Introductory lectures on rings and modules

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✓✕✔✗✖✙✘✛✚✢✜✤✣✦✥★✧✪✩✫✖✕✬
✭✂✮✰✯✲✱✴✳✶✵✷✯✴✸✺✹✼✻✽✻✽✾✿✸✪✮❀✾✽❁❃❂✂✸✪✾❅❄❆✵❇✯❈❁❉✾❊✱●❋
❍✷■❀■❀■
❏▲❑◆▼▲❖◗❉❘❙✲❚❱❯✂❑❳❲ ❨❩▼❬❑❪❭❫❵❴❛❚

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❜❀❝❉❞❢❡★❣❤❝❈✐❦❥✲❧✿♠♦♥✰❞❢❡★✐✕❡✿♣❉❥❉❥❉qr♠ts✕♠t✉✈❧❆❧✽✇①❧✽❝❉♠✪②③✇✈✇●④
⑤t⑥③⑦♦⑧⑩⑨✷❶❸❷❇❹✼⑦❺⑨❈⑧⑩❻❽❼✫❾❿❹✼⑦⑩❷➀⑧➁❾❿➂➃⑨③⑥❽➄◗➅➆⑥❇➇✴➂✕➈❈⑥❇❶❪➉➊⑨➀❶➋❷❇➌➍❾❿➂❦➎
②❿➏◗➐❦✇❦❝❉✉➒➑❫➓❈➔✰♠❺✐❦❣❤❝❿➏❦➓
→❊➣✲➔❀↔➙↕➁➛❅➜❦➝❉➞➟➛➡➠✼➢●➤❦➢●↕✼➛➥➠❈➎●➦➧✇❦❥❿➏❿♥✿❞r➨❦❝✈❧✶➞♦➩❦➩●➩
➦✰✐✼s①②❉♥✽❞r➫✲➨●♠➯➭➲✉❉❞r➳❦♠t♥❤❡✿❞➵❧❅➏❩➸✫♥✿♠❺❡✿❡
➺✫➫❉❞➻✉❿②❉♣❉♥✽➨❦❝➼➔✰♣❉❞➻q❢➫✲❞r✉❉➨
➣❿❝❈✐✼➽➾❧✿♠❺❡❊②❉♣❈♥✿➏➪➚★✇●✐❦➫
➦✰✐✼s①②❉♥✽❞r➫✲➨●♠✪➦✰➔❆➝✕➝✼➚❀➭

➧➦ ✇❦❥❿➏❿♥✽❞➻➨●❝●❧✶➞♦➩●➩❦➩①②❿➏◗➐✼✇●❝❉✉➒➑❫➓❈➔✰♠♦✐●❣❤❝❿➏
➸➋♠t♥✽s✕❞r❡✽❡✿❞➻✇●✉➶❞r❡➯➨●♥✽✐❦✉●❧✽♠♦➫➒❧✽✇➼❣t✇❦❥❿➏➒❧✿❝❈❞r❡✪➫✲✇✲❣t♣❉s✕♠t✉✈❧➯❞r✉❬♠tqr♠♦❣➹❧✽♥✿✇●✉❉❞❢❣✪➽➍✇❦♥✽s➒➎➀✇❦♥➘❧✿✇➼❥❉♥✽❞➻✉✈❧✪❞➻❧
➽➍✇❦♥❆❥③♠t♥❤❡✿✇❦✉❈✐❦q➴♣❈❡❊♠●➎✲♣❉✉❈➫✲♠♦♥❆❧✿❝❈♠♦❡✿♠✶❣t✇❦✉❈➫❉❞➵❧✽❞➻✇●✉❈❡t➷
❞➻❧★s➬♣❈❡❊❧❆②✴♠✪♥✽♠t❥❉♥✽✇✲➫✲♣❈❣t♠♦➫◗❞➻✉➒➮❆❝❉✇●q➻♠●➱
❞➻❧★s➬♣❈❡❊❧❆✉❉✇✼❧★②③♠✪s✕✇❿➫❉❞➵✃❈♠❺➫➼❞➻✉✙✐✼✉❿➏❩➮❀✐⑩➏❐➱
❞➻❧★s➬♣❈❡❊❧❆✉❉✇✼❧★②③♠✪♣❈❡✿♠♦➫➼✐❦❡❀❥❈✐❦♥❊❧❆✇✼➽❵✐✼✉❈✇✼❧✿❝❈♠t♥❆❥❉♣❉②❈q➻❞❢❣t✐✼❧✿❞r✇❦✉➀➓

❒❉✇●♥✿s➃✐✼❧❊❧✿♠❺➫➼❮➶✐⑩➏➶➞♦❰❈➎➴➞♦➩❦➩●➩❉➎✲✐➁❧❆➮❆❝❉❞❢❣❤❝➼❧✿❞rs✕♠✶❧✿❝❉♠✪✇●♥✿❞r➨❦❞r✉❈✐✼q❐➮❀✐❦❡❀✐⑩➳➁✐✼❞rqr✐❦②❉qr♠✶✐✼❧♦➷
❝✈❧❊❧✽❥➀➷ÐÏ●Ï⑩➮❆➮❆➮✪➓ s➃✐➁❧✿❝✷➓ ✉❉❞r♣➀➓ ♠♦➫✲♣❐Ï✼Ñ❸②③♠♦✐❦❣❤❝❿➏❈Ï⑩♥✽❞r✉❉➨●❡ s✕✇✲➫✲♣❉qr♠♦❡➹Ï

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✒ ûÛ×✢ü❩ýÿþ ×
❜❀❝❉♠➲❧✿♠➟ó❿✂❧ ✁☎✄✝✆✟✞✡✠☞☛✍✌✏✎✑✆✒✠✓✞☎✔✖✕✘✗✙✎✚✆✟✌✛✞✜✗✑✢✣✠✍✄✥✤✧✦★✄✪✩✍✢✣✫✓✄✬☛✮✭✯✠☞☛✍✌✛✰✱✗☎✢➧➨❦♥✽♠t➮◆✇❦♣❉❧✰✇❦➽➀❧✿❝❉♠➘✃❈♥❤❡❅✳❧ ✲
➏❦♠❺✐✼♥➃➨●♥✽✐●➫✲♣❈✐➁❧✽♠✙❣➟✇❦♣❈♥✽❡✿♠➒❧✿❝❈✐✼❧➪→✕❝❈✐⑩➳❦♠➼❧❤✐✼♣❉➨●❝●❧➼✐➁❧➪↔★✇●♥❊❧✽❝❉♠t♥✽✉❽→➡q➻qr❞r✉❉✇❦❞❢❡➪➭➲✉❉❞➻➳●♠t♥❤❡❊❞➻❧❅➏❦➓✂→➡✉
④❦♠♦♠t❥❉❞r✉❉➨ ➮❆❞➵❧✽❝ ❧✿❝❈♠◗✉❉✇●✉❈❣➟✇●s✕s➬♣✲❧❤✐➁❧✿❞r➳❦♠❩➽➍✇❿❣t♣❈❡✗✇✼➽★❧✽❝❉♠◗❧✿♠➟ó❿❧❺➎ï→✪❞➻✉✴❣➟qr♣❈➫✲♠♦➫ ✐ ❣❤❝✴✐✼❥✲❧✽♠t♥➬✇●✉
➨❦♥✽✇❦♣❈❥➶♥✿♠♦❥❉♥✽♠♦❡✿♠t✉✈❧✽✐✼❧✿❞r✇❦✉❈❡➘❞➻✉❬❥❉q❢✐❦❣t♠①✇❦➽ï❧✿❝❉♠➃❣❤❝❈✐❦❥✲❧✿♠♦♥✶✇❦✉ ❣t✇❦s✕s➬♣❉❧✽✐➁❧✽❞➻➳●♠①♥✽❞r✉❉➨●❡➘❧✿❝✴✐➁❧✶❞r❡✶❞r✉
✇❦♣❈♥➬❣➟✇●♣❉♥✽❡✿♠❩❡✿➏✈qrq❢✐✼②❉♣❈❡♦➓✤➣❿❞r✉❈❣➟♠◗✐➶❣➟✇●♣❉♥✽❡✿♠❩✐➁❧➬❧✿❝❈✐✼❧➬q➻♠♦➳❦♠♦q➧❡✿❝❉✇❦♣❉q❢➫▲q❢✐⑩➏❬❡✿✇❦s✕♠✕➽➍✇❦♣❈✉❈➫❉✐➁❧✽❞➻✇●✉
➽➍✇❦♥✰q❢✐➁❧✿♠♦♥❀➮➧✇●♥✿④✗❞➻✉➼❣➟✇●s✗s①♣✲❧✽✐✼❧✿❞r➳❦♠➯✐✼qr➨❦♠t②❈♥✽✐❈➎●→❵➽➍♠♦q➵❧✰❧✿❝✴✐➁❧❀→✫❡❊❝❈✇❦♣❉q❢➫❩s➃✐✼④●♠➲s①➏❩❣➟q❢✐❦❡✽❡ï✉❉✇❦❧✿♠♦❡

✐⑩➳➁✐✼❞rqr✐❦②❉qr♠➯✐●❡❆✐✗❡✿♣❉❥❉❥❈q➻♠♦s✗♠♦✉✈❧❆❧✿✇✕❧✿❝❈♠✶❧✿♠➟ó❿❧❺➓
→ï②③♠tqr❞➻♠♦➳❦♠➘❧✿❝❈✐✼❧➧❧✽❝❉♠➯s✕✐✼❧✿♠♦♥✿❞❢✐✼q❐→ï❝❈✐⑩➳●♠➘❣❤❝❉✇✈❡❊♠♦✉➃❧✿✇✗❞r✉❈❣➟qr♣❈➫✲♠➯❞➻✉◗❧✿❝❈❞r❡❀❣❤❝❈✐❦❥✲❧✿♠♦♥➧❞❢❡✰♥✽✐✼❧✿❝❉♠♦♥
❡❊❧✽✐✼✉✴➫❉✐✼♥❤➫➴➓✶→➥❧✪❞r❡➯✉❉✇❦❧✶✐●❡➲♠tó✈❧✽♠t✉❈❡✿❞r➳❦♠①✐●❡➘❧✿❝❈✐✼❧➯❞r✉ ✇❦❧✿❝❉♠♦♥➲❧✽♠➟ó❿❧✽❡♦➎➴②❉♣✲❧✪→★❝❈✇❦❥③♠➬❧✽❝❈✐➁❧✶❞➵❧✪➮❆❞rq➻q
❡✿♠t♥✽➳❦♠➘✐●❡❀✐✗❡❊❧✽✐❦♥❊❧✽❞➻✉❈➨①❥③✇❦❞r✉✈❧➧➽➍✇●♥★❡❅❧✽♣❈➫✲♠t✉✈❧❤❡➧❞r✉✈❧✿♠♦♥✿♠❺❡❅❧✽♠♦➫◗❞➻✉➒✐✼qr➨❦♠♦②❉♥✽✐❈➓❇❜❀❝❉✇✈❡❊♠✶❞r✉✈❧✿♠t♥✽♠♦❡❊❧✿♠❺➫❩❞r✉
➽➍♣❉♥✿❧✿❝❉♠♦♥✪♠➟ó✲❥❉qr✇❦♥❤✐➁❧✽❞➻✇●✉✤✇✼➽✰❧✿❝❈♠✕✃❈♠tq❢➫❬➮❆❞➻qrq➋✃❈✉❈➫▲ñ➯✐⑩➳✈❞❢➫❬➺ï❞❢❡❊♠♦✉✈②❈♣❈✵➫ ✴ ❡✶②✴✇❿✇❦✷④ ✶✸✠✍✹✮✹✺✌✛✆✒✫✓✆✻✦★✼✽✗
✾ ✰ ✩✪✗❀✿✑✞✜✫❂❁✸✦★✆✟❃❄✫❆❅✘✦❇✗✚❁❈✆✒✠✓❁❉✫✍✞✜☛ ✾ ✰ ✩✪✗❀✿✑✞✜✫✓✦❇✎❋❊●✗✡✠✍✹❍✗✚✆✻✞☎✔➃❧✿✇❬②✴♠➒✐✙➽➆✐●❡✿❣t❞➻✉✴✐➁❧✿❞r✉❉➨ ❥✴✇●❞➻✉✈❧✕✇✼➽
♠t✉✈❧✽♥✿➏●➓
■ ✉❉♠✰✇✼➽③❧✿❝❉♠❆✐●➫✲➳➁✐✼✉✈❧✽✐❦➨❦♠♦❡❸✇❦➽✴♠tqr♠♦❣➟❧✿♥✽✇❦✉❉❞❢❣➧❥❉♣❉②❉qr❞r❡✿❝❉❞r✉❉➨✶❞r❡❵❧✿❝❉♠❆✐✼②❈❞➻qr❞➵❧❅➏❫❧✿✇✶s➃✐✼④❦♠❀❣❤❝❈✐❦✉❉➨❦♠❺❡
♣❏ ❉❞❢❣❤④✈qr➏❦➎➴→➲➮➧✇●♣❉qr➫ ✐✼❥❉❥❈♥✿♠❺❣➟❞❢✐➁❧✿♠①♥✿♠❺❣➟♠♦❞➻➳❿❞r✉❉➨◗❣t✇❦♥✽♥✿♠❺❣➹❧✿❞r✇❦✉✴❡➲✐✼✉✴➫✤❡✿♣❉➨❦➨●♠♦❡❊❧✿❞r✇❦✉❈❡➲➽➍♥✿✇●s ✐✼✉❿➏❦✇●✉❉♠
➮❆❝❉✇✕♣❈❡✿♠♦❡✰❧✽❝❉❞r❡★s✕✐✼❧✿♠♦♥✿❞❢✐✼q ➓
➐✼✇●❝❉✉✙➑❫➓❈➔✰♠♦✐●❣❤❝❿➏
ñ➘☞♠ ❑✪✐❦q➻②➀➎✲→➡qrqr❞➻✉❉✇●❞r❡
❮✙✐⑩➏❦➎➴➞❺➩❦➩❦➩

▲

✟ ✆

✞

▼❖◆◗❙❘❯❚❲❱

✄ ✎ ✄ ❩❨

❳

☛

☎ ✂✁

✍

☞

❜❀❝❉♠❆❝❉❞❢❡❊❧✿✇❦♥✽➏❫✇❦➽❐❣t✇❦s✕s➬♣✲❧❤✐➁❧✽❞➻➳●♠❀✐❦q➻➨●♠t②❉♥❤✐➯②✴♠♦➨❦❞r✉❈❡➋❞r✉✕❧✿❝❉♠❆✉❉❞r✉❉♠t❧✿♠t♠♦✉✈❧✿❝❩❣➟♠♦✉✈❧✿♣❉♥✽➏❫➮❆❞➻❧✿❝✕➮➧✇●♥✿④
❞r✉ ✉❿♣❉s➬②③♠t♥①❧✿❝❈♠t✇❦♥✽➏❦➎ï✐❦q➻➨●♠t②❉♥❤✐✼❞❢❣✕➨❦♠♦✇❦s✕♠➟❧✽♥✿➏●➎ï✐✼✉❈➫ ❞➻✉❿➳➁✐✼♥✽❞r✐❦✉✈❧❫❧✿❝❉♠♦✇❦♥✽➏❦➓❂❬ ♠➼➮❆❞rq➻q❆➫✲❞❢❡✿❣t♣❈❡✽❡
❭ ♣❈❡❊❧➬✐➼②❉❞➵❧①✇✼➽✫❧✽❝❈✐➁❧❫❝❈❞r❡❊❧✿✇●♥✿➏●➎✷✐✼✉❈➫❬♥✽♠➟➽➍♠♦♥✶❧✿❝❉♠➃♥✽♠♦✐●➫✲♠t♥➯❧✿✇✤➦➧❝❈✐❦❥✲❧✿♠♦♥➃➞➃✇✼➽✣❪ ➤✍❫ï➽➍✇❦♥❫✐➼s✕✇❦♥✽♠
➫✲♠t❧✽✐✼❞rqr♠♦➫➒✐❦❣♦❣➟✇❦♣❈✉●❧❺➓
❴ ✐✼♣✴❡✿❡❀❡✿❝❉✇➁➮➧♠❺➫❩❧✽❝❈✐➁❧❀❧✽❝❉♠✪♥✿❞r✉❉✥
➨ ❵✂❪ ✱❞ ❫✷❞❢❡❆✐①♣❈✉❉❞ ♣❉♠✶➽➆✐●❣➹❧✽✇❦♥✽✱❞ ❛❺✐➁❧✿❞r✇❦✉➼➫✲✇❦s➃✐❦❞➻✉➀➎❉✐❦✉❈➫◗♣❈❡❊♠❺➫
❧✿❝❈❞r❡★➽➆✐❦❣➹❧➲❧✿✇❩❥❉♥✽✇➁➳❦♠✪♥✽♠♦❡✿♣❉q➻❧✽❡★✐❦②✴✇●♣✲❧➲✇●♥✽➫✲❞r✉❈✐❦♥✿➏❩❞r✉✈❧✿❏ ♠♦➨❦♠t♥❤❡♦❝➓ ❜➲♠➬✐✼q❢❡❊✇❩❡✿❝❉✇➁➮✰♠♦➫◗❧✿❝✴✐➁✣❧ ❵✂❪ ❞✸❫❸❞r❡
✐✗♣❉✉❉❞ ❏ ♣❉♠➯➽➆✐❦❣➹❧✽✇❦♥✽✱❞ ❛❺✐➁❧✽❞➻✇●✉◗➫✲✇●s✕✐❦❞➻✉✷➎✲➮❆❝❉♠t♥✽✂♠ ❞❃❞r❡❆✐✗♥✽✇❿✇✼❧❆✇✼➽❇❧✿❝❉♠✶❥③✇❦qr➏✈✉❈✇❦s✕❞r✐❦✵q ❡✝❢❉❣❤❡✮❣❽➞❦➎
✐✼✉✴➫➒♣❈❡❊♠❺➫➒❧✿❝❈❞r❡★➽➆✐❦❣➹❧➘❧✿✇❩➨●❞➻➳●♠➬✐➃❥❉♥✽✇❿✇✼➽❵✇✼➽ï❒❈♠t♥✽s✕✐✼☞❧ ✴ ❡★q❢✐❦❡❊❧★❧✿❝❈♠t✇❦♥✽♠ts ➽➍✇❦♥➲❧✿❝❉♠①♠➟ó✲❥③✇❦✉❉♠♦✉●❧➯➤
✐ ❡✿♠t♠❩➦➧❝❈✐❦❥✲❧✿♠♦♥➯➩➪✇✼✧
➽ ❪ ❀➝ ❫➋➽➍✇❦♥➯❝❉❞❢❡➘❥❈♥✿✇❿✇✼➽❅➎➴✐❦✉❈➫✙➽➍✇●♥➯❡✿✇❦s✕♠➬❝❈❞r❡❊❧✿✇●♥✿❞❢❣t✐❦q❇✉❉✇❦❧✿♠❺✡❡ ❥➟➓✶❜❀❝❈♠✗❡✿♠♦✐❦♥✽❣❤❝
➽➍✇❦♥➃✐✤❥❉♥✿✇❿✇❦➽➲✇✼➽➘❒❈♠t♥✽s➃✐➁☞❧ ✴ ❡①qr✐●❡❅❧✗❧✿❝❉♠♦✇❦♥✽♠ts qr♠♦➫ ❧✿✇ ❏ ♣❈♠♦❡❊❧✿❞r✇❦✉❈❡①✇✼➽➲♣❈✉❉❞ ❏ ♣❉♠◗➽➆✐❦❣➟❧✿✇●♥✿❦❞ ❛♦✐✼❧✿❞r✇❦✉
❞r✉ ❧✿❝❈♠➪♥✽❞➻✉❉➨✈❍❡ ❵✂❪ ❧✽❫ ➎ï➮❆❝❈♠t♥✽♠♠ ❧➶❞❢❡①✐✤♥✿✇❿✇✼❧✗✇✼➽★♣❉✉❈❞➵❧❅➏●➓ →➥❧✕➮✰✐●❡❫♠♦➳❦♠t✉✈❧✽♣❈✐✼qrq➻➏❬♥✽♠♦✐✼qr❦❞ ❛t♠♦➫❛❧✿❝❈✐✼❧
❧✿❝❈❞r❡✗s✕♠➟❧✽❝❉✇✲➫ ✇✼➽➘❥❉♥✿✇❿✇❦➽➲❣➟✇❦♣❈qr➫❛✉❈✇✼❧✕②✴♠➼♠➟ó❿❧✿♠♦✉❈➫✲♠❺➫ ②③♠t➏❦✇●✉❈➫ ✐ ❣➟♠t♥✿❧✽✐❦❞➻✉ ❥✴✇●❞➻✉✈❧♦➎➧❡❊❞r✉❈❣➟♠➼❞➻❧
❣t✐❦✉❉✉❉✇❦❧★②✴♠✗✐❦❡✽❡❊♣❉s✕♠❺➫➪❧✽❝❈✐➁❧➘♣❉✉❉❞ ❏ ♣❈♠❫➽➆✐❦❣➟❧✿✇●♥✿❦❞ ❛♦✐✼❧✿❞r✇❦✉➼❝❉✇❦q❢➫❉❡♦➓✰→➡✉➒➽➆✐●❣➹❧❺➎❈❞➻❧➲➽➆✐✼❞rq❢❡❆❞➻✉➒❧✽❝❉♠➬♥✽❞r✉❉➨
❵✂❪ ♥✽❢✡♦✍♣❦q✡❢✡r✑❫➥➓
→➡✉❛❧✽❝❉❞r❡✕❣❤❝❈✐❦❥✲❧✿♠♦♥➬➮✰♠➪♥✽♠➟❧✽♣❉♥✿✉ ❧✿✇➶❧✽❝❉♠ ♣❈♠♦❡❊❧✿❞r✇❦✉ ✇❦➽★♣❉✉❉❞ ♣❈♠❩➽➆✐❦❣➟❧✿✇●♥✿❦❞ ❛♦✐✼❧✿❞r✇❦✉❛❞r✉ ❣➟✇●s✗➛
s➬♣❉❧✽✐➁❧✽❞➻➳●♠❩♥✽❞➻✉❉➨✈❡t➓✙➭➲✉❉❞ ❏ ♣❉♠❩➽➆✐❦❣➹❧✽✇❦♥✽✱❞ ❛❺✐➁❧✽❞➻✇●✉❬❏ ✇❦➽❆♠tqr♠ts✕♠t✉✈❧✽❡①❞r✉●❧✽❏ ✇➶❥❉♥✽✇✲➫✲♣❈❣➹❧❤❡❫✇❦➽❀❞r♥✽♥✿♠❺➫✲♣❈❣➟❞r②❉qr♠
♠tqr♠ts✕♠♦✉●❧❤❡➲❞❢❡★❞rs✕❥✴✇✈❡✿❡✿❞r②❉q➻♠①♠t➳●♠t✉✙❞r✉✤❡❊♣✴❣❤❝➶♥✿♠♦qr✐✼❧✿❞r➳❦♠♦q➻➏◗✉❉❞r❣t♠➬♥✽❞➻✉❈➨●❡➲✐●s❡ ❵✂❪ t ✉➲✽➜ ❫ ➓➯ñ➲♠❺➫✲♠t④❿❞r✉❈➫
❞r✉●❧✽♥✿✇✲➫✲♣✴❣➟♠♦➫❩❧✿❝❉♠✶✉❉✇❦❧✿❞r✇❦✉◗✇✼➽❸✐❦✉➪❞❢➫✲♠♦✐❦q❐❞➻✉➼✇❦♥❤➫✲♠t♥➧❧✿✇✕♥✽♠♦❣t✇➁➳❦♠t♥✰❡❊✇●s✕♠➯❡✿♠ts①②❉qr✐❦✉❈❣➟♠➘✇✼➽❸♣❉✉❉❞ ♣❈♠
➽➆✐❦❣➟❧✿✇●♥✿❦❞ ❛♦✐✼❧✿❞r✇❦✉➀✷➓ ❜➲♠✙❥❉♥✽✇➁➳❦♠♦➫ ❧✿❝✴✐➁❧➪❞r✉◆❣➟♠t♥✿❧✽✐❦❞➻✉❽❞rs✕❥✴✇●♥❊❧❤✐✼✉✈❧➪❡❊♣❈②❉♥✿❞r✉❉➨✈❡✕✇✼➽✶❧✿❝❉♠ ❣➟✇❦s✕❥❉❏ qr♠➟ó
➝✼➤❦➩

➁➝ ➢✈↕

✈✏✇ ①✮✇ ②●③✚④⑥⑤⑧⑦⑩⑨
❶❸❷✧①✂❹✧❺❸❻❽❼❿❾⑥✇➀❶➂➁➂➃✯➃❩➄❝❺✝①●❺➆➅✽➇➆❻❩❼➂➅⑧➈✮➉●➊
✉❿♣❉s➬②③♠t♥❤❡♦➎❉✐➁❧❆q➻♠❺✐❦❡❊❧❆❞➵❧★❞❢❡✰❧✿♥✽♣❉♠➯❧✿❝❈✐✼❧★♠t➳●♠t♥✽➏➃❞r➫✲♠❺✐✼q➀❣♦✐✼✉➼②✴♠✪➮❆♥✽❞➵❧✿❧✿♠♦✉➼♣❈✉❉❞ ❏ ♣❉♠♦q➻➏◗✐❦❡❆✐✗❥❉♥✽✇❿➫✲➛
♣❈❣➟❧➬✇✼➽❀❥❉♥✽❞➻s✕♠➃❞❢➫✲♠♦✐❦qr❡♦♠➓ ❬❬♠➃➮❆❞➻qrq➧❡❊❧✿♣❈➫❉➏➶❧✿❝❈♠♦❡✿♠➃♥✿❞r✉❉➨●❡❫❞➻✉❬❧✿❝❈♠❩qr✐●❡❅❧✪❧❅➮✰✇✙❡❊♠❺❣➹❧✽❞➻✇●✉❈❡✪✇✼➽✰❧✿❝❈♠
❣❤❝❈✐❦❥✲❧✿♠♦♥♦➎❐♣❉✉❈➫❉♠t♥➯❧✿❝❉♠✗➨❦♠♦✉❉♠t♥❤✐✼q❸❝❉♠❺✐❦➫✲❞r✉❉➨➪✇❦➽➧ñ➘♠♦➫✲♠♦④✈❞r✉❈➫❬➫✲✇❦s➃✐❦❞➻✉❈❡♦➓ ✐ ↔➲✇✼❧✿♠✗❧✽❝❈✐➁❧➯❧✿❝❉♠✗q❢✐❦❡❊❧
❧❅➮✰✇✕❡✿♠♦❣➟❧✿❞r✇❦✉❈❡❆➫❉✇✗✉❈✇✼❧➲➫✲♠♦❥✴♠♦✉❈➫➼✇❦✉◗❧✿❝❉♠✶✃❈♥❤❡❊❧❆❧❅➮➧✇✴➎❿✐❦✉❈➫➒❣t✐❦✉◗②③♠✪♥✿♠❺✐❦➫◗❞➻✉✴➫✲♠t❥③♠t✉❈➫❉♠t✉✈❧✿qr➏❦➋➓ ❥
➑ç❥❈✐❦♥✽✐❦q➻qr♠tq✰➫✲♠t➳●♠tqr✇❦❥❉s✕♠♦✉●❧➬✐❦q➻✇●✉❉➨✤❡✿✇❦s✕♠t➮❆❝✴✐➁❧➬➫✲✱❞ ➌③♠♦♥✿♠♦✉✈❧①qr❞➻✉❉♠❺❡❫✇✲❣t❣t♣❉♥✽♥✿♠❺➫❬➽➍✇❦♥➬❞❢➫✲♠❺✐✼q❢❡
❞r✉❃❥③✇❦qr➏❿✉❉✇❦s✕❞❢✐✼q★♥✽❞r✉❉➨●❡✕❞r✉❪❡❊♠♦➳❦♠♦♥✽✐❦q✰❞r✉❈➫✲♠t❧✿♠♦♥✿s✕❞r✉❈✐➁❧✽♠♦❡♦❆➓ ➍✷✐●❡❊④●♠t♥➃✐✼✉✴➫❽❮➶✐❦❣t✐❦♣❉qr♠t➏ ➨✈✐⑩➳❦♠➒✐
➫✲♠❺❣➟✇❦s✕❥③✇●❡✿❞➵❧✽❞➻✇●✉➪❧✽❝❉♠t✇●♥✿♠♦sÛ➽➍✇❦♥★❡✿♣❈❣❤❝➼❞r➫✲♠❺✐✼q❢❡t➎❉❡✿❝❉✇➁➮❆❞r✉❉➨①❧✿❝❈✐✼❧❀♠♦➳❦♠♦♥✿➏➃❞❢➫✲♠♦✐❦q➴❞r❡❆✐❦✉◗❞r✉✈❧✿♠♦♥✽❡✿♠♦❣➟➛
❧✿❞r✇❦✉ ✇✼➽➘✃❈✉❉❞➻❧✿♠tqr➏❛s➃✐✼✉❿➏❛❥❉♥✽❞➻s➃✐❦♥✿➏▲❞❢➫✲♠♦✐❦qr❡♦➓ ❜❀❝❉❞❢❡✗➮✰✐●❡➬♠tó✈❧✽♠t✉❈➫❉♠♦➫ ❧✿✇▲✐✼qrq❀❣t✇❦s✕s➬♣❉❧✽✐➁❧✽❞➻➳●♠
↔★✇❿♠t❧✿❝❉♠♦♥✿❞❢✐✼✉ ♥✿❞r✉❉➨●❡➯❞r✉ ➞❺➩●➝❉➞➬②❿➏➶➺ïs✕s➬➏ ↔★✇❿♠➟❧✽❝❉♠t♥❺➎➴❞➻✉▲✐➼➳❦♠♦♥✿➏➒❞r✛✉ ➎❈♣❉♠♦✉●❧✽❞r✐❦q❵❥❈✐✼❥③♠t♥❺➓①❜❀❝❈♠
❥❉♥✽❞➻s➃✐❦♥✿➏▲s✕✇✼❧✽❞➻➳➁✐➁❧✽❞➻✇●✉❛➽➍✇❦♥✗❧✽❝❉♠➼➫❉♠t➳❦♠♦q➻✇●❥❉s✕♠t✉✈❧①✇❦➽★❧✿❝❈❞r❡①❧✿❝❈♠t✇❦♥✽➏❛❣➟✇●s✗♠❺❡❫➽➍♥✽✇❦s ✐❦q➻➨●♠t②❉♥❤✐✼❞❢❣
➨❦♠♦✇❦s✕♠➟❧✽♥✿➏●➏➓ ❬ ♠➃➮❆❞rqrqï❥❉♥✽✇➁➳❦♠✗❧✿❝❉♠♠ ➍❇✐❦❡✿④❦♠♦♥❊➛➡↔★✇❿♠➟❧✽❝❉♠t♥➯❥❉♥✽❞➻s➃✐❦♥✿➏✤➫❉♠♦❣➟✇●s✕❥✴✇✈❡❊❞➻❧✿❞r✇❦✉❬❧✿❝❈♠t✇❦♥✽♠ts
❞r✉➶❧✿❝❈♠❫✃❈♥❤❡❅❧✶❡❊♠❺❣➹❧✽❞➻✇●✉➶✇✼➽ï❧✽❝❉♠①❣❤❝✴✐✼❥✲❧✽♠t♥❺➓➘➑Ø❥❈✐✼♥✿❧➘✇❦➽❵❧✿❝❉♠✗➨❦♠♦✉❉♠t♥❤✐✼q✷❧✿❝❉♠♦✇❦♥✽➏◗✇❦➽✫↔★✇❿♠➟❧✽❝❉♠t♥✽❞r✐❦✉
♥✽❞➻✉❉➨✈❡❀❞r❡❀✇●♣✲❧✿qr❞r✉❉♠♦➫➼❞r✉◗❧✽❝❉♠❫❡✿♠♦❣➟✇●✉❈➫➼❡❊♠❺❣➹❧✿❞r✇❦✉➼✇✼➽❸❧✿❝❈♠❫❣❤❝❈✐✼❥✲❧✽♠t♥❺➓
→➡✉❿➳➁✐✼♥✽❞r✐❦✉●❧➋❧✽❝❉♠t✇●♥✿➏✗➨❦♥✽♠t➮❃✇❦♣✲❧➧✇✼➽➀✐✼✉➃❞r✉✈❧✿♠t♥✽♠♦❡❊❧ï❞r✉➃❧✿❝❉♠➲➨❦♠t✇●s✕♠➟❧✿♥✽❞❢❣❀❥❉♥✿✇●❥✴♠♦♥❊❧✽❞➻♠❺❡❵✇✼➽➴❥❉q❢✐✼✉❈♠
❣➟♣❈♥✿➳●♠♦❡➪❧✿❝❈✐✼❧➼♥✽♠ts➃✐✼❞r✉❪❞r✉❿➳⑩✐❦♥✿❞❢✐✼✉✈❧➪♣❈✉❈➫✲♠t♥✙❣t♠t♥✿❧✽✐✼❞r✉❱❣tqr✐●❡✿❡✿♠♦❡◗✇✼➽✪❧✽♥✽✐❦✉❈❡❅➽➍✇●♥✿s➃✐✼❧✿❞r✇❦✉❈❡♦➓ ❜❀❝❈♠
➨❦♠♦✉❉♠t♥❤✐✼q❇❥❉♥✽✇❦②❉qr♠ts ➮❀✐❦❡★♠♦➳❦♠♦✉●❧✽♣❈✐✼qrqr➏➼❡❊❧✽✐✼❧✿♠♦➫✤❞➻✉➶❧✿❝❉♠①➽➍✇❦qrq➻✇➁➮❆❞r✉❉➨❩➮❀✐⑩➏❐➷❀❞➵➽➧✐❦✉✤✐✼❥❈❥❉♥✿✇●❥❉♥✽❞r✐✼❧✿♠
➨❦♥✽✇❦♣❈✥❥ ➐➊✐❦❣➟❧✽❡✰✐❦❡❀✐✼♣❉❧✿✇❦s✕✇●♥✿❥❉❝❈❞r❡✿s➃❡ï✇✼➽❸✐➬❥③✇❦qr➏❿✉❉✇❦s✕❞❢✐✼q③♥✿❞r✉❉✮➨ ➑➓➒→➔➏❪ ❡✬➣✍↔✚↕☞↕✚↕✚↔✜❡✝➙✪❫ ✐ ➮❆❝❈♠t♥✽♠
➔❪❞❢❡❵✐➲✃❈♠tq❢✏➫ ❥➹➎●➮❆❝❈✐➁❧❵❞❢❡❸❧✿❝❉♠❆❡✿♣❉②❉♥✽❞➻✉❈s
➨ ➑✣➛ ✇✼➽✴♠♦q➻♠♦s✕♠t✉✈❧✽❡➋qr♠➟➽➾❧➋✃❉ó✲♠♦➫①②❿➜➏ ➐➞➝➒❒❉✇●♥➋♠➟ó❉✐✼s✕❥❉qr♠❦➎✼❞➻➽
➐❪❞❢❡❸❧✿❝❈♠❀❡✿➏❿s✕s✗♠t❧✿♥✽❞r❣➧➨❦♥✽✇❦♣❈✺
❥ ➟✵➙❐➎➁❧✽❝❉♠t❍✉ ➑✣➛✤❞❢❡❇❧✿❝❉♠❆♥✽❞r✉❉➨➘✇❦➽✴❡✿➏✈s✕s✕♠➟❧✽♥✿❞❢❣➧➽➍♣❉✉❈❣➟❧✿❞r✇❦✉❈❡♦➎✼➮❆❝❉❞❢❣❤❝
❣t✐❦✉➒②✴♠✗❡❊❝❉✇➁➮❆✉➼❧✽✇❩②✴♠➬➨❦♠t✉❈♠t♥❤✐➁❧✿♠❺➫ ✐ ✐❦❡➲✐✼❯✉ ➔➯➛➡✐✼qr➨❦♠t②❈♥✽✪✐ ❥✫②❿➏➪❧✿❝❉♠①♠tqr♠ts✕♠t✉✈➙ ❧✽✐❦♥✿➏◗❡❊➏❿s✕s✕♠➟❧✿♥✽❞❢❣
➽➍♣❉✉❈❣➟❧✿❞r✇❦✉❈✧❡ ➠➡➣➂➒→❡✵➣➢❣➥➤✚➤✚➤✽❣❤❡➦➙➴✏➎ ➠ ❢ ➒➀➧ ➣☎➨ ♣❇➩➭➫ ➨✬➙ ❡ ♣ ❡ ➫ ➯➎ ↕☞↕✚↕r✝➎ ➠✓➙✺➒➀➲ ♣✱➳ ➣ ❡ ♣ ➓
❜★❞rqr②✴♠♦♥❊❧ï❡✿✇❦qr➳❦♠♦➫✪❧✿❝❉♠✰➽➍♣❉✉❈➫❈✐✼s✕♠t✉✈❧✽✐❦q❿❥❉♥✿✇●②❉qr♠ts ✇✼➽③❞➻✉❿➳➁✐✼♥✽❞❢✐✼✉✈❧✷❧✽❝❉♠t✇●♥✿➏●➎➁②✈➏①❡❊❝❉✇➁➮❆❞r✉❉➨➲❧✿❝❈✐✼❧
❧✿❝❈♠➯♥✽❞r✉❉➨➬✇❦➽❇❞r✉✈➳➁✐❦♥✿❞❢✐✼✉✈❧✽❡➧❞❢❡✫✃✴✉❉❞➵❧✽♠tqr➏❩➨❦♠♦✉❉♠t♥❤✐➁❧✽♠♦➫➃❞r✉➒✐➬②❉♥✽✇●✐●➫➃♥❤✐✼✉❉➨●♠➲✇✼➽❇❞➻✉✈❧✿♠♦♥✿♠❺❡❅❧✽❞➻✉❈➨✗❣♦✐❦❡✿♠♦❡♦➓
❬❬♠ï❝❈✐⑩➳❦♠ï✐❦q➻♥✽♠♦✐●➫✲➏★➨●❞➻➳●♠t✉✪✐❀❥❉♥✽✇✈✇❦➽✈✇❦➽❿❧✿❝❉❉♠ ❜➲❞➻qr②③♠t♥✿❧✷②❈✐❦❡✿❞❢❡❐❧✿❝❉♠♦✇❦♥✽♠ts ✐ ❡✿♠t♠✫❜❀❝❉♠♦✇❦♥✽♠ts✂➝❉➓ ➢✴➓➻➞❺⑩↕ ❥➟➎
➮❆❝❉❞❢❣❤❝◆➮✰✐●❡➃❧✽❝❉♠➶✃❈♥❤❡❊❧◗❡❅❧✽♠t❥❪❞r✉❪❝❉❞❢❡❩❥❈♥✿✇❿✇✼➽✪✇❦➽✪❧✿❝❉♠✤✃❈✉❉❞➻❧✿♠t✉❈♠♦❡✽❡❩✇✼➽❫❞r✉❿➳➁✐✼♥✽❞r✐❦✉●❧❤❡t➓➙→➥❧➼➮✰✐●❡
➺ïs✕s①➏◗↔★✇❿♠t❧✿❝❉♠♦♥➲➮❆❝❉✇❩♥✽♠♦❣t✇❦➨●✉❉✱❞ ❛♦♠♦➫➪❧✿❝❉♠➬➨❦♠t✉❈♠t♥❤✐✼q➀❞rs✕❥✴✇●♥❊❧❤✐✼✉❈❣t♠✪✇✼➽➋❧✿❝❉♠✗✐❦❡✽❣➟♠♦✉❈➫✲❞r✉❉➨❩❣❤❝❈✐✼❞r✉

❣➟✇●✉❈➫✲❞➻❧✿❞r✇❦✉➀➎✲✐❦✉❈➫➪❡✿✇➬❧✽❝❉♠➯②❈✐❦❡✿❞r❡➧❧✽❝❉♠t✇●♥✿♠♦sç❞r❡✰♣❈❡✿♣❈✐✼qrqr➏✕❡❊❧✽✐✼❧✿♠❺➫➪❞r✉❩❧✽❝❉♠➯➽➍✇❦qrq➻✇➁➮❆❞r✉❉➨➬➮❀✐⑩➏❐➷❇❞➻➵➽ ➑
❞❢❡❆✐➃↔★✇❿♠➟❧✽❝❉♠t♥✽❞r✐❦✉◗♥✽❞r✉❉➨❈➎❿❧✽❝❉♠t✉✙❡✿✇✗❞❢❡✰❧✿❝❈♠✪❥✴✇●q➻➏❿✉❉✇●s✗❞❢✐✼q➴♥✽❞r✉❉➏➨ ➑✺❪ ❡➭❫➥➓
➑★q➻❧✿❝❈✇❦♣❉➨●❝◗❞r✉➼❧✿❝❉❞❢❡❆❣❤❝❈✐✼❥❉❧✿♠t♥❆➮✰♠✶s➃✐✼④❦♠➘❧✿❝❈♠✪♣❉✉❈➫✲♠♦♥✿qr➏❿❞➻✉❉➨➃✐●❡✿❡✿♣❉s✕❥✲❧✿❞r✇❦✉➪❧✿❝❈✐✼❧➲✐✼qrq➴♥✿❞r✉❉➨✈❡
♣❉✉❈➫❉♠t♥✙❣➟✇●✉❈❡❊❞❢➫✲♠♦♥✽✐✼❧✿❞r✇❦✉❪✐✼♥✽♠✤❣t✇❦s✕s➬♣✲❧❤✐➁❧✽❞➻➳●♠ ✐ ➮❆❞➻❧✿❝✌❞❢➫✲♠t✉✈❧✿❞➻❧❅➏❽♠tqr♠ts✕♠t✉✈☎❧ ❥➹➎➯➮➧♠ ➮❆❞➻qrq✶✇✼➽➾❧✿♠♦✉
♥✽♠♦❡❊❧✽✐➁❧✽♠➯❧✿❝❉❞❢❡❆❞r✉◗❧✽❝❉♠✪❝❿➏❿❥✴✇❦❧✿❝❉♠❺❡❊♠❺❡❀✇✼➽✷❧✽❝❉♠✪s➃✐ ❭ ✇●♥✰♥✽♠♦❡✿♣❉q➻❧✽❡♦➓
➸ ☞✜ ➺

➻❈➼➢➽✚➾ ✖
✧ ➼➋✬➪➚✙✥★✩❆✔✮➾➹➶❬✔➜➘❸➽✙➴❸➽t✔①✘

➍➀♠t➜
❧ ➔ ②③♠❩✐➼✃❈♠♦qr➫➴➎➋✐✼✉✴➫➶✃❈♥❤❡❊❧➬❣➟✇❦✉✴❡❊❞❢➫✲♠t♥✶❧✽❝❉♠❩♥✽❞➻✉❈➷➨ ➔➏❪ ❡➭❫➧✇✼➽❀❥✴✇●q➻➏❿✉❉✇●s✗❞❢✐✼q❢❡✶❞r✉❛✇❦✉❉♠✕❞r✉❈➫✲♠➟➛
❧✿♠♦♥✿s✕❞r✉❈✐➁❧✽♠❦➓➬➣❿❞r✉❈❣t♠➬❧✽❝❉❞r❡✶♥✽❞r✉❉➨➪❞❢❡✶✐➪❥❉♥✽❞r✉❈❣➟❞r❥❈✐✼q❸❞❢➫✲♠♦✐❦q➋➫❉✇❦s➃✐✼❞r✉➀➎➴♠♦✐●❣❤❝➶❞❢➫✲♠♦✐❦q❸❞❢❡➯✐➪❥❉♥✽✇✲➫✲♣❈❣➟❧
✇✼➽❸❥❉♥✽❞➻s✕♠✶❞r➫❉♠♦✐✼q❢❡♦➓➋➭➲✉✲➽➍✇❦♥✿❧✿♣❈✉❈✐➁❧✽♠tqr➏❦➎❉✐✼q➻❧✿❝❈✇❦♣❉➨●❝➪❧✽❝❉♠✶♥✿❞r✉❉❍➨ ➔➏❪ ❡➵↔✳➬✪❫➀✇✼➽❸❥✴✇●q➻➏❿✉❉✇●s✗❞❢✐✼q❢❡❀❞r✉➪❧❅➮✰✇
❞r✉❈➫✲♠➟❧✽♠t♥✽s✕❞➻✉❈✐✼❧✿♠❺❡✪❞r❡➬✐◗♣❈✉❉❞ ❏ ♣❉♠❩➽➆✐❦❣➹❧✽✇❦♥✽✱❞ ❛❺✐➁❧✽❞➻✇●✉ ➫✲✇●s✕✐❦❞➻✉✷➎➀❧✿❝❈♠❩❞r➫❉♠♦✐✼qï❡❊❧✿♥✽♣❈❣➟❧✿♣❉♥✽♠➃❞r❡❫✉❉✇✼❧➬❡✿✇
❡✿❞➻s✕❥❉qr♠❦➓❩❒❈✇❦♥✪✐✼✉▲♠➟ó❉✐❦s✗❥❈q➻♠✗❧✿❝✴✐➁❧✪❞➻qrqr♣❈❡❅❧✽♥✽✐✼❧✿♠❺❡➯❧✿❝❉❞❢❡✪❥❈✐❦♥❊❧✽❞r❣t♣❉qr✐❦♥✪➫✲➱❞ ➮❩❣t♣❉q➵❧❅➏●➎❇❣t✇❦✉❈❡✿❞r➫❉♠t♥✶❧✿❝❈♠
❞❢➫✲♠♦✐❦➵q ✃✟❡✝❢⑩↔✳➬➭❐➋➨❦♠♦✉❉♠t♥❤✐➁❧✽♠♦➫➯②❿➏➲❧✽❝❉♠✫♠♦q➻♠♦s✕♠t✉✈❧✽✵❡ ❡➦❢✫✐❦✉❈✣➫ ➬❐➓✷→➡➞✉ ➔➏❪ ❡✘↔✳➬✪❫❇❒ ✐ ➬➭❥➢❮✷➔➏❪ ❡✏❫ ➎❺❧✽❝❉♠ï✇❦✉❈q➻➏
❥❉♥✽❞➻s✕♠➃❞❢➫✲♠♦✐❦q❵❧✿❝✴✐➁❧➬❣➟✇●✉✈❧✽✐✼❞r✉❈❯❡ ✃✟❡✝❢➡↔✳➬➭❐➵❒ ✐ ➬➭❥✶❞r❡ ✐ ❡✘↔✜➬➭❥✏❒ ✐ ➬➭❥➟➓❩→➥❧❫➽➍✇❦qrqr✇➁➮★❡➯❧✿❝❈✐✼❧➬❞➻❤✉ ➔➏❪ ❡✘↔✜➬⑩❫

ẽéềẹsẽsể

ễế

qrsrqrr r ệ
tqtr rrsqú
rsqt
rtq r rrqr

qrsrqq qrtr
qr tqttrsq
ì rs ùrq
stststt ù r
tqrtstsqrttrr trqt
sqrqtt
ĩ ỉù õ ứ ứ ĩíị ò
ịịịĩ
ịĩ ỏõó
ẽỏọ
õ t
ỏõ ọểồ ổ ỏ ọểồ ổ ỗ ọọ ồ ổ ỏ ọ õ ổ ọọồổ ổ ỏ ọ ổ õ õ ọểồ ổ
sr rúr ỏõọểồ ổ tt t
ttỏọ õ ốóẽ ốỏ ố ỏ
sqtrrqrtqsq ờộ

ựở õ ứ ởỡớẽĩợírqtqịù
ủũ
ú ụẽóừ ịửó ồữ
ồứự õ ứ ỡợĩ
ỳ ỷíịú ỹĩ

ỳý
ỷ íịỵịòịĩ
ịĩ ỏó ỏú rqtú ũỏ óú
sử ỏ ọ s ỏóẽú rỏú
tt
ỏóú tẽỏ sửỏ qsrq
rsqrỏ tqrrsrq
tqỏ ó ú tỏ ọ qrq ó ồ

qsstúrqsúsqt
ỏ
ọ
ó qq rqỉ
rtqrtt
úểửũỏ óỏóqrqr
rsrq rsqrỏ rrr
qrqsqr ờộ

qú rqrtqrqrò ể srqrr
tsrttúttss
rrtstq
trqq
sqr
ựở õ ứ ợểịĩ
í
t ụẽó ừ óịửóẽ ồểữ
tqịĩ
rq t srẽ
rqrq t q qqqr t r
rqrqsrqt
rtqqsrùtúùtt
stùqr rttrrqtqrtst

ttqrsqrtsrttqr
qrsrqrrtt tr
ự ở õ ứ õ ịĩ
ỳ ỷẽssẽ
ịịỏõóệ
ịẽểỏõó òỗỏó õ óịửóồĩ
ỳý ỷẽũrrq ị òỗ
ị

ịỵềĩ

t rrqqsrqt rrqrqs
qr ểỏõó ỏõót ừỏõtừỏừõ
ỏó tỏsqrr ừõ ttõór
sq
ỗrq rrsq
ùqr rsrqỉtqq
rt
rsrq ùrúsqrrsrq
rsq
ĩ ỉù õ ứ
ữ ũớĩí
ị òĩ
ịĩ qrrrqqù
srqrqqr qr
tqrsst rq

ẽéềẹsẽsể

ễế

rrsrq túrỏõóỏõểỏ
qqửớóồqr õ õ s r
rstsrrtr õọ õọồ
trrq ỏẽ õ ọ óỏõ ọ tố ỏ
ố õọ s ố ố ó t ố õọõ ố ỏõ ố ỏõ
rsqrũ ố óỗ õọ õọể ồ ố õọ
ỏõọ rrqrq ờ
ộ
õ

ĩỉù õ ứ ĩ ịsị
t
ịòịĩ
ịĩ tỏõó ỏõóõ ósử
õ ó t õ rqrsqr t t tqrt
t rrqể qqr
õ rtrqrsqr
tỏõó rsqrỏó ờộ
ĩỉù õ ứ sĩ ịsòị
t òịĩ
ịĩ ỏõó t ỏó t tỏ õ ỏõ ó
srtử ỏ ó rỏ ó t õ ọ ó ùs
rttrsq qqrõsó t t
rsrq ờộ
ựự õ ứ ớĩ ịụ ữ ềị
òị t ềị

ớử ò

ị ĩ
ịĩớ t t
ử tỏũó t tùtú
ỏọó ỏó s úụ ữ ỏó
t
ỏõó ỏ ó tẽỏó s
ũõó sõó s t
rrsrq ờộ

ựở õ ứ ứ
ỡ
òịẽĩ
ẽ t trrsqịĩị t ể
tqrrsrq rrsĩ

ựự õ ứ ứứòòịĩ
ò
ịòỗũ òĩ
íò ịòẽị ị ịũ
ỗ ị ỏóẽ
ụốóẽ ừốỏũ

ó ữ ểò
ị
ĩ

ịĩ sqtqr
ỗrrsq sử
ttqstểỏóẽ ỏụốóẽừốỏ ữ
sùsr ùt túr
tttqrtst ỏó ẽ ỏó ù
ỏ ũ
ỏ ỏtể ốỏ ốó
ốỏềó rsqr
ỏó s ũ ỏó t s
qrqr
ỏ t
qrq ỏrsq óỗ
ớó ỏ
ó ỏ ỏ ỏó t
ỏó
q
ỏ ó ó ỏ
ỏ
ó qrq s ó ỏ
tq ỏr tttqrtstể ỗ ỏr
srsq rt ỏ s
ỏó
s
stts ỏó
ử ỏó ốũó ọ ttúr

ẽ ốỏóọ r ốỏó ốót
ọ t
rrss s
t t ốósqr ốỏ ó s ốó
t ỏó ù ỉrtrs tsqrr
ờộ

ồứ ự õ ứ ứở ỳ ốứựự ỉồứựỷ
ũ ịĩ
í òụ ữ ẽ
ểịểò s
òĩ
ũò
ị ịò
ửỗ ịò
ĩ

ẽéềẹsẽsể

ễế

ịĩ trqttrr
tqrrqttsúrsqq rt
rqtrrqrùtútr
qtqrsrrrrrqr
qrrrrq t
rtqsrrqqr

s q rq rtq
rss rọ rr ttt
s strsrq tt
tqt rrss
sq
trqrtsssqr s
qrtqrtsr q ọ r
sqt t rs
q ờ
ộ

íỳíờíờrờíồóố õ ứ
stt
t
tt
t
t
t
t
t
t
t t
t
t

t
tt
t

t t

qttt qr
sqù rtùr rrqrtrsqrù r
ssrttqrsrq r
rtrúùúsqrtqqtr
t
í ự ỉ õ ở ứ

ssr r
qrq ị
ò qq tt ỏ ỏỏ ỏ
tsrsqqtrrtr
ỏ ỏỏ õ õõ
t ồ ỏ õ qr
r rtqrtsts ỏ
qrsqr t
qq qrtqrst s

ồứự õ ở ứ ỳ ứỷ ĩí
ịỗ ịòị ủỗĩ
ịĩ rttq qt
tq trù qrqq
tqrtrsụ ữ rr

rqùt srrtt

r q ttsq
qr qssqrsúrsqtqrtsrt
sq srttrsrqrqt
ttúr ỏõóớ ỏõó õớ ụốẽóớ ừốõó ữ
qrtqt tstqrt
s ỏ ỏ ỏ ọ t ụốóừốõsó ữ õõ õ
t ềõ t s õ õ óẽ ớó
r tqrts õ ốõốõ ốõ
ốõó
ốỏ ỏ ốõtúr
ỏõỏ ọ õõọ ọ õt sr
strờ
ộ
õ ở ở ị
ịịòĩ

ễể

ễế

ịĩủsss ẽ ỏ ỏ
qrq ẽ ỏ ó rsrq q
trqttỏ ỏ ọ tt
úqs ẽ ỏ ótổ ts rỏ
é ó
ỏ ẽ ỏ tqrổ
ẽ ỏ ểó

ọ ố ỏ ẽ ỏ
ỉrt
ỏ ỏ ọ
ẹỉ
ó

t ỉ ttqt
ẽ ỏ ó
ỏ ọ ố ỏ sẽọ ố ố ọ ó
ọ ố ểề s ềẽó r ềó ó
rsqrq ềórrqrúst
rrtqrr ọ ễ ố ệế ề s ề óề
qrq ũ ọ ì ì ẽ ố ờ
ộ
ồ ứ ự õ ở ỡ ỡớĩ í

ị òĩí óẽồú ọ ĩ
ểịĩ
ú q rrr qrq
ỏ õọ ốỏõ ồọ ốó
rrs ỏỏ tể ú
ỏ ọ tẽ
ú ọ ỵ
ộ
õ ở ị ẽòịẽ
ò ũ t ọĩ

ựự õ ở õ ịể
ẽ
ĩ íĩ

ịĩ rqr tsr r
ttrr ọ rs
qr ỉrsrútstú
õ
ó ỏ
ó ỏõ
ó ỏ
ó s
ử t rrs q r t qqrs
qrqé sửr
s ờộ
útss ssé s
qrtss rtrú tq
qrt q rqtqt
rsúsqtqrtstrỗ
tt rsqr
sqrrrqr rùrrq
sqr sqrqrq

ồứ ự õ ở ữ ỳ ỷũ ĩí
ịòịĩỹĩíể
ẽ ũ

ĩ ịĩ
ịĩ ẽ trq
tqrqrs s qss t
trqssqr ờộ

tqqùtr
rrtrttqqrtqrqst
tsqrsúsq qrrsq
q
s í rqú qrqtr
rtqrqts rtr ỏ
trqq rrsqssqtể ỏt
rrsqrt í
r
ííí rsrqq
rrsttqrọ rqqtts
rrsqqqrtqrqr qrq ttqr rqrqt
ts qrqrs tùqsrq
t

ồứự õ ở ỳ ộ ịỉỉứựỷ

òòị ĩịỡể
ò ịòí í
ẽ ĩ

tòò qrqrsờộ
ùrst ttqrtqqts
tr rtrtrrsrq

sss qrrs
qrtr rtrsq
q ửqt q
ử
qr t srqsq
t rtùrũ tt
tqr trqqtsts qrqrst
qsqr t ùqrtqrqrtq
tsúrsqrq t ửtqrtstể ỏ
ịĩ

ễể

ễếỏ

ỏ r ỏùqrqrrrsrqq
s ử ttqửrt
í íí í ũ

qqstrử
trsts rqt

ựự õ ở ỗủ ọ
ịòỗ ĩ ị

ọ
ỗ ủũịỗ ũĩ

ồứ ự õ ở ớ ỳ ừ ý õrốtịỷ ỗ
ủịsòỗ ĩí
t ịũó ỏ ỏ ỏ
ị ỏỏ ỏũ ề ỏỏ ỏ
ị ề
ó ĩ
ểịợ
ĩ qrqrqqrt
r qrtss
rò ộ
íỳíờíờrờíồóố õ ở
stt
ót
tọtồ
ọọổt
tỗ
ốộ ờở ỗtốốt
tỗỡtó
ỗớợùủũùúụừửủữứừựỳ
ỗỷ
ỹ ỗý
tỗ
ỗt

t
ỵ
ù
qrtqrtstt rrtqqstt
q sểỏ stỏó ỏ
tqtqrtst qqr
sqtr ỏỵ r
ủtrs
ựở õ ỡ ứ ủtrs ịể
òòị
òịểủịò

ị ĩ
rqq r ts ủtr ss
trtqùqùsttqrqrủtsr s
t trsùqủtsssú
rsq ùr srtqủtr
srtúsq rs t
trsrq
rqqùsủrsr
ì r rq rr qqrr

ự ở õ ỡ ởờsủĩ
qrqị ũỹềịũ
ó ĩ

ịịịủ

ổ ụóẽừ ữ
trq ị ổ ĩ

tqr qrqr tr
rtqs rttqớt rq
rqqt t
ụ ừ ó ó ữ
íự ỉ õ ỡ ứ

ẹsẹsẹẹ

ễ

tqrqstt qqsqrqrù
rrqq qrqrq
r
tqrqr rqsr qr
qt
ttqt sqr
tst
t

rổ rqq rt
rqrtqrts ót qrt
q
ựự õ ỡ ỡ ủ
ị ũịĩũí

ịẽĩ
ỳ ỷí ủĩ
ỳý ỷẽ
ị òịòòẽò
ĩ
ịĩ tổ rtrqrrqq t ổ t
úqs ó ó ử
tqrtsó r ớó
tù
ù s

ùrsrq
ọ r ổ ổ ọ rr
sq rqrt rs
qqr rrs t
tstr ọ ổ ổ sổ ể ổ
q rổ sqrrt

trrsqrtsqr
ổ tổt q
qrqr ọ tử
ọ s rqr
rrs
sqtờộ

ồứự õ ỡ íịịĩ
ỳ ỷỹịĩ

ỳý ỷòò
ị ỗòề
òịủịòị
ỳ
ỷ
ĩ
ỳ ỷểỹòị ĩ

ểịĩ rt ttq
q s
sqtttttsrqrq
t trsq qt tqstù
ể sqr
sq
rqrr rtrqr rrs
s s t ùsúrsq ts
rrqr
sqrrqqỉ trqrsrq
súrsq s ỗrqrrsq qts ỏó
rể ỏt rtrqr
ỏớr ỏớqùrtrqrqstù ũ
t ũtq
qrs ỏt s

ủ srqrqs tt trq
ũể
s q íttr
ớ rsq rtq ttr
srq ũ t
ũ ỏ ệ
ỏệ tr
qrsq ọ
rtqrq ũùtrqr
qrtssrs ỉ r ũs
s t ttrsq
ùs ọ
ỏỏỏtqrtst óỉ
ỏềs
ỏ ó ót ỏẽ ó ó
t ỏó r ỏrqrs
tsqr
qrqrsrqrtss
qqr r
ộ
rrqt rủtrsrt
rqùrsqqrrtqùqùsrt
tqr tsqrt ttq t
ủrsrr trqr rq
tttqttsqs
útt
ĩ ỉù õ ỡ õ ẽĩ ịị
ịỗ ịểòĩ
ịĩ ổ s rtrqrq rqt
ú

ó
ó ử

ẽó ớót

ẹsẹsẹẹ

ễ
ssrs ề
ề s ề qrqrs

rsssqr
tqs sss
s tsq qrrssrsề
t r tsùrtú

qr q st ú ùtst
qr t tt ũótqrtst ề qrq
s tst
ề ề ề ề
tt ề ú ó
ó r
ề ề
rùrqr r
ề

ề

ổ ề
r ổ rttq ổ ề ó ổ q
ó rề ó ề ểó
ề ề ũ
ổ ề

tqqrrrtq qrqrsttt
st ề
ổ ề
r ổ ề ũó ổ óq ử r
rtrqrờ
ộ
ồ ứ ự õ ỡ ữ íịũịẽ

ỳ ứ ỷ
ỳ ở ỷỹị
ỳ ỡ ỷịị

ỳ ỷỹịểòĩ
ịĩ rqqrs ts
rr é
qq
ó
rrsrq rssrs qrq
ó

t qrqs ù é
trq
rrsqrrrqr
stú ttq t
tsqr ttt ttrq
rrqrtt ttrqù q tt r
ttrt tqú
ùrsrqtssùsúrsqqs
ùrq ttqstsúsq t
úsúrsqq ổ st
trq q r ùs
ttú ó ổ óù ổ ửổ ổ
qrqrổs t
t ổ r q
sqrr
ttúrsqt
qr ổ rsrqtr
sqtờ
ộ
rủrổ s tq ỉ
ổ
sqq sqqr
stqrqrrqqtrúr rq
rủtsr
ĩ ỉù õ ỡ ẽủĩ
ợỹểòịợĩ
íịòòỹ ị óẽ

ĩ
ểịĩ ttt ổt qrrrqq
ỏ t ỏ ổ ó
ỏ rrrq qr
ỏ
t tqrtsqrsúrsqq
srsqrts t
qtsrt sqr

tr rqr súrsq rq rsùtt
rqrtqtrrrst
rs tútsq

ỏqs
r r ỗrssrt t
sq súrsq qrq
ỏ

srsrqs ổ
r ỏtqrts õó ỏ ỏ õó

ếểs

ễ

tõóẽ ỏ

ỏ ổ õ ỏ ổ õ ềỏ ổ
ỏ ổ ỏ ệỵ
rsqr ộ

íỳíờíờrờíồóố õ ỡ
stọọó
ọt
tọt
ọ t
tọtọ

ọ t
tọtọ

ỹ
ọ

ọ
ọt

qrqútqr r tqrtstr
t qrsqt rt ùqtt t
rsqtttrú rtsrqrr

tq
ự ở õ ứợịĩ

ỳ ỷ ó rtqt ịũ
òỗ ó ũ ĩ
ỳý ỷ í ẽrtqút
ịợ ịị
ệĩ

ĩùỉ õ ởỡ ềịĩ í
ịẽị ó
ỳ ứỷ
ỳ ởỷũ ũ ủỗ

ỳ ỡỷ

ệ

ủỗũ

ỳ ỷ ịị ị ủỗẽ

ĩ

ểịĩ t ềỏổ ổ ềỏổ ềỏ s

qrsrqùr t ổ ỏ ổ ềỏ ỏ
rrs tổ ọ qrq
tt sqrụ ữ
rsqqt

rsq
r r sqr

sũ
rq r sqr

órt ó ù ử
ỏ ỏ óẽ
t
rtỏ sú ỏ

qr ỗ qrstrỗ tr súỗ s
r
ũ
ửử tsú
t ểs qrqrsú ũ
rùs ú ớử ùrt
q sqr qrq
úr
t rtqù tús õổ ổ õ õ
s qt tsqsqr
ờộ

õ ỡù ịẽĩ ị
ủỗũệ ịĩ

tstúsqrtqút
ù rtttqúrùù t
úsqủrtqrtsqrt
t
rqtsqr

t rqr ù
qrsrqr rtqtútr
qúsqrqsrq rtq
útùũ t ẽ ttqrổt
rtt sq ụ ữ
õ ịĩí
ụ

ó ừ ữ

ịĩ
ịĩ ó ớ ỗề srqrsq
r ùtửtqrrù

ếểs

ễ

ttsq ụ ữ ử
ùr tqr qrqq

ùsqr rờộ
ự ở õõ
ỳ ỷí
qrị ĩ

ợịĩ
ị ềrtq

ỳý ỷ ị

rtqqrqrĩ
ị
ỗủsòỗ
rtqqrqrĩ

íự ỉ õ ứ
qrqrtqrqsrrqrqqr
rtqr ỉrrqrqs rtqr
tqs úr
s ỏõ
t ỏõ tqst ổ ỏõ ỏõ
sổ qsq ổ ổ t
ỏ ổỏ õ ỏõ
õ rsqr
õ
r ỏ rrrsqrqs õrrt
ỏõó
túsqrùtqúr
ềtúsqrtrqrtqtútr
tr

túr rqút

ĩùỉ õ ữ ị
ịĩíủũ ịẽỗũ ị
ủĩ

ịĩ s
rtq t tttqrtst
qt ỏổ ổ ỏỏ sqrsrqr
srrsổ qtqrsrqrr
ỏ ỏ ỏ tq
ỏổ
rsqsq qrttổ ổ ùsù
ỏ
t
ỏổ ỏỏ
trqr qr ỏ q t rs
tqqrqr tq

tqs tqũỏ t tqrtst
ỏ ổ úr rổ rtqtúổr srqổ s rq
ỏ ổ
ỏ ỏ ỏ ù ỏ

ỏ ổ ỏ ổ ổ ổ ỏ ỏ ổ ỏ t sqổr qrỏ rổ
ỏ ổ ỏểớ ỏ ỏ
ỏ ỏ
ùểỏ ỏ ổ ẽỏ ỏ
rtqr rtqộ
õ sị
ịĩ ị òểị
ịệ ịỗ ị ịĩ
ểịĩ rsùrq
qrts
rqr

q
rsss
ttq trrsss
r sr rt
rtqút
ỗ
rsqrrt
rtsq
tqrts sqrsq
tr ùr rqrùqr
rqrỉrsúrsqqrrsúsq ờộ
ĩùỉ õ ị
ịĩ ị òỗểị

ịĩ
t ttqrtst ó ót
ịĩ t
ùrtqúr túùqrsr q ỏ ổ ổ