh_ih UL?_|L?tG LS n S ' L ? 2e ES uhL4 |i LtiL*_< ThLM*i4( Re n ? ' 2 E n S E n S S ' ? ' uhL4 h4 E ThLM*i4( ,e ' ,6 ' uhL4 h4 E ThLM*i4( e E n S E n S Re ? E n 6 R6 ? EnS E. EH Eb Eef R6 E n S ' ? k uhL4 h4 E ThLM*i4 AL LM|@? |i 4T*i4i?|@M*|) UL?_|L? ESc T*} |i ht|Lh_ih UL? _|L?t ES ?|L |i LtiL*_<t M_}i| UL?t|h@?| AL LM|@? |i i ThittL? uLh ThL|tc ? ?|t Lu UL?t4T|L?c ' Re e ' Re e ? r R6 E n 6 6c n S Nt?} Eb @?_ Eef |L hiT*@Ui Re @?_ R6 E n 6 hitTiU|i*)c @?_ t?} ESc ? c i LM|@? |L hiT*@Ui n S ' L E& , ES E n S c 6 LS hLLu Lu hLTLt|L? 2 Oihi i tL |@|c @| |i LT|44c L E& n b| : f `i? & c |i |ih4 t t|hU|*) TLt|ic MiU@ti |i 4*|T*iht @hi t|hU|*) TLt|i W? u@U|c : f @| |i LT|44 t?Ui | 4i@thit |i i Uitt Mh _i? Lu |@ @|L? `i? & c @? @h}4i?| t4*@h |L |i L?i ti_ ? 2D Lhhi@ @?_ Ai*it EbbS i?thit |@| |i |ih4 t t|** t|hU|*) TLt|i AL tii Lc tMt|||i b| | |i i ThittL? }i? M) E2D 5?Ui |i ThLM *i4 t t|@|L?@h)c 4@?T*@|?} |i 4T*i4i?|@M*|) UL?_|L? i LM|@? ( E| S| ' d | n E& , E|o c ihi ( E| LLS EE|| t |i 4@h}?@* h@|i Lu tMt|||L? Mi|ii? UL?t4T|L? @?_ *ithi Nt?} |t i ThittL? @?_ hi@hh@?}?} |ih4tc i LM|@? |@| dL E& n b| o ' L n dL E| ( E| S| n L E| &o : f Ai t}? }i? |L |i i ThittL? uL**Lt uhL4 |i u@U| |@|c u UL?t4T|L? t @ ?L? ?uihLh }LL_c @? ?Uhi@ti ? *ithi ?Uhi@tit |i 4@h}?@* h@|i Lu tMt|||L?c tL |@| ( E| f 2S
© Copyright 2026 Paperzz