GUSTAVO ANDRÉ NUNES FERREIRA
DESENVOLVIMENTO DE UMA ARQUITETURA DE
CONTROLE BASEADA EM OBJETOS PARA UM ROBÔ
MÓVEL AQUÁTICO
Dissertação apresentada à Escola
Politécnica da Universidade de
São Paulo para obtenção do
Título de Mestre em Engenharia.
GUSTAVO ANDRÉ NUNES FERREIRA
DESENVOLVIMENTO DE UMA ARQUITETURA DE
CONTROLE BASEADA EM OBJETOS PARA UM ROBÔ
MÓVEL AQUÁTICO
Dissertação apresentada à Escola
Politécnica da Universidade de
São Paulo para obtenção do
Título de Mestre em Engenharia.
Área de Concentração:
Engenharia Mecatrônica e
Sistemas Mecânicos
Orientador:
Prof. Dr.
Ettore Apolônio de Barros
FICHA CATALOGRÁFICA
Ferreira, Gustavo André Nunes
Desenvolvimento de uma arquitetura de controle baseada em
objetos para um robô móvel aquático. São Paulo, 2003.
137 p.
Dissertação (Mestrado) – Escola Politécnica da Universidade
de São Paulo. Departamento de Engenharia Mecatrônica e
Sistemas Mecânicos.
1. Robôs 2.
Softwares
Orientado a Objeto 3. Sistemas de
A meus pais, que muito se esforçaram
por minha educação e a quem devo
Agradecimentos
Agradeço inicialmente o financiamento da Fundação de Amparo à Pesquisa
do Estado de São Paulo (FAPESP), tanto através do projeto individual de mestrado
“Arquiteturas de Controle Aplicadas a Robôs Móveis Oceânicos” (proc. FAPESP
2000/01121-6
), como através do projeto temático "Comportamento em Ondas de
Embarcações de Alto Desempenho" (proc. FAPESP 1997/13090-3), financiamento
sem o qual este projeto não seria possível.
Agradeço também a orientação do Prof. Dr. Ettore Apolônio de Barros,
juntamente com os demais professores que fazem parte do projeto temático já citado.
Agradeço a ajuda inestimável do amigo Flávio José Aguiar Soares, pela sua
supervisão na construção do modelo ITTC em fibra de vidro, juntamente com os
técnicos do Departamento de Engenharia Naval do Instituto de Pesquisas
Tecnológicas (IPT), pela sua cooperação nos diversos ensaios realizados no decorrer
de todo o projeto e pelo estímulo e amizade como colega de laboratório.
Agradeço aos estagiários Daniel Barbuto Rossato e Hélder Flores Silva pelo
trabalho realizado nas implementações eletrônicas deste projeto e ao estagiário
Cassius Resende Duarte pelos estudos iniciais com a unidade inercial e o
equipamento DGPS.
Agradeço a ajuda dos mestrandos Fábio Villas Boas e Fernanda de Sá
Teixeira nos ensaios de finalização deste projeto.
Resumo
Este trabalho trata do estudo de concepções de arquitetura do controle
aplicadas aos robôs móveis autônomos e da proposição de um delas à instrumentação
e controle em tempo real de um modelo de embarcação naval de alto desempenho.
Tal veículo remotamente operado foi desenvolvido como parte das atividades do
projeto temático "Comportamento em Ondas de Embarcações de Alto Desempenho"
(proc.Fapesp 1997/13090-3). Realizou-se uma investigação dos diversos paradigmas
de inteligência artificial que orientaram a evolução dos robôs móveis autônomos até
o presente momento e, em particular, as concepções baseadas em modelos
sócio-antropológicos e computacionais (teoria de agentes e orientação a objetos) através de
sua aplicação à implementação de um sistema de aquisição e controle orientado a
objetos, modelado através da UML (
Unified Modeling Language
), para o veículo
Abstract
☞✍✌✏✎✒✑✔✓✖✕✘✗✚✙✛✌✢✜✤✣✘✥✦✓✧✎ ✌✩★
☞✍✌✏✎✒✑✔✓✖✕✘✗✚✪✫✓✭✬✮✗✰✯✢✓✧✎ ★✘✌✏✌✏✌
✱✳✲✵✴
✑✔✥✦✶✷✕✸✣✸✹✻✺✭✶
✱
✼✻✽✾✼❀✿❂❁❄❃❆❅✾❇❉❈❄❊●❋❄❁✂✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ✼
✼✻✽❑❏▼▲❖◆✭P◗❅◗❘●❈❄❊●❋❉❁❚❙✮❯❱◆❳❲✵❘✵❨✾❩✧❘●❈▼✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❏
✼✻✽❬❪❭❴❫✰❵❛❲✒❃❆❅✾❇✻❁✻❯❝❜✧❈❡❞❖❅◗❯❱❯❱❲✵❢❛❃❣❈❄❊●❋❄❁❤✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬
✼✻✽✐❪❙✮❯❛❃❆❢❱❥❦❃❆❥✭❢❆❈❡❜✧❈❡❞❖❅◗❯❱❯❱❲✵❢❛❃❣❈❄❊●❋❄❁❧✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬
♠♦♥
✌✏✎✵✺✭✶q♣r✗s✥✦✓✧✯t✎✵✶❳✬✸✥✦✗✈✉✇✶❳✬✮①✤✎❡②❤③✰★✤✗✰✌✏✎❡④r✣✷✑✔①
✴
✶✤⑤⑥✶✤✎ ⑦
❏✰✽✾✼⑧▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❄❯✛❜✭❲❶⑩✍❁✻❷s❃❆❢❱❁✻P◗❲❸◆✧❈❄❢❆❈❡❹❝❁✻❫✤❺✻❯❻✿❂❼✔❇❽❲✵❅◗❯❝▲❖❥❦❃❆❺✻❷✭❁✻❾❚❁✻❯❿✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀
❏✰✽✾✼✻✽✾✼ ▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❄❯❻➁❻❅✾❲✵❢❆➂❄❢❱⑨s❥✭❅◗❘●❈❄❯➃✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✻✼
❏✰✽✾✼✻✽❑❏ ▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❄❯❻➁❻❲➄❃❣❲✒❢❣➂❉❢❆⑨s❥✭❅✾❘●❈❄❯❻✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔❬
❏✰✽✾✼✻✽❬ ▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❄❯❸➅❳➆❦➇➄➈✒➆✰➉❖➊✤➋➍➌➍➎❉➏➐✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼●✐
❏✰✽✾✼✻✽✐ ▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❄❯❻➁❻❨✾❫✭❢❆❅✾❜✧❈❄❯➑✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✦➒
❏✰✽❑❏▼▲❖➓✻❲✵❷❽❃❆❲✵❯❻❲■❞❖❲✵❯❱❲✵❷s❇✻❁✻P✾❇✰❅◗❾❚❲✵❷s❃❆❁❚➔t❈❄❯❱❲●❈❄❜✭❁❚❲✵❾→❭❴❫✰❵❛❲✒❃❆❁✻❯✚✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔➣
❏✰✽❑❏✰✽✾✼ ❞❖❲✒❩✧❷✭❅◗❊●❋❄❁❡❜✭❲■▲❖➓✻❲✵❷s❃❆❲❴✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✦↔
❏✰✽❑❏✰✽❑❏ ⑩✫❁✻❷✭❘✵❲✵❅✾❃❆❁❡❜✭❲↕❭❴❫❦❵❛❲➄❃❣❁➙✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔➛
❏✰✽❑❏✰✽❬ ▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲↕⑩✫❁✻❷❽❃❆❢❱❁✻P◗❲■➝✮❢❱❁✻◆✤❁✻❯❛❃❣❈➞✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏❄➠
➡⑧✲ ⑤⑥➢➤✯✏✌✏➥✻✓✧✹✻➦☛✗✰✎➜✕✘✗✚✪✍✗✰⑤⑥➢✮✶⑥✉✇✗s✓✧✯ ✴ ✓⑥④✇✥❉➧☛✣✸✌✩✑✔✗❽✑✦✣✘✥✦✓✚➨❍✥✦✶❳➢✮✶✤✎✒✑✔✓ ♠❳➡
❬❦✽✾✼❀➩✰❅◗❯❛❃❆❲✵❾➫❈❄❯✛❜✭❲■➭✸❲✵❾❚◆❳❁➫❹❝❲●❈❄P➯✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏❉✐
❬❦✽❑❏➲⑩t❈❄❢❆❈❄❘✒❃❆❲✵❢❱❨◗❯❛❃❆❅◗❘●❈❄❯❻➳❸❲✵❢❆❈❄❅◗❯t❜✭❲↕➩✰❅◗❯❛❃❆❲✵❾➫❈❄❯✛❜✭❲■➭✸❲✵❾❚◆✤❁➫❹❝❲●❈❄P❶✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏✻➒
❬❦✽❑❏✰✽❬ ➝✮❢❱❲✒❇✰❅◗❯❱❅◗❫✭❅◗P◗❅✾❜✧❈❄❜✭❲ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏✻↔
❬❦✽❑❏✰✽✐ ❞❖❲✵◆❳❲✵❷✭❜✧❈❄❫✭❅◗P◗❅◗❜✧❈❄❜✭❲✳✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏✻↔
❬❦✽❬❪➩✰❅◗❯❛❃❆❲✵❾➫❈❄❯❻❭❴◆❳❲✵❢❆❈❄❘✵❅◗❁✻❷✧❈❄❅◗❯✛❜✭❲■➭✸❲✵❾❚◆❳❁➫❹❝❲●❈❄P ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏❄➀
❬❦✽❬❦✽✾✼ ✁✄✂
❘✵P◗❲✵❁✻❯❝❜✭❲■➭✘❲✵❾❚◆✤❁➫❹❝❲●❈❄P☛✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏❄➛
❬❦✽❬❦✽❑❏ ✿❂❥✭P✾❃❆❅✆☎ ➝✮❢❱❁s❘✵❲✵❯❱❯❱❁✻❯ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬✻➠
❬❦✽❬❦✽❬ ⑩✫❁✻❾❶❥✭❷✭❅◗❘●❈❄❊●❋❄❁✞✝ ❷s❃❆❲✵❢❱◆✭❢❱❁✰❘✒❲✵❯❱❯❆❁✻❯ ✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬❦✼
❬❦✽❬❦✽✐ ▲❖P◗➓✻❁✻❢❱❅❃❆❾❚❁❄❯t❜✭❲❍❙✮❯❱❘●❈❄P◗❁✻❷✧❈❄❾❚❲✵❷s❃❆❁ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬❽❏
❬❦✽✐❪❙✮❯❱❘✵❁✻P✠✟✧❈➜❜✧❈❚➝✮P❈❉❃❣❈☛✡✢❁✻❢❱❾❚❈↕❜✭❲✞☞✍✌✏✎✒✑✏✓✔✌✏✎✖✕■❲➜➅☛➎✘✗❣➋✙✓✔✌✏✎✖✕ ✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬✻❬
❬❦✽✐✭✽✾✼ ❞❖❅◗❯❱◆❳❁✻❯❱❅✾❃❆❅✾❇❽❁✻❯✛❜✭❲↕⑩✍❁✻❾❚◆✭❥❦❃❣❈❄❊●❋❄❁❚❙✮❾➜❫✧❈❄❢❱❘●❈❄❜✧❈ ✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬❄✐
❬❦✽✐✭✽❑❏ ➩✰❅◗❯❛❃❆❲✵❾➫❈❡❭❴◆✤❲✵❢❆❈❄❘✵❅◗❁✻❷✧❈❄P☛❜✭❲➜➅☛➎✘✗❣➋✙✓✔✌✏✎✖✕ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬❽➒
✚
➨❍✥✦✶❳➢ ✶✤✎✒✑✔✓✖✕✘✗✈④✇✥❉➧☛✣✸✌✩✑✔✗❽✑✦✣✸✥✔✓ ✕✘✗✜✛✣✢✥✤✏✦★✧✪✩✬✫✥✭
✚✯✮
✐✭✽✾✼❀✿✱✰✒❃❆❁s❜✭❁✻❯❴❭❴❢❱❅◗❲✵❷❽❃❣❈❄❜✭❁✻❯❝❈❚❭❴❫❦❵❛❲✒❃❆❁✻❯❚✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽☎✐s❏
✐✭✽❑❏ ✲✴✳✱✵✷✶✹✸✷❅◗❷✭➓✻❥✧❈❄➓✻❲✵❾✻✺❻❷✭❅✾❩✧❘●❈❄❜✧❈➜❜✭❲↕✿❂❁✰❜✭❲✵P❈❄➓✻❲✵❾ ✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽☎✐❽❬
✐✭✽❬ ✲✴✳✱✵ ❜✭❲■➭✸❲✵❾❚◆✤❁❚❹❝❲●❈❄P ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽☎✐❽➣
✐✭✽✐ ✲✴✳✱✵ ❲■▲❖➓✻❲✵❷❽❃❆❲✵❯ ✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽☎✐❽➀
✐✭✽❑➒➲✿❂❁s❜✭❲✵P ❈❄➓✻❲✵❾ ❜✧❈➜▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❡❜✭❲↕⑩✫❁✻❷❽❃❆❢❱❁✻P◗❲■➝✮❢❱❁✻◆✤❁✻❯❛❃❣❈➑✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽☎✐❽➛
✐✭✽❑➒✰✽✾✼ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈❉❯✛❜✭❲↕⑩✫P◗❈❄❯❱❯❆❲✒❯➜✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❄➠
✐✭✽❑➒✰✽❑❏ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈❉❯✛❜✭❲↕➳❸❢❆➂❉❩✧❘✵❁❡❜✭❲❍❙✮❯❛❃❣❈❄❜✭❁✻❯❝❲■❜✭❲■▲t❃❆❅✾❇✰❅◗❜✧❈❄❜✭❲✵❯ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❄❬
✐✭✽❑➒✰✽❬ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈❉❯✛❜✭❲✍✝ ❷❽❃❆❲✵❢❆❈❄❊●❋❄❁ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒✻➒
⑦
✲
⑤⑥➢➤✯✢✗✰⑤⑥✗
✴
✑✔✓✧✹✻➦☛✗✰✎❶✗✈✉✇✗✰✎●✣✸✯✩✑✔✓✧✕✘✶✤✎ ✼✹✼
➒✰✽✾✼ ❙✮❯❛❃❆❢❱❥❦❃❆❥✭❢❆❈❡❜✭❲✽☞✍✌✏✎✒✑✏✓✔✌✏✎✖✕■❲➜➅☛➎✘✗❣➋✙✓✔✌✏✎✖✕✍✝ ❾❡◆✭P◗❲✵❾❚❲✵❷s❃❣❈❄❜✧❈ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻➀
➒✰✽✾✼✻✽✾✼ ⑩t❈❄❯❱❘✵❁✾✝ ➭✛➭❻⑩➙❲✵❾ ❲✵❯❱❘●❈❄P ❈➜❢❱❲✵❜✭❥❀✿✵❅◗❜✧❈❿✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻➛
➒✰✽✾✼✻✽❑❏ ✿❂❅◗❘✵❢❱❁s❘✵❁✻❾❚◆✭❥❦❃❣❈❄❜✭❁✻❢✛❜✭❲❍➔✫❁✻❢❱❜✭❁❚➝✍⑩❂❁✰✼✔➠❄✐❚✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻➛
➒✰✽✾✼✻✽❬ ➩✰❲✵❢❛❇✻❁✻❯★☎❛➩✰❅◗❯❛❃❆❲✵❾➫❈❄❯❝❲■▲t❃❆❥✧❈❄❜✭❁✻❢❱❲✵❯⑥✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➠
➒✰✽✾✼✻✽✐ ➩✰❲✵❷✭❯❱❁✻❢❱❲✵❯❤✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➠
➒✰✽✾✼✻✽❑➒ ❙✮⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁✻❯❝❜✭❲↕⑩✫❁✻❾❶❥✭❷✭❅◗❘●❈❄❊●❋❄❁ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❉✐
➒✰✽✾✼✻✽➣ ➔t❈❉❃❆❲✵❢❱❅ ❈❄❯ ✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➣
➒✰✽❑❏ ❙✮❷✭❯❆❈❄❅◗❁✻❯❝❹❝❲●❈❄P◗❅✠✿●❈❄❜✭❁✻❯☎✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➣
➒✰✽❑❏✰✽❬ ❙✮❷✭❯❆❈❄❅◗❁✻❯✛❜✭❲ ✁ ❈✔❇✻❲✵➓❽❈❄❊●❋❄❁ ✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔➀
✼✁↕✶ ✴ ➥❽✯✏✣✸✎✵➦✷✗✰✎➜✗✄✂✷✣✘✜❳✗✰✎✒✑✔➦✷✗✰✎➜➢✸✓✭✥✦✓ ✪✍✥✦✓✭✬✸✓✧✯✆☎✘✶✤✎❚✙✘✣✷✑✦✣✘✥✦✶✤✎ ✱✰♠✞✝
❏✰✽✾✼✏✎✫➌➍➎❉➏ ✕ ✕ ✎ ✶✬✺❻▲✒✑✞❥❦❃❆❅◗P✾❅✠✿●❈❄❜✭❁❶❷✧❈➫➳❸❥✭❲✵❢❱❢❆❈➜❜✭❁✇➳❸❁✻P✡✢❁❶❲■❷✭❁✻❯❻❈❉❃❣❈❄⑨s❥✭❲✵❯❻❈❄❁❡▲✄✡✢❲✵➓❽❈❄❷✭❅◗❯❛❃❣❋❄❁✭✽ ✽■✽❍✽❍✽ ➣
❏✰✽❑❏ ➅☛➎✔✓✵➎❉➆ ✎➄➏ ✕ ✎ ✶❦❇✻❲✵❨◗❘✵❥✭P◗❁❡❜✭❲■❲✖✕❦◆✭P◗❁✻❢❆❈❄❊●❋❄❁❡❲✵❷❽❇✰❅❈❄❜✭❁❚❈❄❁❡◆✭P ❈❄❷✭❲✒❃❣❈❚✿✠❈❄❢❛❃❆❲❄✽✍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ↔
❏✰✽❬ ✳ ✌✏✎➄➋✏➌✩➏✬✶❽▲ ✺✗✑➙❜✭❲✵❯❱❲✵❷❽❇❽❁✻P❇✰❅◗❜✭❁❍◆✤❲✵P❈✪✳ ✌✏✎➄➌✙✑ ✌❄➏✙✘✫➊❳➅ ❜✭❲✵❯❛❃❆❅◗❷✧❈❄❜✭❁■❈❸❅◗❷✭❯❱◆✤❲✵❊●❋❄❁■❜✭❲❝❁✻P◗❲✵❁✰❜✭❥❦❃❆❁✻❯
❲❸❘●❈❄❫✤❁✻❯❝❯❱❥✭❫✭❾➫❈❄❢❱❅◗❷✭❁✻❯✵✽❳✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ↔
❏✰✽✐ ❭❴➭✛➭❝❙ ❹✍✶✛✚✢✜ ✕✖✌❄➏✤✣✹✕✥✜✥✦❦➏✤➎★✧✾➎✥✩❄➌ ✕❆➈✪✣✯✕❣➈✒➋ ➇ ✕✖✑✄✗✵➎☛✎✬✫✫➏✭✩❄➌✩➏ ✕ ✕ ✎➄➌✩➏✭✩✯✮ ✕❣➈✥✕✖✌✏✎✰✜✥✦✰✽➟✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✦❏
❏✰✽❑➒ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❲✵❯❱⑨s❥✭❲✵❾➫➂❉❃❆❅◗❘✵❁❡❜✧❈❚❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲■❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❸❜✭❁✇❭❴➭✛➭❝❙ ❹■✽⑥✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✦❏
❏✰✽➣➲➝ ❃❆❲✵❢❱❁❽❈ ☎❣✼✦➒❄➠ ✶☛▲ ✺✗✑ ❜✭❲✵❯❱❲✵❷❽❇✻❁✻P✾❇✰❅◗❜✭❁❂❷✭❁✌✱➄➏❦➈✒➋✏➌✩➋✏➆✰➋ ✕✇➎✘✗✲✱➄➏✯✑❄➆❽➈✒➋✙✎➄➌✙✌★✧✸➅☞✜✒➌ ✕✒➏✳✜ ✕❡❜✧❈ ✲✘➏✧➌✵✴✏✕ ✎❆➈✒➌✩➋✷✶
➎✘✗✸✣✤➎✺✹✻✶❽➎❉✽✭✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔❬
❏✰✽❑↔ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❲✵❯❱⑨s❥✭❲✵❾➫➂❉❃❆❅◗❘✵❁❡❜✧❈❚❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲■❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❸❜✭❁➫➝ ❃❆❲✵❢❱❁❽❈ ☎❣✼✦➒❄➠✰✽✸✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔❬
❏✰✽➀ ▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲■❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❸❜✭❁❚▲ ✺✗✑ ➅✴✕✖✌❡➅✳✼✵➆✰➌ ✎➄➋✏✽❤✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼●✐
❏✰✽➛ ✎✛✦✧➎✥✕✒➏✧➌✾✽ ✶❦▲✄✺✿✑✞❜✭❲❍❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈✞✟✭❨◗❫✭❢❱❅◗❜✧❈❦✽➤✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔➣
❏✰✽✾✼✔➠➞❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❲✵❯❱⑨s❥✭❲✵❾➫➂❉❃❆❅◗❘✵❁❡❜✧❈❚❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲■❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❸❜✭❁❀✎✛✦✧➎✥✕✒➏✧➌✾✽✻✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔➣
❏✰✽✾✼✻✼ ▲❖➓✻❲✵❷❽❃❆❲■❅◗❷❽❃❆❲✵❢❆❈❄➓✻❅◗❷✭❜✭❁➜❘✵❁✻❾✂❈❄❾❶❫✭❅◗❲✵❷s❃❆❲❸❈❉❃❆❢❆❈✔❇ ✰✵❯❝❜✭❲■❯❱❲✵❷✭❯❱❁✻❢❱❲✵❯❻❲❍❈❉❃❆❥✧❈❄❜✭❁✻❢❱❲✵❯✵✽✖✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔➀
❏✰✽✾✼✦❏➯❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❯❱❅◗❾❚◆✭P◗❅❩✧❘●❈❄❜✭❁➜❜✧❈❡❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲■❘✵❁✻❷s❃❆❢❱❁✻P◗❲❸◆✭❢❱❁✻◆❳❁✻❯❛❃❣❈❦✽❝✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏❄➠
❬❦✽✾✼⑧▲❖❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲❁✦❀✌✏✎✒✑✏✓✔✌✏✎✖✕■❲✵❯❱❘✵❁✻P✠✟✭❅◗❜✧❈❦✽ ✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬❽➒
❬❦✽❑❏ ❙✮⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁✻❯✛❜✭❲■❘✵❁✻❾❚◆✭❥❦❃❣❈❄❊●❋❄❁❡❲✵❾➜❫✧❈❄❢❱❘●❈❉❜✧❈❡❫✧❈❄❯❱❲●❈❄❜✭❁✻❯❝❷✭❁❚❫✧❈❄❢❱❢❆❈❄❾❚❲✵❷❽❃❆❁❡➝✍⑩❂❁✰✼✔➠❄✐✭✽❖✽❍✽❍✽ ❬✻➣
❬❦✽❬❪❭ ➉➜➌❂✜ ✎❆➎✺✹ ✕ ✎➄➏ ✕❃✧❅❄ ✁✗❆ ❘✵❁✰❁✻❢❱❜✭❲✵❷✧❈❄❷✭❜✭❁❚❁✻❯✛➓✻❲✵❢❱❲✵❷✭❘✵❅❈❄❜✭❁✻❢❱❲✵❯❝❜✭❁❚❯❱❅◗❯❛❃❆❲✵❾➫❈❦✽✇✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ❬✻➀
✐✭✽✾✼❀❭❴❢❱❅◗➓✻❲✵❾ ❜✭❁✇✿✱✰✒❃❆❁✰❜✭❁✾✺❴✿ ✸✮✽❦✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽☎✐✻✐
✐✭✽❑❏ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲■❘✵P ❈❄❯❱❯❱❲✵❯❝❜✧❈❚❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲❶➈✔➎✘✗❣➋✙✓✔✌✏✎✖✕■◆✭❢❱❁✻◆✤❁✻❯❛❃❣❈❦✽❴✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❄➠
✐✭✽❬ ➭✛❅◗◆❳❁✻❯❝❜✭❲■❾❚❲✵❷✭❯❆❈❄➓✻❲✵❷✭❯❝❜✭❁❚❯❱❅◗❯❛❃❆❲✵❾➫❈❈❇❉✣✴✳❂➈✰✩✇❲■❯❱❥✧❈❄❯❻❲✵❯❱◆❳❲✵❘✵❅❈❄P◗❅✠✿●❈❄❊❋❊✰❲✵❯✵✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒✰✼
✐✭✽✐➲➭✛❅◗◆❳❁✻❯❝❜✭❲■❲✵❯❛❃❆❢❱❥❦❃❆❥✭❢❆❈❄❯❝❜✭❲❍❜✧❈❉❜✭❁✻❯❝◆✭❢❱❲✵❯❱❲✵❷s❃❆❲✵❯❻❷✧❈❚❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜❜✭❲❶➈✔➎✘✗❣➋✙✓✔✌✏✎✖✕■◆✭❢❱❁✻◆✤❁✻❯❛❃❣❈❦✽✂✽❍✽➟➒✻❏
✐✭✽❑➒ ❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕➳❸❢❆➂❉❩✧❘✵❁❡❜✭❲❍❙✮❯❛❃❣❈❄❜✭❁✻❯❻❜✭❁❚❈❄➓✻❲✵❷❽❃❆❲✝●✄✕ ✎✖✕✒➏✳✜✒➌✙✌ ✑s➎☛✎➄✽☎✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❉✐
✐✭✽➀➲❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕➳❸❢❆➂❉❩✧❘✵❁❡❜✭❲❍❙✮❯❛❃❣❈❄❜✭❁✻❯❻❜✭❁❚❈❄➓✻❲✵❷❽❃❆❲❉✘❖➋✏➆❀✌ ✑s➎☛✎➄✽✍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❄➀
✐✭✽➛➲❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕➳❸❢❆➂❉❩✧❘✵❁❡❜✭❲❍❙✮❯❛❃❣❈❄❜✭❁✻❯❻❜✭❁❚❈❄➓✻❲✵❷❽❃❆❲➜➅✴✕✒➏❦➈✔➎☛✎➄✽ ✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❄➛
✐✭✽✾✼✔➠➞❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕➳❸❢❆➂❉❩✧❘✵❁❡❜✭❲❍❙✮❯❛❃❣❈❄❜✭❁✻❯❻❜✭❁❚❈❄➓✻❲✵❷❽❃❆❲❁✮❂✌ ✑❄➌➍➎❉✽✈✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒❄➛
✐✭✽✾✼✻✼q❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕⑩✫❁✻P❈❄❫✤❁✻❢❆❈❄❊●❋❄❁➜◆✧❈❄❢❆❈❡❈➜❜✭❲✒❃❆❲✵❢❱❾❚❅◗❷✧❈❄❊●❋❄❁❡❜✭❲■❢❱❲ ✡✢❲✵❢✁✵❷✭❘✵❅ ❈❄❯❝◆✧❈❄❢❆❈➜❁✻❯❻❈❉❃❆❥✧❈❄❜✭❁✻❢❱❲✵❯✵✽ ➣❽❏
✐✭✽✾✼✦❏➯❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕⑩✫❁✻P❈❄❫✤❁✻❢❆❈❄❊●❋❄❁➜◆✧❈❄❢❆❈➜❁❡❾❚❁✻❷✭❅✾❃❆❁✻❢❆❈❄❾❡❲✵❷❽❃❆❁➜❜✧❈❚❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❦✽t✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻❬
✐✭✽✾✼✔❬➞❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕➩✰❲✵⑨✄✂☎✵❷✭❘✵❅ ❈❡❾❚❁✻❯❛❃❆❢❆❈❄❷✭❜✭❁❡❥✭❾ ❘✵❲✵❷✧➂❄❢❱❅◗❁❡❜✭❲■❲✖✕❦❲✵❘✵❥✭❊●❋❄❁➫❜✭❲■❾❚❅◗❯❱❯❆❋❄❁✭✽✫✽❍✽❍✽■✽❍✽❍✽ ➣❄✐
✐✭✽✾✼●✐❧❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲↕➩✰❲✵⑨✄✂☎✵❷✭❘✵❅ ❈❡❾❚❁✻❯❛❃❆❢❆❈❄❷✭❜✭❁❡❥✭❾ ❘✵❲✵❷✧➂❄❢❱❅◗❁❡❜✭❲■❾❚❁✻❷✭❅✾❃❆❁✻❢❆❈❄❾❡❲✵❷❽❃❆❁➜❜✭❲■❥✭❾ ❯❱❲✵❷✭❯❱❁✻❢✵✽ ➣❽➒
➒✰✽✾✼ ❙✮❾❶❫✧❈❄❢❱❘●❈❄❊●❋❄❁❡❥❦❃❆❅◗P◗❅✿●❈❄❜✧❈❶❲✵❾ ❃❆❲✵❯❛❃❆❲✵❯✄✝ ➭✛➭❻⑩❖✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻➣
➒✰✽❑❏➲✿❂❁s❜✭❲✵P◗❁ ✝ ➭✛➭❻⑩➙❲✵❾✂❲✒❯❆❘✵❈❄P ❈❡❢❱❲✵❜✭❥❀✿✵❅◗❜✧❈❦✽❻✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣❽↔
➒✰✽❬➲❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❲✵❯❱⑨s❥✭❲✵❾➫➂❉❃❆❅◗❘✵❁❡❜✭❁❚❾❚❁✰❜✭❲✵P✾❁❡❲✵❾ ❲✵❯❱❘●❈❄P ❈➜❜✭❲■❷✧❈●❇✰❅◗❁✭✽■✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻➀
➒✰✽✐❪➔ ✂ ❯❱❯❱❁✻P❈➜❲✵P◗❲✒❃❆❢❱❺✻❷✭❅◗❘●❈❶➭❻⑩✛✿✈❏✰✽ ✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✰✼
➒✰✽❑➒ ❙✮⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁❡❜✭❲■◆✤❁✻❯❱❅◗❘✵❅◗❁✻❷✧❈❄❾❚❲✵❷❽❃❆❁➜➓✻P◗❁✻❫✧❈❄P✏✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻❏
➒✰✽➣ ✺❻❷✭❅◗❜✧❈❄❜✭❲❸❅◗❷✭❲✵❢❱❘✵❅❈❄P ✑❴➳■➣✻➠✻➠❄▲❖▲↕✽➞✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄❬
➒✰✽❑↔ ❙✮⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁ ✓✮➌✎✖✕❃✧✠✕❣➈❣➈ ✸✷▲
✁
❜✧❈✝✆ ✮✟✞ ✵➤➋ ✑ ✌❄✽✰✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻➒
➒✰✽➀ ▲❖❷❽❃❆❲✵❷✧❈■❲✖✕✰❃❆❲✵❢❱❷✧❈■❜✭❅◗❢❱❲✵❘✵❅◗❁✻❷✧❈❄P ✁✡✠ ▲ ☎ ✐s❏❄➠✻➠ ✶✻❫✧❈❉❃❆❲✵❢❱❅❈❴❲✖✕✰❃❆❲✵❢❱❷✧❈ ✁ ➔t➔ ☎ ✐s↔❄➣❴❲❻❈❄❷❽❃❆❲✵❷✧❈■❲✖✕✰❃❆❲✵❢❱❷✧❈
❁✻❷✭❅◗❜✭❅◗❢❱❲✵❘✵❅◗❁❄❷✧❈❄P ✁✡✠
▲ ☎❛❏❄➠✻➠❦✽↕✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻➒
➒✰✽➛➲❙✮⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁❡◆✧❈❄❢❆❈❶❃❆❲✵P◗❲✵❘✵❁✻❾➫❈❄❷✭❜✭❁❡❜✭❲❍❈❄❲✵❢❱❁✻❾❚❁s❜✭❲✵P◗❁✻❯✵✽↕✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻➒
➒✰✽✾✼✔➠➞➝✸❁✻❯❱❅◗❊●❈❄❁↕❜✭❁↕❘✵❲✵❷❽❃❆❢❱❁❶❜✭❲❖➓✻❢❆❈●❇✰❅◗❜✧❈❄❜✭❲☞☛✙✸✸⑩✛➳✍✌✮❜✭❁❍❇❽❲✵❨◗❘✵❥✭P◗❁❀✶s❘✵❁✻❅◗❷✭❘✵❅◗❜✭❲✵❷❽❃❆❲❻❘✵❁✻❾ ❯❱❲✵❥✇❘✵❲✵❷s❃❆❢❱❁❶❜✭❲
✎ ❥❦❃❆❥✧❈❄❊●❋❄❁✏☛✙✸✸⑩t➔✑✌➄✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻↔
➒✰✽✾✼✻✼ ➩✰❅◗❯❛❃❆❲✵❾➫❈❶❜✭❲■❘✵❁✰❁✻❢❱❜✭❲✵❷✧❈❄❜✧❈❄❯❻❈❄❜✭❁❄❃❣❈❄❜✭❁❡❲■❾❚❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁✻❯✛❾❚❲✒❜✭❅◗❜✭❁✻❯✛❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁✻❯✵✽❂✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➀
➒✰✽✾✼✦❏ ✑ ❲✵P✾❁✰❘✵❅◗❜✧❈❄❜✭❲■❈❄❷✭➓✻❥✭P❈❄❢
ω
x
❷✭❁❚❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾ ❢❱❲✵◆✤❁✻❥✭❯❱❁✭✽✫✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➛
➒✰✽✾✼✔❬✤✑ ❲✵P✾❁✰❘✵❅◗❜✧❈❄❜✭❲■❈❄❷✭➓✻❥✭P❈❄❢
ω
y
❷✭❁❡❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾✂❢❱❲✵◆❳❁✻❥✭❯❱❁✭✽❝✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄➛
➒✰✽✾✼●✐ ✑ ❲✵P✾❁✰❘✵❅◗❜✧❈❄❜✭❲■❈❄❷✭➓✻❥✭P❈❄❢
ω
z
❷✭❁❚❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾ ❢❱❲✵◆✤❁✻❥✭❯❱❁✭✽❻✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀✻➠
➒✰✽✾✼✦➒➞✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈●❇❄❈❄❷✭❊✵❁
A
x
❷✭❁❚❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾ ❢❱❲✵◆✤❁✻❥✭❯❱❁✭✽⑥✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀✻➠
➒✰✽✾✼✔➣❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡P❈❉❃❆❲✵❢❆❈❄P
A
y
❷✭❁❚❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾ ❢❱❲✵◆✤❁✻❥✭❯❱❁✭✽✠✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❦✼
➒✰✽✾✼✦↔➞✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈❄❢✘✡✏❈❄➓✻❲✵❾
A
z
❷✭❁❚❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾ ❢❱❲✵◆✤❁✻❥✭❯❱❁✭✽ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❦✼
➒✰✽✾✼✔➀➞❹❝❁❄❃❣❈❄❊❋❊s❲✵❯❝❜✭❁✻❯❝◆✭❢❱❁✻◆✭❥✭P◗❯❱❁✻❢❱❲✵❯❝❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲❸❇✰❅◗❫✭❢❆❈❄❊●❋❄❁✭✽✫✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀✻❬
➒✰✽✾✼✔➛❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈●❇❄❈❄❷✭❊✵❁
A
x
❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲❸❇✰❅◗❫✭❢❆❈❄❊●❋❄❁✭✽ ✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀✻❬
➒✰✽❑❏❄➠❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡P❈❉❃❆❲✵❢❆❈❄P
A
y
➒✰✽❑❏✰✼ ✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈❄❢✘✡✏❈❄➓✻❲✵❾
A
z
❲✵❾✂❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲❸❇✰❅◗❫✭❢❆❈❄❊●❋❄❁✭✽ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❄✐
➒✰✽❑❏✻❏ ✑ ❲✵P✾❁✰❘✵❅◗❜✧❈❄❜✭❲■❈❄❷✭➓✻❥✭P❈❄❢
ω
x
❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❚❜✭❲❸❇✰❅✾❫✭❢❣❈❉❊●❋❄❁✭✽ ✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❽➒
➒✰✽❑❏❄❬✤✑ ❲✵P✾❁✰❘✵❅◗❜✧❈❄❜✭❲■❈❄❷✭➓✻❥✭P❈❄❢
ω
y
❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲❸❇✰❅◗❫✭❢❆❈❄❊●❋❄❁✭✽☎✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❽➒
➒✰✽❑❏❉✐ ✑ ❲✵P✾❁✰❘✵❅◗❜✧❈❄❜✭❲■❈❄❷✭➓✻❥✭P❈❄❢
ω
z
❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲❸❇✰❅◗❫✭❢❆❈❄❊●❋❄❁✭✽➟✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀✻➣
➒✰✽❑❏✻➒➯❞❴❈❄❜✭❁✻❯❝❜✭❲■❾❚❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁➜❜✭❁❡❲✵❷✭❯❆❈❄❅◗❁❚❲✵❾✂➂❄➓✻❥✧❈❄❯✛❘●❈❄P◗❾➫❈❄❯✵✽ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❽↔
➒✰✽❑❏❄➣➞❞❴❈❄❜✭❁✻❯❝❜✭❲■❜✭❲✵❯❱P◗❁✰❘✵❈❄❾❚❲✵❷s❃❆❁❚❈❄❷✭➓✻❥✭P❈❄❢t❜✭❁❡❲✵❷✭❯❆❈❄❅◗❁❚❲✵❾✂➂❄➓✻❥✧❈❄❯✛❘●❈❄P◗❾➫❈❄❯✵✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❽↔
➒✰✽❑❏✻↔✁❖❷✭➓✻❥✭P◗❁➜❜✭❲■❢❱❥✭❾❚❁❡❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❯❱❁✻❫❂❘✵❁✻❾➫❈❄❷✭❜✭❁❡❾➫❈❄❷s❥✧❈❄P➍✽☎✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛✻➠
➒✰✽❑❏❄➀➞❹❝❁❄❃❣❈❄❊●❋❄❁➜❜✭❁✻❯❝❾❚❁❄❃❆❁✻❢❱❲✵❯✛❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❯❱❁✻❫❂❘✵❁✻❾➫❈❄❷✭❜✭❁❡❾➫❈❄❷s❥✧❈❄P➍✽ ✽❍✽❍✽❍✽■✽❍✽❍✽ ➛❦✼
➒✰✽❑❏❄➛❧⑩✫❁✻❢❱❢❱❲✵❷❽❃❆❲■❅◗❷✭❯❛❃❣❈❄❷s❃✄✂❄❷✭❲●❈➜❲✵❾ ❾❚❁❄❃❆❁✻❢❱❲✵❯✛❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❯❱❁✻❫❂❘✵❁✻❾➫❈❄❷✭❜✭❁❡❾➫❈❄❷s❥✧❈❄P➍✽ ➛❦✼
➒✰✽❬✻➠☎❖❷✭➓✻❥✭P◗❁➜❜✭❲■❢❱❥✭❾❚❁❡❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❯❱❁✻❫❂❘✵❁✻❾➫❈❄❷✭❜✭❁❡❾➫❈❄❷s❥✧❈❄P➍✽☎✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛❽❏
➒✰✽❬❦✼q❹❝❁❄❃❣❈❄❊●❋❄❁➜❜✭❁✻❯❝❾❚❁❄❃❆❁✻❢❱❲✵❯✛❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❯❱❁✻❫❂❘✵❁✻❾➫❈❄❷✭❜✭❁❡❾➫❈❄❷s❥✧❈❄P➍✽ ✽❍✽❍✽❍✽■✽❍✽❍✽ ➛❽❏
➒✰✽❬❽❏➯❹❝❲✵❯❱◆❳❁✻❯❛❃❣❈❡❃❆❨◗◆✭❅◗❘●❈↕❜✭❲❍❥✭❾ ❲✵❷✭❯❆❈❄❅◗❁❚❲✵❾✝✆✵➌✩✟✞✠✆✥✌✺✩❄✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛✻❬
➒✰✽❬✻❬☎❖❷✭➓✻❥✭P◗❁➜❜✭❲■❢❱❥✭❾❚❁❡❲■P◗❲✵❾❚❲❴❜✭❁❚❾❚❁s❜✭❲✵P◗❁➜❲✵❾✂❲✵❯❱❘●❈❉P❈❡❜✭❲■❷✧❈●❇✰❅◗❁❡❲✵❾ ❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲✡✆✵➌ ✩✟✞✠✆✥✌✺✩❄✽❖✽❍✽❍✽ ➛❽➒
➒✰✽❬❄✐❧❞❖❅❈❄➓✻❢❆❈❄❾➫❈↕❜✭❲■❫✭P◗❁✰❘✵❁✻❯✛❢❱❲✵◆✭❢❱❲✵❯❱❲✵❷❽❃❣❈❄❷✭❜✭❁➫❾❚❁✰❜✭❲✵P◗❁➜❜✭❁➜❇❽❲✵❨◗❘✒❥✭P◗❁❡❾➫❈❄❅◗❯t❘✵❁✻❷s❃❆❢❱❁✻P❈❄❜✭❁✻❢✛➝✣✝❣✽➟✽❍✽❍✽ ➛✻➣
➒✰✽❬❽➒ ✑❴❅◗❯❆❋❄❁➜❯❱❥✭◆✤❲✵❢❱❅◗❁✻❢✛❜✭❁❚❾❚❁✰❜✭❲✵P◗❁➜❲✵❾ ❲✵❯❱❘●❈❄P❈➜❜✭❲■❷✧❈●❇✰❅◗❁✭✽ ✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛❽↔
➒✰✽❬✻➣➞❞❖❲✒❃❣❈❄P✠✟✭❲■❾❚❁✻❯❛❃❆❢❆❈❄❷✭❜✭❁❡❫ ✂ ❯❱❯❱❁✻P❈❡❲✒P◗❲✒❃❆❢❱❺✻❷✭❅◗❘●❈➜➭❻⑩✛✿✈❏ ✶❳❲✵⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁✱✓✮➌ ✎✖✕❃✧✠✕❣➈❣➈ ✸✷▲ ✁ ❲■❥✭❷✭❅✆☎
❜✧❈❄❜✭❲■❅◗❷✭❲✵❢❱❘✵❅❈❄P ✑❖➳■➣✻➠✻➠❄▲❖▲↕✽❧✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛❽↔
➒✰✽❬❽↔➯❞❖❲✒❃❣❈❄P✠✟✭❲✍❾❚❁✻❯❛❃❆❢❆❈❄❷✭❜✭❁❖❾❚❁❄❃❆❁✻❢❱❲✵❯✸❜✭❲✫◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❀✶❉❯❆❲✒❢❱❇✻❁ ✑✏✎➄➌✵✴✏✕❣➈ ✶✻➝✍⑩❖✼✔➠❄✐ ☛✢❘✵❲✵❷s❃❆❢❱❁✄✌✷❲✫❥✭❷✭❅◗❜✧❈❄❜✭❲
❅◗❷✭❲✵❢❱❘✵❅❈❄P ✑❖➳■➣✻➠✻➠❄▲❖▲ ☛✠☛➜❜✭❅◗❢❱❲✵❅✾❃❣❈ ✌➄✽ ✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛✻➀
➒✰✽❬✻➀➞❞❖❲✒❃❣❈❄P✠✟✭❲❡❾❚❁✻❯❛❃❆❢❆❈❄❷✭❜✭❁❂❘✵❁✻❷❉❵❛❥✭❷❽❃❆❁❂❜✭❲❚❫✧❈❉❃❆❲✵❢❱❅ ❈❄❯ ☛✢❲✵❯❱⑨s❥✭❲✵❢❱❜✧❈ ✌■❥❦❃❆❅◗P◗❅✿●❈❄❜✧❈❄❯ ✶✘❯❱❲✵❢❛❇✻❁✜✑✏✎➄➌✵✴✏✕ ☛✢❜✭❅✆☎
❢❱❲✵❅✾❃❣❈ ✌✍❲■❾❚❲✵❘●❈❄❷✭❅◗❯❱❾❚❁➜◆✧❈❄❢❆❈➜◆✤❁✻❯❱❅◗❘✵❅◗❁✻❷✧❈❄❾❚❲✵❷❽❃❆❁➜❜✭❁✻❯❝P◗❲✵❾❚❲✵❯✵✽ ✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛✻➀
➒✰✽❬✻➛☎❖❷✭➓✻❥✭P◗❁➜❜✭❲■❢❱❥✭❾❚❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽✂✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻❬
➒✰✽✐❽➠➞❹❝❁❄❃❣❈❄❊●❋❄❁➜❜✭❁✻❯❝❾❚❁❄❃❆❁✻❢❱❲✵❯✛❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❻✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻❬
➒✰✽✐✭✼ ⑩✫❁✻❢❱❢❱❲✵❷❽❃❆❲■❅◗❷✭❯❛❃❣❈❄❷s❃✄✂❄❷✭❲●❈➜❲✵❾ ❾❚❁❄❃❆❁✻❢t❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽➟✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠❄✐
➒✰✽✐s❏➞⑩✫❁✻❢❱❢❱❲✵❷❽❃❆❲■❅◗❷✭❯❛❃❣❈❄❷s❃✄✂❄❷✭❲●❈➜❲✵❾ ❾❚❁❄❃❆❁✻❢t❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽➟✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠❄✐
➒✰✽✐❽❬➞❙✮❯✘✡✢❁✻❢❱❊✵❁❚❜✭❲■❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❸❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❿✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠❽➒
➒✰✽✐✻✐❧❞❖❲✵❯❱P◗❁s❘●❈❄❾❚❲✵❷s❃❆❁✻❯❝❈❄❷✭➓✻❥✭P❈❄❢❱❲✵❯✛❲✵❾✂❙✮❷✭❯❣❈❉❅◗❁✾✝✚✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠❽➒
➒✰✽✐s➒➞✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❲✵❾ ✮❝➎✻✧✵✧
ω
x
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻➣
➒✰✽✐❽➣❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❲✵❾ ✎✫➌✩➋ ✜✥✦
ω
y
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽❡✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻➣
➒✰✽✐s↔➞✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❲✵❾✌☞✹✌✏✓
ω
z
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠❽↔
➒✰✽✐❽➀❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈●❇❄❈❄❷✭❊✵❁
A
x
➒✰✽✐❽➛❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡P ❈❉❃❆❲✵❢❆❈❄P
A
y
❲✵❾✂❙✮❷✭❯❣❈❉❅◗❁✾✝❣✽ ✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻➀
➒✰✽❑➒❄➠❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈❄❢✘✡✏❈❄➓✻❲✵❾
A
z
❲✵❾→❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻➀
➒✰✽❑➒✰✼ ❖❷✭➓✻❥✭P◗❁➜❜✭❲■❢❱❥✭❾❚❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✦❏
➒✰✽❑➒✻❏➯❹❝❁❄❃❣❈❄❊●❋❄❁➜❜✭❁✻❯❝❾❚❁❄❃❆❁✻❢❱❲✵❯✛❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✦❏
➒✰✽❑➒❄❬❧⑩✫❁✻❢❱❢❱❲✵❷❽❃❆❲■❅◗❷✭❯❛❃❣❈❄❷s❃✄✂❄❷✭❲●❈➜❲✵❾ ❾❚❁❄❃❆❁✻❢t❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔❬
➒✰✽❑➒❉✐➙⑩✫❁✻❢❱❢❱❲✵❷❽❃❆❲■❅◗❷✭❯❛❃❣❈❄❷s❃✄✂❄❷✭❲●❈➜❲✵❾ ❾❚❁❄❃❆❁✻❢t❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔❬
➒✰✽❑➒✻➒➯❙✮❯✘✡✢❁✻❢❱❊✵❁❚❜✭❲■❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❸❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽❻✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼●✐
➒✰✽❑➒❄➣➞❞❖❲✵❯❱P◗❁s❘●❈❄❾❚❲✵❷s❃❆❁✻❯❝❈❄❷✭➓✻❥✭P❈❄❢❱❲✵❯✛❲✵❾✂❙✮❷✭❯❣❈❉❅◗❁✾✝ ✑❶✽✭✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼●✐
➒✰✽❑➒✻↔➞✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❲✵❾ ✮❝➎✻✧✵✧
ω
x
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽✧✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✦➒
➒✰✽❑➒❄➀❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❲✵❾ ✎✫➌✩➋ ✜✥✦
ω
y
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽r✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✦➒
➒✰✽❑➒❄➛❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❲✵❾✌☞✹✌✏✓
ω
z
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽➐✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔➣
➒✰✽➣✻➠❧✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈●❇❄❈❄❷✭❊✵❁
A
x
❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔➣
➒✰✽➣❦✼ ✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡P ❈❉❃❆❲✵❢❆❈❄P
A
y
❲✵❾✂❙✮❷✭❯❣❈❉❅◗❁✾✝ ✑❶✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✦↔
➒✰✽➣❽❏➞✿❂❁✔❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❍❈❄❢✘✡✏❈❄➓✻❲✵❾
A
z
❲✵❾→❙✮❷✭❯❆❈❄❅◗❁ ✝ ✑❶✽✛✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✦↔
➒✰✽➣✻❬❧➩✰❅◗❯❛❃❆❲✵❾➫❈❡➳■➝✍➩✤✽ ✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔➀
➒✰✽➣❄✐➙➩✰❅◗❯❛❃❆❲✵❾➫❈❶❜✭❲■❘✵❁✰❁✻❢❱❜✭❲✵❷✧❈❄❜✧❈❄❯❻❙✍⑩t❙ ✁ ❲❍❙ ✁ ✺❍✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✦❏❄➠
➒✰✽➣❽➒ ✑❴❅◗❯❛❃❣❈➜❯❱❥✭◆❳❲✵❢❱❅◗❁✻❢❝❁❡❾❚❁✰❜✭❲✵P◗❁➜❲✵❾ ❲✵❯❱❘●❈❄P❈➜❜✭❲■❷✧❈●❇✰❅◗❁✭✽ ✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✦❏✰✼
➒✰✽➣✻➣➞❞❖❲✒❃❣❈❄P✠✟✭❲❸❾❚❁✻❯❛❃❆❢❆❈❄❷✭❜✭❁❚❈❄❷❽❃❆❲✵❷✧❈❡❲■❢❱❲✵❘✵❲✵◆❦❃❆❁✻❢❖➳■➝✍➩✯✶❳➝✍⑩❖✼✔➠❄✐❡❲■❾❚❁❄❃❆❁✻❢❱❲✵❯✛❜✭❲■◆✭❢❱❁✻◆✭❥✭P◗❯❆❋❄❁✭✽✖✽❍✽❍✽■✼✦❏✰✼
➒✰✽➣❽↔➯➝✸❁✻❯❱❅◗❊●❋❄❁
❆
❲✄✂❿❜✭❁❡❇✻❲✵❨◗❘✵❥✭P◗❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✼✻✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✦❏✻➒
➒✰✽➣✻➀☎❖❷✭➓✻❥✭P◗❁➜❜✭❲■❢❱❥✭❾❚❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁ ✼✻✽❧✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✦❏✻➒
➒✰✽➣✻➛➞➝✸❁✻❯❱❅◗❊●❋❄❁
❆
❲✄✂❿❜✭❁❡❇✻❲✵❨◗❘✵❥✭P◗❁❡❲✵❾✂❙✮❷✭❯❆❈❄❅◗❁➫❏✰✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✦❏❄➣
❏✰✽✾✼ ➝✮❢❱❁✻◆✭❢❱❅◗❲✵❜✧❈❄❜✭❲❸❜✭❲✵❯❱❲ ❵❱➂●❇❽❲✵❅◗❯❻◆✧❈❄❢❆❈➜❥✭❾✂❈❄➓✻❲✵❷❽❃❆❲❄✽❖✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➃✼✔➀
❏✰✽❑❏▼▲❖➓✻❲✵❷❽❃❆❲✵❯❻❜✧❈❡❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈➜◆✭❢❱❁✻◆✤❁✻❯❛❃❣❈➜❲■❢❱❲✵❯❱◆✤❲✵❘✒❃❆❅✾❇❉❈❄❯❻❜✭❲✵❯❱❘✵❢❱❅◗❊❋❊✰❲✵❯ ✎ ✘❁● ✫✫✽ ✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟❏✰✼
✐✭✽✾✼ ❞❖❲✵❯❱❘✵❢❱❅◗❊●❋❄❁❚❜✭❁❡❘✵❁✻❾❚◆✤❁✻❢❛❃❣❈❄❾❚❲✵❷❽❃❆❁➜❅◗❷❽❃❆❲✵❢❱❷✭❁❡❜✭❁➫❈❄➓✻❲✵❷❽❃❆❲✝●✄✕ ✎✖✕✒➏✳✜✒➌✙✌ ✑s➎☛✎➄✽✇✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟➒✻➒
✐✭✽❑❏ ❞❖❲✵❯❱❘✵❢❱❅◗❊●❋❄❁❚❜✭❁❡❘✵❁✻❾❚◆✤❁✻❢❛❃❣❈❄❾❚❲✵❷❽❃❆❁➜❅◗❷❽❃❆❲✵❢❱❷✭❁❡❜✭❁➫❈❄➓✻❲✵❷❽❃❆❲✽✳✖➎❉➏✧➌✩➋ ➎☛✎➄✽✞✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣✻➠
✐✭✽❬➲❞❖❲✵❯❱❘✵❢❱❅◗❊●❋❄❁❚❜✭❁❡❘✵❁✻❾❚◆✤❁✻❢❛❃❣❈❄❾❚❲✵❷❽❃❆❁➜❅◗❷❽❃❆❲✵❢❱❷✭❁❡❜✭❁➫❈❄➓✻❲✵❷❽❃❆❲❉✘❻➋✏➆❀✌ ✑s➎☛✎➄✽❿✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣❦✼
✐✭✽✐❪❞❖❲✵❯❱❘✵❢❱❅◗❊●❋❄❁❚❜✭❁❡❘✵❁✻❾❚◆✤❁✻❢❛❃❣❈❄❾❚❲✵❷❽❃❆❁➜❅◗❷❽❃❆❲✵❢❱❷✭❁❡❜✭❁➫❈❄➓✻❲✵❷❽❃❆❲➜➅✴✕✒➏❦➈✔➎☛✎➄✽✈✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣❦✼
✐✭✽❑➒ ❞❖❲✵❯❱❘✵❢❱❅◗❊●❋❄❁❚❜✭❁❡❘✵❁✻❾❚◆✤❁✻❢❛❃❣❈❄❾❚❲✵❷❽❃❆❁➜❅◗❷❽❃❆❲✵❢❱❷✭❁❡❜✭❁➫❈❄➓✻❲✵❷❽❃❆❲❁✮❂✌ ✑❄➌➍➎❉✽❦✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➣❽❏
➒✰✽✾✼ ❹❝❲✵❯❱❥✭❾❚❁❡❜✧❈❄❯❝❅◗❷ ✡✢❁✻❢❱❾➫❈❄❊❋❊s❲✵❯❝❈➜❢❱❲✵❯❱◆✤❲✵❅✾❃❆❁❡❜✧❈❡❫ ✂ ❯❱❯❱❁✻P❈➜❲✵P◗❲✒❃❆❢❱❺✻❷✭❅◗❘●❈➜➭❝⑩✛✿✈❏✰✽❶✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻❏
➒✰✽❑❏ ❹❝❲✵❯❱❥✭❾❚❁❡❜✧❈❄❯❝❅◗❷ ✡✢❁✻❢❱❾➫❈❄❊❋❊s❲✵❯❝❈➜❢❱❲✵❯❱◆✤❲✵❅✾❃❆❁❡❜✭❁❚❲✵⑨s❥✭❅◗◆✧❈❄❾❚❲✵❷❽❃❆❁➫➳■➝✍➩✤✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄❬
➒✰✽❬➲❹❝❲✵❯❱❥✭❾❚❁❡❜✧❈❄❯❝❅◗❷ ✡✢❁✻❢❱❾➫❈❄❊❋❊s❲✵❯❝❈➜❢❱❲✵❯❱◆✤❲✵❅✾❃❆❁❡❜✧❈❡❥✭❷✭❅◗❜✧❈❄❜✭❲❸❅◗❷✭❲✵❢❱❘✵❅ ❈❄P✳✑❖➳■➣✻➠✻➠❄▲❖▲↕✽✛✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔❄❬
➒✰✽✐❪➝✸❁✻❯❱❅◗❊❋❊✰❲✵❯✸❢❱❲✵P ❈❉❃❆❅✾❇❄❈❄❯✘❜✧❈❻❥✭❷✭❅◗❜✧❈❄❜✭❲✍❅✾❷✭❲✵❢❱❘✵❅❈❄P❽❲✫❜✧❈❻❫ ✂ ❯❱❯❱❁✻P❈❝❲✵P◗❲✒❃❆❢❱❺✻❷✭❅◗❘●❈❝❲✵❾ ❢❱❲✵P❈❄❊●❋❄❁❖❈❄❁❻❘✵❲✵❷s❃❆❢❱❁
❜✭❲■➓✻❢❆❈●❇✰❅◗❜✧❈❄❜✭❲ ☛✙✸✸⑩✛➳✍✌✫❜✭❁❡❇✻❲✵❨◗❘✵❥✭P◗❁✭✽ ✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽➟↔✻↔
➒✰✽❑➒ ✑✍❈❄P✾❁✻❢❱❲✵❯❝❾ ✰✵❜✭❅◗❁✻❯✛❲■❜✭❲✵❯❛❇✰❅◗❁✻❯❝❾✾✰✵❜✭❅◗❁✻❯✛❜✭❁✻❯❝❜✧❈❄❜✭❁✻❯❝❜✭❲■❲✵❷✭❯❆❈❄❅◗❁❡❲✵❾ ❢❱❲✵◆✤❁✻❥✭❯❱❁✭✽➟✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❽❏
➒✰✽➣✏✑✍❈❄P✾❁✻❢❱❲✵❯❝❾ ✰✵❜✭❅◗❁✻❯✛❲■❜✭❲✵❯❛❇✰❅◗❁✻❯❝❾✾✰✵❜✭❅◗❁✻❯✛❜✭❁✻❯❝❜✧❈❄❜✭❁✻❯❝❜✭❲■❲✵❷✭❯❆❈❄❅◗❁❡❜✭❲❸❇✰❅◗❫✭❢❆❈❄❊❋❊✰❲✵❯✵✽❡✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀❽❏
➒✰✽❑↔ ✑✍❈❄P✾❁✻❢❱❲✵❯❝❾ ✰✵❜✭❅◗❁✻❯✛❜✭❲■❜✧❈❄❜✭❁✻❯❝❜✭❁❡❲✵❷✭❯❆❈❄❅◗❁❚❲✵❾✂➂❄➓✻❥✧❈❄❯✛❘●❈❄P◗❾➫❈❄❯✵✽ ✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➀✻➀
➒✰✽➀❪➳■❈❄❷❀✟✭❁✻❯✛❥❦❃❆❅◗P◗❅✿●❈❄❜✭❁✻❯t◆✧❈❄❢❆❈❡❁❡❘✵❁✻❷❽❃❆❢❱❁✻P❈❄❜✭❁✻❢✛➝✣✝❣✽⑥✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽ ➛✻➣
➒✰✽➛➲❹❝❲✵❯❱❥✭❾❚❁❡❜✭❁✻❯❝❢❱❲✵❯❱❥✭P✾❃❣❈❄❜✭❁✻❯✛❜✭❁➫❙✮❷✭❯❆❈❄❅◗❁ ✝❣✽r✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻➠
➒✰✽✾✼✔➠➞❹❝❲✵❯❱❥✭❾❚❁❡❜✭❁✻❯❝❢❱❲✵❯❱❥✭P✾❃❣❈❄❜✭❁✻❯✛❜✭❁➫❙✮❷✭❯❆❈❄❅◗❁ ✝✒✝❣✽ ✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✔➠✻➛
➒✰✽✾✼✻✼q❹❝❲✵❯❱❥✭❾❚❁❡❜✭❁✻❯❝❢❱❲✵❯❱❥✭P✾❃❣❈❄❜✭❁✻❯✛❜✭❁➫❙✮❷✭❯❆❈❄❅◗❁ ✝✒✝✒✝❣✽r✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽❍✽■✽❍✽❍✽■✼✻✼✔➠
✝✟✞ ✄ ✝❂✡ ✞☎✁✡✠☞☛✞✡
❹❝❁✻❫✤❺✻❯ ❾❚❼✔❇✻❲✵❅◗❯ ❯❱❲✵❢❛❇✻❲✵❾ ❘✵❁✻❾❚❁❴◆✭P ❈❉❃❣❈☛✡✢❁✻❢❱❾❚❈❄❯✸❜✭❲t❃❆❲✵❯❛❃❆❲✵❯✮◆✧❈❄❢❆❈❴❯❱❅◗❯❛❃❆❲✵❾➫❈❉❯ ❾❚❲✵❘●❈❉❃❆❢❱❺✻❷✭❅◗❘✵❁✻❯✵✽✮❭➯❜✭❲✵❯❱❲✵❷s❇✻❁✻P✾❇✰❅✆☎
❾❚❲✵❷❽❃❆❁➜❜✭❲❖❃❣❈❄❅◗❯✫❾➫➂❄⑨s❥✭❅◗❷✧❈❄❯✫❜✭❲✵◆❳❲✵❷✭❜✭❲■❜✭❲❴❘✵❁✻❷✭❘✵❲✵❅✾❃❆❁✻❯t❜✧❈❄❯✛❾➫❈❉❅◗❯✫❜✭❅✾❇✻❲✵❢❱❯❆❈❄❯❝➂❄❢❱❲●❈❄❯t❜✭❁❶❘✵❁✻❷❀✟✭❲✵❘✵❅◗❾❚❲✵❷❽❃❣❁ ✶✭❜✭❲✵❷❽❃❆❢❱❲
❲✵P❈❄❯❻❜✧❈❡❃❆❲✵❁✻❢❱❅❈❡❜✧❈❚❘✵❁✻➓❄❷✭❅◗❊●❋❄❁❀✶❳❜✭❁➫❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❍❲↕❈❄❥❦❃❆❁✻❾➫❈❄❊●❋❄❁❀✶✧❜✭❁➫❯❱❲✵❷✭❯❱❁✻❢❱❅❈❄❾❚❲✵❷❽❃❆❁❀✶❳❜✧❈❚❲✵❷✭➓✻❲✵❷❀✟✧❈❄❢❱❅❈❚❲✵P✠✰✒❃❆❢❱❅◗❘●❈
❲■❾❚❲✵❘ ✂❄❷✭❅◗❘●❈❦✽
✁ ❥✭❾ ❢❱❁✻❫✤❺❶❾❚❼✔❇✻❲✵P ✶✰❁❶➓✻❢❆❈❄❥✇❜✭❲❸❈❄❥❦❃❆❁✻❷✭❁✻❾❚❅❈■❜✭❲✵◆✤❲✵❷✭❜✭❲❸❅◗❷❽❇❄❈❄❢❱❅❈●❇✻❲✵P◗❾❚❲✵❷❽❃❆❲❻❜✧❈↕❅◗❾❚◆✭P◗❲✵❾❡❲✵❷s❃❣❈❄❊●❋❄❁↕❈↕❫✤❁✻❢❱❜✭❁
❜✭❲❶❥✭❾➫❈❚❜✭❅✾❇✻❲✵❢❱❯❱❅◗❜✧❈❄❜✭❲❶❜✭❲✪✡✢❥✭❷✭❊❋❊✰❲✵❯❴⑨s❥✭❲❶❇✻❲✵❷❀✟✧❈❄❾ ❈➫❘✵❁✻P❈❄❫✤❁✻❢❆❈❄❢❻❘✵❁✻❾→❁✻❯❖❁✻❫❦❵❛❲✒❃❆❅✾❇✻❁✻❯❖❜✧❈➫❯❱❥✧❈✇❾❚❅◗❯❱❯❆❋❄❁✭✽❻➭➤❈❄❅◗❯
✡✢❥✭❷✭❊❋❊✰❲✵❯✸◆❳❁✰❜✭❲✵❾❤❯❱❲✵❢✘❘✵P❈❄❯❱❯❱❅✾❩✧❘●❈❄❜✧❈❄❯✘❲✵❾❤❢❱❲✵P ❈❄❊●❋❄❁❻❈✛❘✵❁✻❷✭❘✵❲✵❅✾❃❆❁✻❯✘❃❣❈❄❅◗❯✷❘✵❁✻❾❚❁❝◆❳❲✵❢❱❘✵❲✵◆✤❊●❋❄❁❖❜✭❁❖❈❄❾❶❫✭❅◗❲✵❷s❃❆❲✮❲✖✕✰❃❆❲✵❢❱❷✭❁❀✶
❈❄❷✧➂❄P◗❅◗❯❱❲❶❲❡❈●❇❄❈❄P◗❅ ❈❄❊●❋❄❁➫❜✭❁❂❈❄❷✭❜✧❈❄❾❚❲✵❷❽❃❆❁ ❜✧❈r❾❚❅✾❯❆❯❆❋❄❁ ✶☛◆✭P ❈❄❷✭❲ ❵❱❈❄❾❚❲✵❷s❃❆❁✇❜✭❲❚❈❄❊❋❊s❲✵❯■❲❡❈r❯❱❥✧❈r❲✖✕❦❲✵❘✵❥✭❊●❋❄❁❀✶✸❜✭❲✵❷❽❃❆❢❱❲
❁✻❥❦❃❆❢❱❁✻❯✵✽
❭❤❯❱❅◗❯❛❃❆❲✵❾➫❈❍❜✭❲ ✦❀✌✏✎✒✑✏✓✔✌✏✎ ✕❖❲❍➈✔➎✘✗❣➋✙✓✔✌✏✎✖✕❴❢❱❲✵❯❱◆✤❁✻❷✭❯❆➂●❇✻❲✵P✷◆❳❲✵P❈↕❲✖✕❦❲✵❘✵❥✭❊●❋❄❁❀✶✧❘✵❁✻❷❽❃❆❢❱❁✻P◗❲❖❲❖❘✵❁✰❁✻❢❱❜✭❲✵❷✧❈❄❊●❋❄❁➜❜✭❲✵❯❛❃❣❈❄❯
✡✢❥✭❷✭❊❋❊✰❲✵❯ ❲✵❾❤❃❆❲✵❾❚◆✤❁☛☎ ❢❱❲●❈❄P ✰✫❜✭❲✵❷✭❁✻❾❚❅◗❷✧❈❄❜✧❈❻❜✭❲✛❈❄❢❱⑨s❥✭❅✾❃❆❲✒❃❆❥✭❢❆❈❻❜✭❲t❘✵❁✻❷❽❃❆❢❱❁✻P◗❲✍❜✭❁❴❢❱❁✻❫✤❺✭✽➤❙✮❯❛❃❣❲✫❃❆❼✻◆✭❅✾❘✵❁❀✶❄❘✵❢❱❥✭❘✵❅❈❄P✰❷✭❁
❜✭❲✵❯❱❲✵❷❽❇❽❁✻P✾❇✰❅◗❾❚❲✵❷❽❃❆❁❡❜✭❲❸❃❆❁✰❜✭❁❡❢❱❁✻❫✤❺❚❈❄❥❦❃❆❺✻❷✭❁✻❾❚❁❀✶❦❘✵❁✻❢❱❢❱❲✵❯❱◆✤❁✻❷✭❜✭❲↕❈❄❁➜❃❆❲✵❾➫❈➜❜✭❲✵❯❛❃❣❈❡❜✭❅◗❯❱❯❱❲✵❢❛❃❣❈❄❊●❋❄❁❚❜✭❲■❾❚❲✵❯❛❃❆❢❆❈❄❜✭❁✭✽
✌✎✍✏✌ ✑✓✒✕✔✗✖✙✘✛✚✎✜✣✢✕✒
❞❖❲✵❷s❃❆❢❱❲✠❁✻❯➫❜✭❅✾❇❽❲✵❢❱❯❱❁✻❯❚❃❆❲✵❾➫❈❄❯❚⑨s❥✭❲✠❃❆❢❆❈✏✿✵❲✵❾ ❾❚❁❄❃❆❅✾❇❄❈❄❊❋❊s❲✵❯❚◆✧❈❄❢❆❈⑥❁⑥❜✭❲✵❯❱❲✵❷❽❇❽❁✻P✾❇✰❅◗❾❚❲✵❷❽❃❆❁⑥❜✧❈❄❯✇❈❉❃❆❅✾❇✰❅◗❜✧❈❄❜✭❲✵❯
❢❱❲●❈❄P◗❅✠✿●❈❄❜✧❈❄❯t❷✭❲✵❯❛❃❆❲■❃❆❢❆❈❄❫✧❈❄P✠✟✭❁➜❜✭❲■❜✭❅◗❯❱❯❱❲✵❢❛❃❣❈❄❊●❋❄❁❚❜✭❲■❾❚❲✵❯❛❃❆❢❆❈❄❜✭❁❀✶✭◆✤❁s❜✭❲✵❾✂❯❱❲✵❢❝❘✵❅✾❃❣❈❄❜✭❁✻❯✛❁✻❯❝❯❱❲✵➓✻❥✭❅◗❷❽❃❆❲✵❯❋❇
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