UCRL-PROC-201748
L AW R E N C E
LIVERMORE
N AT I O N A L
LABORATORY
Probing Chiral Interactions
in Light Nuclei
P. Navratil
Janaury 15, 2004
17th International IUPAP Conference on Few-Body Problems
in Physics
Durham, NC
June 5-10, 2003
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✁ ✂✆☎✞✝✠✟☛✡✌☞✎✍✑✏✒✟✓✂✕✔✞✖✗✟☛✡✙✘✆✚✛✂✕✔✞✍✜✘✕✟☛☎✢✡✒✣✤✟☛✡✥✖✦✟✦☞✙✏✙✘✧✡✩★✒✍✪✖✦✚✛✟
✄
✫✄✬✮✭✰✯✑✱✑✱✜✲✕✳✵✴✷✶✹✸✹✬✷✸✒✺✼✻✾✽❀✿✮✲❂❁❄❃❆❅✑✴✷❇❈✬✮✭❉✲✵❊✪❋✮✕●✲ ❍❏■❑✽▼▲◆✴P❖◗✬✼❘❙✽❯✯✑❚ ❱❳❲❨✽❑✻❩❅❂✴✷❬❭✬✷❪❭✲✕❃✧✲❂❫❄✲✕❴❂✴❄❵❛✽❀❜❞❝❡❘❆✬❄❢❣✻✾■❀❤✑✐❄✻❥❋❧❦❩✴
❬♠✬P❖♥■▼❍❳✲✕♦✽❑✲✆♣❡✴✷q❉✬sr❙✬✮qt✲❂❋❧❋❏✻❥❍❧❍ ✳ ✴✷✉P✬s❇✩✬❄✈✇✲✕❋❧①❨②
✳❳❵❛✐P■❀❊✑✻❥❋❏③❧■❀❍④①⑤✯❂❜✩✫❉❋❧■❑⑥❥✯✑✐✮✲P✴❄⑦❈❁❄❱❥③❏✯✑✐✢✴✷✫⑨⑧⑩✴✮❵⑨❶✛✫
❅❷r✹❁❄❸❄❋❡❝❡❵❛✐P■❀❊✑✻❥❋❏③❧■❀❍❹✲✆❚ ❍✰q❺✯✛❱❳❸❨❁❄❃❻✴✷q❺✯✪❱❳❸❨❁❄❃❣✴✮❘❙✻❥❋❏❃❼✲❂✐✜①
▲❾❽❿✲❷➀✹❋❧✻✾✐❄❱❥✻✄❽✙■▼❊✑✻✾❋❧❃❼✯❂❋❏✻❙✭❉✲✆❍➁■❑✯❂✐✮✲❂✽✢❽❿✲❂✿✼✯✑❋❏✲✕❍➁✯✑❋❾①✑✴✮❽✙■▼❊✑✻✾❋❧❃❼✯❂❋❏✻❂✴✮➂t✲❂✽❑■▼❜➃✯✑❋❏✐❄■❑✲P✴✛❵⑨❶✛✫
❴ ❪⑨①✪❁❄③❏❸❨❁❣➄④✐❄③❧❍❏■❀❍➁❁✛❍➁✻❙✯❂❜✩⑦✩✻❥❱❳❸❄✐❄✯✑✽❀✯✑✱❂①✑✴✷❪➅■▼❍❳✲❂❲✜①✪❁❄③❏❸❨❁✢✴➆✉✑✲❂✺❄✲❂✐
❦❾❵❛✐❄■▼❊✑✻❥❋❏③❏■▼❍❹✲✕❚ ❍✰q➇✯✑✐❄✐✢✴✷❬✰✻✾✽❑❃✤❸❄✯✑✽▼❍➁⑥⑨➄④✐P③❧❍➁■▼❍➁❁P❍✗❜❳❁❄❚ ❋✰❶❨❍➁❋➁✲✕❸❄✽❑✻❥✐✛❝✇❁❄✐❄❫❣❪➅✻✾❋❏✐P✺❄❸✜①✛③❧■❑❲➆➈✓⑦✗❸P✻✾✯✑❋❧■❑✻❷➉◆✴✼q❺✯✑✐❄✐✢✴
❘❙✻❥❋❏❃❼✲❂✐✜①
♣ ✉✑✲❂✱✑■❀✻✾✽❑✽❀✯✑✐❄■❑✲❂✐➊❵✰✐❄■❀❊❂✻✾❋❏③❧■❀❍④①❂✴✞➂❺❋❏✲❂❱✾✯❷➀❙✴✷❇❈✯✑✽❞✲❂✐P❫
② ➄④✯❷➀t✲❼❶✪❍❳✲✆❍➁✻❭❵❛✐❄■▼❊✑✻❥❋❏③❏■▼❍④①✑✴✮✫❛❃❼✻❥③✾✴✮➄④✯❷➀t✲✛✴✷❵⑨❶✛✫
❺➂ ❸P■❑❋➁✲✕✽✰❍④➀➇✯✕❝✤✲❂✐P❫➋❍➁❸❄❋❧✻✾✻❩❝❯✐❨❁❄❱✾✽❀✻✾✯✑✐♥■❑✐✜❍❏✻✾❋➁✲✕❱❥❍➁■❀✯✑✐❄③✧✲❂❋❏✻➌③❾❍➁❁❄❫P■❑✻✾❫➍■❀✐➎❜➃✻❥➀t❝❯✐❨❁❄❱✾✽❀✻✾✯✑✐♥③❧①✪③❾❍➁✻✾❃✤③✾✬◗❖➏✻
■❑✐✜❊✑✻❥③❧❍❏■❑✱✜✲✕❍❏✻➅❍➁❸❄✻❭❱✾❁P❍❾❝④✯❂➐➑❫P✻✾✺✼✻✾✐❄❫❄✻❥✐❄❱✾✻✄✲❂✐❄❫❣❱✾✯✑✐✜❊✑✻❥❋❏✱✑✻❥✐❄❱✾✻♠➀✹■❀❍➁❸❻❋❏✻❥③❏✺✼✻✾❱❩❍❉❍➁✯❆❍➁❸P✻❭❱❳❸P■❑❋➁✲✕✽✙✻❩➒✛✺✮✲❂✐❄③❧■❑✯✑✐✞✬
➄❯❍❙■❑③⑨✺✼✯✑■❀✐❨❍❏✻✾❫➑✯✑❁P❍➅❍❏❸✮✲✕❍➅❍❏❸❄✻➓③❏✺✼✻✾❱❩❍➁❋➁✲➔✯❂❜➇✽❑■❀✱✑❸✜❍⑨✐❨❁❄❱✾✽❀✻✾■✠✲❂❋❧✻➓③❏✻❥✐❄③❏■▼❍➁■❀❊❂✻➓❍➁✯⑤❍➁❸❄✻→❍❏❸❄❋❏✻❥✻❩❝❯✐✪❁P❱✾✽❑✻❥✯✑✐➑❜➃✯✑❋❏❱❥✻
③❧❍❏❋❏❁❄❱❩❍➁❁❄❋❧✻❂✬➊✫❛③✄✲❂✐➣✻❩➒P✲❂❃✤✺❄✽❀✻❂✴✙➀❺✻❼✺❄❋❏✻❥③❏✻❥✐❨❍✄❱✵✲❂✽❀❱✾❁❄✽❑✲✕❍➁■❀✯✑✐❄③⑨✯✕❜❺❍➁❸P✻ ❷↔ ✲❂✐❄❫➏↕ ↔ ③❧❍➁✲✕❍➁✻❥③✄✯❂❜❺➙❳❽✙■✒❁❄③❏■❀✐❄✱
❍➁❸❄✻♠✐❄✯✕❝❯❱✾✯✑❋❧✻♠③❧❸❄✻✾✽❀✽✩❃✤✯✛❫P✻✾✽✩✲❂✺❄✺❄❋❧✯✜✲❂❱❳❸✢✬✰⑦✗❸❄✻→❋❧✻✾③❏❁P✽❀❍➁③❛③❏❸❄✯❷➀➛❱✾✯❂✐❨❍❏❋❏■❀✿❄❁P❍➁■❀✯✑✐❄③❛✯❂❜✌❍➁❸P✻✄✐❄✻◆➒✛❍❾❝❯❍❏✯✕❝④✐❄✻◆➒✪❍❧❝❯❍❏✯
✽❑✻✾✲❂❫❄■❑✐P✱✄✯✑❋❧❫❄✻✾❋❺❍❏✻✾❋❧❃❼③t❍❏✯✄❍➁❸❄✻➅③❧✺➆✻❥❱❥❍❏❋➁✲P✴P➀✹❸P■❑❱❳❸❻✲❂❋❏✻❉✐❄✯❂❍✗❱❥✯✑❋❏❋❧✻✾✽❞✲✆❍➁✻✾❫➊❍❏✯→❍➁❸❄✻❛❍➁❸❄❋❧✻✾✻❩❝❯✐❨❁❄❱✾✽❀✻✾✯✑✐➔✿❄■❀✐❄❫❄■❑✐P✱
✻✾✐❄✻❥❋❏✱❂①➊✺❄❋❏✻❥❫❄■❑❱❩❍➁■❑✯❂✐✢✬
➜✮➝❼➞❥➟➡➠❭➢⑤➤❆➥❻➦➡➧✄➠♠➞❷➤✤➟
⑦✗❸P✻t✲❂✺❄✺P✽❑■❑❱✾✲✕❍➁■❀✯✑✐❙✯❂❜❄❱❳❸P■❑❋➁✲✕✽✪✺✼✻✾❋❾❍➁❁❄❋❧✿✮✲✕❍❏■❑✯✑✐❭❍➁❸❄✻❥✯✑❋❧①❙❍➁✯✰✐❨❁❄❱✾✽❀✻✵✲❂❋✩③❧①✪③❧❍❏✻✾❃✤③⑩✺❄❋❧✯✑❃✤■❑③❏✻❥③⑩✲✰❃→❁❄❱❳❸→✿✼✻❥❍❧❍➁✻❥❋
❁❄✐❄❫❄✻❥❋❏③❾❍❳✲❂✐❄❫P■❑✐❄✱➌✯✕❜❛✐❨❁❄❱❥✽❑✻✾✲❂❋♠❜➃✯✑❋❧❱✾✻❥③✾✬➨➄❯❍➁③→✲❂✺❄✺❄✽❀■❑❱✵✲✆❍➁■❑✯❂✐➏❸✮✲✕③→❋❏✻❥❱✾✻✾✐✜❍❏✽❀①➩✿✼✻✾✻❥✐➫✻❩➒✪❍➁✻❥✐❄❫❄✻❥❫✎❍❏✯➑↕✑✭➭✲✕✐❄❫
➯ ✭➲③❧①✪③❾❍➁✻✾❃✤③❼➳ ◆➵ ↕✕➸✦✬→⑦✗❸❄■❑③➅❫P✻❥❊✑✻❥✽❑✯✑✺P❃❼✻❥✐❨❍❭■❀③➅❱✾✯✑❃✤✺❄✽❑■❀❱✵✲✕❍❏✻✾❫➌✿✜①➌❍❏❸❄✻➓❜✓✲❂❱❥❍✾✴✢❍➁❸✮✲✆❍➅❍➁❸❄✻❆③❏❁P✿❄✽❑✻✾✲❂❫❄■❑✐P✱❻➺✆➻
✻❩➒✛❱❳❸✮✲❂✐P✱✑✻❛❍❏✯✛✯❭③❧❍❏❋❏✯✑✐❄✱❂✽❀①➓❱❥✯✑✐✜❍➁❋❏■❀✿❄❁P❍❏✻✾③✠❍➁✯❙❍➁❸❄✻✰❍④➀❺✯✕❝❯✐❨❁❄❱✾✽❀✻✾✯✑✐➌➈☛➺❂✭❉➉✌❜➃✯❂❋❏❱✾✻❛✲✕❍✇③❏❸P✯✑❋❧❍➇❫❄■❑③❾❍❳✲❂✐P❱✾✻✾③❥✴✪➀✹❸P■❑❱❳❸
✽❑✻✾✲❂❫❄③❿❍➁✯❉③❧✺❄❁❄❋❧■❑✯✑❁❄③✩✿➆✯❂❁❄✐❄❫→③❾❍❳✲✕❍❏✻✾③✾✬✩⑦✗❸❄■❑③✩■❑③✩✲❉❃❼✲❹➼❧✯✑❋❿✯✑✿❄③❾❍❳✲❂❱❥✽❑✻➇❜➃✯❂❋❈❜➃✻❩➀t❝④✐❨❁❄❱✾✽❀✻✾✯✑✐⑤➈✦➽✌✭❉➉❿❱✾✲❂✽❑❱❥❁❄✽❞✲✕❍❏■❑✯✑✐P③✾✬
✫➾✐❄✻❥➀➾✲❂✺❄✺❄❋❧✯✜✲❂❱❳❸➔❜➃✯✑❋t❍➁❸❄✻❙❋❧✻✾✱✑❁❄✽❑✲❂❋❏■❀⑥✵✲✕❍❏■❑✯✑✐❼➀✹■❑✽❑✽➆③❏✯✑✽▼❊✑✻➅❍➁❸P■❑③✗✺❄❋❧✯✑✿❄✽❑✻❥❃➚➳ ➯ ➸✦✬
❇✩✲❂❋➁✲✕✽❑✽❑✻❥✽✪❍❏✯❉❍➁❸P■❑③✌❫❄✻❩❊✑✻❥✽❑✯✑✺❄❃✤✻✾✐✜❍✾✴✑➀❺✻t➀➇✯✑❁❄✽❀❫➓✽❑■❑❲✕✻➇❍❏✯➅③❧❍➁❁P❫P①✄❍❏❸❄✻t❱✾✯❂✐❨❊❂✻✾❋❧✱✑✻✾✐❄❱❥✻❛✺P❋❏✯✑✺✼✻✾❋❾❍➁■❑✻❥③✌✯❂❜✷❱❳❸❄■❀❋➁✲❂✽
■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❀✯✑✐❄③❙■❑✐➏➽✌✭➪③❧①✪③❧❍❏✻✾❃✤③✾✬➔✫❉③♠❃❼✯❂❍❏■❀❊✕✲✕❍❏✻✾❫➑■❑✐➏r✰✻❩❜❡✬➇➳s➺✆➸✦✴✩➀➇✻✧❱❥❁❄❋❏✻✤❍➁❸❄✻✤③❧❍❏❋❏✯✑✐P✱➌✲✕❍❧❍➁❋➁✲✕❱❥❍➁■❀✯✑✐➣✿❨①
❋❏✻❥❫❄❁❄❱✾■❀✐❄✱❉❍❏❸❄✻t③❧❍❏❋❏✻❥✐❄✱❂❍➁❸❆✯❂❜✮❍❏❸❄✻t③❧❁❄✿❄✽❑✻✾✲❂❫❄■❀✐❄✱❙➺✆➻➔✻◆➒P❱❳❸❄✲❂✐❄✱✑✻✕✬✒⑦✗❸❄■❑③✩✽❑✻✵✲✕❫❄③⑩❍➁✯⑨✲⑨✱✑✯✛✯✪❫→✲✕✱✑❋❏✻❥✻✾❃✤✻✾✐✜❍✌➀✹■❀❍❏❸
❍➁❸❄✻✇➺✕✭➶❫✮✲✕❍➁✲✰✲✕✐❄❫❙❋❏✻✾❃✤✯❷❊✑✻❥③❿❍❏❸❄✻✒③❏✺P❁❄❋❏■❀✯✑❁❄③✙✿✼✯✑❁❄✐❄❫❙③❧❍➁✲✕❍➁✻❥③✾✬✩⑦✗❸❄✻✾❋❧✻❥❜➃✯✑❋❧✻❂✴❹❍➁❸❄✻✒❱❳❸❄■❀❋➁✲❂✽✕■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❀✯✑✐➅✿✮✲❂③❧✻✾❫
✯✑✐⑤❍➁❸❄■❀③✹✲❂✺❄✺❄❋❧✯✜✲❂❱❳❸❻■❑③✹✲❂✐➔■❀❫❄✻✵✲❂✽✞❃❼✯✪❫❄✻✾✽✼❍➁✯❆■❑✐✜❊❂✻✾③❧❍❏■❑✱✜✲✆❍➁✻➅❍➁❸❄✻❙❱❥✯✑✐✜❊✑✻✾❋❧✱✑✻✾✐P❱✾✻✄✯✕❜✩❍❏❸❄✻➅❱❳❸❄■❑❋❏✲❂✽✢✻◆➒P✺❄✲❂✐❄③❏■❀✯✑✐
➹❡➘❹➴☛➷❧➬✦➷❾➮✾➱❿✃❩❐❹❐❷➴☛➷❧➬☛➬❧❒✛❮❰➮✆➬✓➱✦Ïs➱✦Ð❹➱✦➷✒ÑÓÒ❥➴❿Ô❿Ð✆Õ❾Ös➷❏✃◆➴❿×✢Ø❹➷❧Ò❩➴☛Ù❩Ú❷Û❿➮❹ÏÝÜ❩➷❧➴☛➬✦Ïs➱➃Ù✹Ò◆Ñ❄Þ✄✃❥➬✓Ø✆Ïs➮❹ß❩➱✦Ò❥➮❨Ú✆à✵➷❧✃◆➱✓➱☛Ös➷❥Ú❹Þ❭á➨â❩ã✆ä❧â✾å➁æ❯ä❏å❩å❩ç
➺
■❀✐❣➽⑩✭✥③❧①✪③❧❍❏✻✾❃✤③✾✬✒❖➶✻❭✲❂✽❀③❏✯➓③❾❍➁❋❏✻❥③❏③✹❍➁❸✮✲✆❍✗➀❺✻❙❃❼✲❂■❑✐✜❍❳✲✕■❑✐❼❍❏❸❄✻❙❱✾✯✑✐P③❏■❑③❾❍➁✻❥✐❄❱❥①➔✯❂❜⑩➺❂✭➾✲✕✐❄❫⑤❍➁❸❄❋❧✻✾✻❩❝❯✐❨❁❄❱✾✽❀✻✾✯✑✐
➈✓↕✑✭⑨➉❺❜➃✯✑❋❧❱✾✻✾③❥✴✮✿➆✻❥❱✵✲❂❁P③❏✻❙❍➁❸❄✻❙③➁✲✕❃❼✻➅③❾❍➁❋❏✻❥✐❄✱❂❍❏❸➡❱✾✯❂✐❄③❧❍➁✲❂✐✜❍➁③✰✻✾✐✜❍➁✻❥❋✰■❀✐⑤❍➁❸❄✻❭↕✑✭✥❜➃✯✑❋❧❱✾✻✤➈✦↕❂✭❉➽✒➉◆✬
➄④✐➌❍➁❸❄■❀③❉➀❺✯❂❋❏❲✷✴✢➀❺✻➓❱❥✯✑✐❄③❧■❑❫❄✻❥❋❉❍④➀❺✯⑤➀❺✲✵①✛③➅❍❏✯➊✱✑✻❥❍⑨■❑✐❄③❧■❑✱✑❸✜❍⑨■❀✐✜❍➁✯➊❍➁❸P✻→③❏■❀⑥✾✻→✯❂❜✇❸❄■❀✱✑❸❄✻❥❋❉✯✑❋❧❫❄✻✾❋➅✻❩➐✞✻❥❱❥❍➁③❥✬
➽⑩■❀❋❏③❾❍➁✽❀①❂✴✰➀➇✻➣❱✾✯✑❃✤✺✮✲❂❋❧✻➌❍➁❸❄✻➨❋❧✻✾③❏❁P✽❀❍➁③➔✯❂❜♠✺❄❋❧✻✾❫❄■❀❱❥❍➁■❀✯✑✐❄③➔✲✕❍❻✭❛❽✁ ❍➁✯✎✺❄❋❧✻✾❫❄■❀❱❥❍❏■❑✯✑✐❄③➔✲✆❍❻✭❉✭❉✁❽ →✴✹✲❂✐❄❫✞✴
③❧✻✾❱✾✯❂✐❄❫❄✽❀①❂✴❺➀➇✻❻③❾❍➁❁❄❫✛①➫❍➁❸❄✻➔❫❄✻❥✺➆✻❥✐❄❫❄✻✾✐P❱✾✻➡✯❂✐ ❍❏❸❄✻➔❱✾❁P❍❾❝④✯❂➐➋❊✕✲❂✽❀❁❄✄
✻ ✂❉✴✠➀✹❸❄■❀❱❳❸ ❫❄✻❩❍➁✻❥❋❏❃✤■❑✐❄✻❥③❼✲✆❍➓➀✹❸❄■❑❱❳❸
❃✤✯✑❃✤✻✾✐✜❍➁❁❄❃ ③❧❱✵✲❂✽❀✻❼❍➁❸P✻⑤❽✙■❑✺❄✺❄❃❼✲❂✐❄✐✪❝❾❶✛❱❳❸✜➀✹■❑✐P✱✑✻✾❋❭✻✆☎❨❁✮✲✕❍❏■❑✯✑✐➶■❑③♠❍❏❋❏❁❄✐P❱✵✲✕❍❏✻✾❫➩❜➃✯✑❋❙❍➁❸❄✻✧❋❏✻✾✱❂❁❄✽❞✲❂❋❧■❑⑥✾✲✕❍➁■❀✯✑✐✢✬
⑦✗❸❄✻❣❫❄✻✾✺✼✻✾✐P❫❄✻✾✐❄❱❥✻➡✯❂❜⑨➽✌✭ ✯✑✿❄③❧✻✾❋❧❊✕✲❂✿P✽❑✻✾③❆✯✑✐✎❍➁❸P✻❣❱❥❁P❍❧❝❯✯❂➐♥③❏❸❄✯❂❁❄✽❑❫ ■❑✐✎❃❼✲❂✱✑✐❄■▼❍➁❁❄❫❄✻⑤✿✼✻➔❱✾✯✑❃✤✺✮✲❂❋❏✲❂✿❄✽❀✻
❍❏✯✧❸❄■❀✱✑❸❄✻✾❋✹✯✑❋❧❫❄✻✾❋✰❱✾✯❂✐❨❍❏❋❏■❀✿❄❁P❍➁■❀✯✑✐❄③❥✴✮✿➆✻❥❱✵✲❂❁❄③❧✻✄■▼❍✞✝✮✐✮✲❂✽❀✽❀①⑤❃→❁P③❧❍❛✿➆✻❭✲❂✿❄③❧✯✑❋❏✿✼✻✾❫➡■❑✐✜❍➁✯❆❸❄■❀✱✑❸❄✻✾❋✹✯✑❋❧❫❄✻✾❋✰❱✾✯❂✐✛❝
❍➁✲❂❱❥❍❙■❀✐❨❍❏✻✾❋❏✲❂❱❥❍❏■❑✯✑✐❄③❥✬✄➽✮✯✑❋❧❱✾✻→❃✤✯✪❫❄✻✾✽❀③❛❜➃✯✑❋⑨✿✼✯❂❍❏❸➣✯❂❋❏❫❄✻❥❋❏③❙✲❂✐❄❫➨❫P✻✾✺✼✻✾✐❄❫❄■❀✐❄✱➔✯✑✐➌❍➁❸P✻➓❱✾❁P❍❾❝④✯❂➐➶❸✮✲✵❊✑✻❆✿➆✻❥✻✾✐
❫❄✻❩❊✑✻❥✽❑✯✑✺✼✻✾❫❣■❑✐❻r✰✻❩❜➃③✾✬❈✠➳ ✟✛✴Ý➺✆➸☛✬
➅✐P✻➌■❑❃✤✺➆✯❂❋❧❍❳✲✕✐❨❍❼✲❂③❧✺➆✻❥❱❥❍⑤✯✕❜⑨❍➁❸❄■❀③✧③❾①✛③❾❍➁✻❥❃✧✲✕❍❏■❑❱➡✲❂✺❄✺❄❋❧✯✜✲❂❱❳❸➋❍➁✯➶✐✪❁P❱✾✽❑✻✾✲❂❋✧■❀✐✜❍➁✻✾❋❏✲❂❱❥❍❏■❑✯✑✐P③❼■❀③❼❍➁❸❄✲✕❍➊■▼❍
❋❧✻✾③❏❁P✽❀❍➁③✤■❑✐✎❱❥✯✑✐❄③❏■❀③❧❍❏✻✾✐✜❍⑤➺✕✭ ✲✕✐❄❫➎↕❂✭➭❜➃✯✑❋❏❱❥✻✾③✾✬ ✫t❍❼✭❉✁❽ ✐❄✯➣↕✑✭❛➽ ✲❂✺P✺➆✻✾✲❂❋❏③❥✴➇➀✹❸❄✻❥❋❏✻✵✲✕③✧✲✕❍❼✭❛✭❉✁❽ →✴
✲❂❫P❫❄■❀❍❏■❑✯✑✐✮✲✕✽❑✽❀①❣❍➁✯➡❍❏❸❄✻⑤➺❹➻➍✻❩➒✛❱❳❸✮✲❂✐P✱✑✻⑤↕✑✭❛➽❺✴❈❍④➀➇✯➌❃✤✯✑❋❏✻❼③❧❍❏❋❏❁❄❱❩❍➁❁❄❋❧✻✾③→③❧❸❄✯❷➀ ❁P✺✢✴✌➀✹❸❄■❑❱❳❸➶■❑✐✜❊✑✯✑✽▼❊✑✻✤❍④➀❺✯
❁❄✐P❲✪✐P✯❹➀✹✐➨✽❀✯❷➀t❝④✻✾✐P✻✾❋❏✱✕①➔❱✾✯✑✐❄③❾❍❳✲❂✐✜❍❏③➓➈✦❽❿✸✇☛➂ ✡ ③❳➉✄✌➳ ☞P✴s↕✕➸✦✬✹q❺✻✾❱✾✲❂❁❄③❏✻♠✯❂❜⑩❍❏❸❄✻✾③❧✻✄❜➃❋❏✻❥✻♠✺❄✲❂❋➁✲❂❃✤✻❥❍❏✻✾❋❧③❛■▼❍❛■❀③✹✻✵✲❂③❾①
❍❏✯❙✲❂❫✆➼❧❁❄③❾❍⑩❍➁❸P✻❺❜➃✯✑❋❏❱❥✻✾③⑩❍❏✯⑨✺❄❋❧✻✾❫❄■❀❱❥❍⑩❍❏❸❄✻t✻◆➒P✺✼✻✾❋❧■❑❃✤✻✾✐✜❍❳✲✕✽❄↕✑✭ ✿❄■❑✐❄❫P■❑✐❄✱❛✻✾✐❄✻❥❋❏✱❂①➊➈✦qt✸✇➉◆✬❂⑦✗❸❄✻❺❜➃✯❂❁❄❋❾❝❯✐✪❁P❱✾✽❑✻❥✯✑✐
➈ ➯ ✭⑨➉❈qt✸➣■❀③✩✐P✯❂❍✌✻◆➒P✺✼✻✾❱❩❍➁✻❥❫❆❍❏✯⑨✿✼✻❺③❏✻❥✐❄③❏■▼❍➁■▼❊✑✻❺❍❏✯❛❍➁❸P✻t③❧❍❏❋❏❁❄❱❩❍➁❁❄❋❧✻t✯❂❜✮❍➁❸P✻➇❜➃✯✑❋❧❱✾✻✾③❥✴✑✿✼✻✾❱✵✲✕❁❄③❏✻✗■▼❍⑩■❀③✩③❾❍➁❋❏✯❂✐❄✱✑✽❀①
❱❥✯✑❋❏❋❧✻✾✽❞✲✆❍➁✻✾❫➏❍➁✯➡❍❏❸❄✻⑤↕✑✭ qt✸➭✠➳ ✆✍ ➸✦✎
✬ ⑨✐➩❍➁❸P✻✧✯❂❍❏❸❄✻✾❋→③❧■❑❫❄✻❼■❀❍♠■❑③♠❲✪✐P✯❹➀✹✐➫❍❏❸✮✲✕❍✄❍❏❸❄✻➊③❧✺➆✻❥❱❥❍➁❋❏✲➨✲❂✐❄❫➫q❺✏✸ ✡ ③
✯❂❜❭✽❀■❑✱✑❸✜❍❼✐✪❁P❱✾✽❑✻❥■⑨❫❄✻❥✺➆✻❥✐❄❫♥✯✑✐➋❍➁❸❄✻➨③❾❍➁❋❧❁❄❱❥❍❏❁❄❋❏✻➨✯❂❜❙❍❏❸❄✻➨↕✑✭❛➽ ✠➳ ✑P✓✴ ✒✕➸✦✬◗⑦✗❸❄✻✾❋❧✻❥❜➃✯✑❋❧✻❂✴✹❍➁❸❄✻❩①➋✺❄❋❧✯✑❃❼■❀③❏✻❻❍➁✯
✿✼✻❆✲❂✐➨■❑✐✜❍❏✻✾❋❏✻❥③❧❍❏■❑✐❄✱➊✽❑✲❂✿✼✯✑❋➁✲✕❍❏✯✑❋❧①➔❜➃✯✑❋❛❱❳❸❄■❑❋❏✲❂✽⑩■❀✐✜❍➁✻✾❋❏✲❂❱❥❍❏■❑✯✑✐P③✾✬➅⑦✗❸❄■❀③⑨■❑③➅✲✕✐➨■❑❃✤✺➆✯✑❋❾❍❳✲❂✐✜❍❛③❏❁❄✺P✺❄✽❑✻❥❃❼✻❥✐❨❍❉❍➁✯
■❀✐❨❊❂✻✾③❾❍➁■❑✱✑✲✕❍➁■❀✯✑✐❄③✤✯❂❜❙↕✑✭ ③❏❱✾✲✕❍❏❍❏✻✾❋❏■❀✐❄✱❄✴❺➀✹❸P✻✾❋❏✻➡↕✑✭ ❜➃✯✑❋❏❱❥✻➡✻❥➐➆✻✾❱❩❍➁③➊❸❄✲❷❊❂✻➡✿✼✻✾✻❥✐➋■❑❫❄✻❥✐✜❍➁✔■ ✝❄✻✾❫➎❃✤✯✑③❾❍➁✽❀①➶❜➃✯✑❋
❸❄■❀✱✑❸❄✻❥❋✰✻❥✐❄✻✾❋❧✱✑■❑✻❥③♠➳ ✖✕ ➸☛✬
✗✢➝➊➠✙✘✛✚✢✜✮➟✤✣⑤➟➡➥✦✥✼➟
✧✩★✪✧✢➠✙✚✬✫✭✧
✫ ❱✾✯✑❃✤✺❄✽❀✻❥❍➁✻♠③❧❍❏❁❄❫P①➌✯✕❜✒❍➁❸❄✻➓↕❂✭ ③❧①✪③❧❍❏✻✾❃ ✲❂✐❄❫➌❍➁❸P✻ ➯ ✭ ✿✼✯✑❁❄✐❄❫➨③❾❍❳✲✕❍❏✻→❱✵✲✕✐➨✿➆✻✄❜➃✯❂❁❄✐❄❫➌■❀✐➨r✰✻❩❜❡✬✒➳ ↕✕➸✦✬
➲
❬✰✻✾❋❏✻❙➀➇✻❭✱❂■❀❊✑✻❭✲➓③❏❸P✯✑❋❧❍✰③❏❁P❃❼❃❼✲❂❋❧①✧✯❂❜❈❍➁❸❄✻❙❋❏✻❥③❏❁❄✽▼❍➁③❥✬
✫t❍➓✭❉❽✁➭❍➁❸P✻➊❬❉✲✕❃❼■❀✽❀❍➁✯❂✐❄■❞✲❂✐➨■❀③♠❱❥✯✑❃✤✺❄✽❑✻❩❍➁✻✾✽▼①➑❫❄✻❥❍❏✻✾❋❧❃❼■❀✐❄✻✾❫➩✿✜①➏✲✛✝❄❍♠❍➁✯➌➺❂✭ ❫✮✲✆❍❳✲P✴❈➀✹❸❄✻✾❋❧✻✵✲❂③→❍❏❸❄✻
↕✑✭❛➽➩✲✕❍❺✭❉✭❛✮❽ ■❀✐✜❊✑✯✑✽▼❊✑✻❛❍④➀➇✯→❁❄✐P❲✪✐P✯❹➀✹✐➔❽❿✸✇☛➂ ✡ ③✾✴P➀✹❸❄■❀❱❳❸✧➀➇✻✾❋❏✻❉❫❄✻❥❍❏✻✾❋❏❃✤■❑✐P✻✾❫✧✿✜①✧✯✲ ✝❄❍✇❍➁✯♠❍➁❸❄✻✱✰❳❬ qt✸
✲❂✐P❫❼❍➁❸P✻✰❫P✯✑❁❄✿❄✽❀✻❥❍✇✐❄✻✾❁✛❍➁❋❏✯❂✐✛❝④❫❄✻❥❁P❍➁✻❥❋❏✯✑✐➌➈✓✐❄❫✮➉✠③❧❱✵✲✕❍❧❍➁✻✾❋❧■❑✐❄✱❭✽❑✻❥✐❄✱❂❍❏❸✢✬✌q❺✻❥❱✵✲❂❁P③❏✻❛❍❏❸❄✻✰❱✾❁❄❋❧❋❏✻✾✐✜❍➇■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❀✯✑✐
❃✤✯✛❫P✻✾✽✠❫❄✯✪✻✾③✄✐P✯❂❍✄■❀✐❄❱✾✽❀❁❄❫❄✻✤❱❳❸✮✲❂❋❧✱✑✻❩❝❯■❑✐❄❫❄✻❥✺➆✻❥✐❄❫❄✻❥✐❄❱✾✻➊✿P❋❏✻✵✲✕❲✪■❀✐❄✱✎➈✦➂❺➄❡q✗➉❩✴❿➀❺✲
✻ ✝❄❍❏❍❏✻✾❫➶❍❏✯➡✻◆➒P✺✼✻✾❋❧■❑❃✤✻✾✐✜❍❳✲✕✽
❊✕✲❂✽❀❁❄✻✾③❥✴✰➀✹❸❄■❀❱❳❸➋➀❺✻❥❋❏✻➨❱❥✯✑❋❏❋❧✻✾❱❥❍❏✻✾❫➍❜➃✯✑❋✤❍➁❸❄■❀③✧❜✓✲❂❱❥❍➨➈✓③❧✻✾✻➑r✹✻❥❜❡✬➅➳ ↕✕➸❞➉❩✬➾⑦✗❸❄■❀③✧➀❺✲❂③⑤✺➆✻❥❋❧❜➃✯✑❋❧❃❼✻❥❫➎❜➃✯✑❋✤❍④➀❺✯
❫❄■▼➐✞✻❥❋❏✻❥✐❨❍❛❱✾❁✛❍❧❝④✯✕➐➨❊❂✲✕✽❑❁❄✻❥③✱✂✴✳✵✟ ✕✶✕ ✲❂✐❄✛
❫ ☞ ✕✶✕ ❢❣✻❥✈✄✬✷⑦✗❸❄✻❥①❣✲❂❋❧✻♠✿✼✯✑❁❄✐❄❫❄✲❂❋❏■❀✻✾③✹✯❂❜✒✷
✲ ✂ ❋❏✻✾✱❂■❑✯✑✐✢✴✛➀✹❸❄■❑❱❳❸
✻❥✐❄③❏❁❄❋❧✻✾③✗❍➁❸❄✲✕❍t✺❄❸✜①✪③❏■❀❱✵✲❂✽❀✽❀①✤■❑✐✜❍❏✻✾❋❏✻❥③❧❍❏■❑✐❄✱→❃✤✯✑❃✤✻✾✐✜❍❳✲♠✲❂❋❏✻❉✐❄✯❂❍✗✲✆➐✞✻❥❱❥❍➁✻❥❫⑤✿✜①✧❍➁❸P✻⑨❱✾❁P❍❾❝④✯❂➐➡✲❂✐❄❫➊✲❂✽❑✽➆❽❿✸➇☛➂ ✡ ③
❋❧✻✾❃❼✲❂■❑✐❆✐✮✲✕❍❏❁❄❋➁✲✕✽✮✲✕❍✠❍➁❸❄✻✹③❏✲❂❃❼✻t❍❏■❑❃✤✻❂✬✩⑦✗❸❄✻✹❋❏✻✾③❧❁❄✽❀❍❏■❑✐❄✱❭❽❿✸✇☛➂ ✡s③✇✯❂❜✼❍➁❸❄✻✰↕✑✭❛➽➏✲✕❋❏✏✻ ✸✺✹✻✳ ✽↕ ✼✾☞✛✿✴ ✸❁❀❂✳ ✕ ✼s❃↕ ✍
✲❂✐P❂
❫ ✸✺✹✻✳ ✼✓✑P❄✴ ✸✺❀❂✳❆❅ ✕ ✼ ✑ ✴✮❋❧✻✾③❏✺✼✻✾❱❩❍➁■▼❊✑✻✾✽▼①✑✬
➂❺✯✑❃❼✺❄✲❂❋❏■❀✐❄✱➨❍➁❸❄✻❣❫❄■❀➐➆✻✾❋❧✻✾✐✜❍➁■❑✲❂✽✗✻✾✽❑✲❂③❧❍❏■❑❱➔✐❄❫➎❱❥❋❏✯✑③❧③✧③❧✻✾❱❥❍❏■❑✯✑✐➎✲✕❍❼✽❑✯❷➀ ✻❥✐❄✻✾❋❧✱✑■❑✻❥③✾✴t✻✕✬s✱❄✬♥↕➶❢❣✻❥✈✄✴✒❜➃✯✑❋
✭❛✮❽ ✲❂✐P❫➑✭❉✭❉✁❽ →✴✼✯✑✐❄✙✻ ✝❄✐❄❫❄③➅✲❂✽❀❃❼✯❂③❧❍❛■❑❫❄✻❥✐❨❍❏■❑❱✾✲❂✽❿✺❄❋❏✻❥❫❄■❑❱❩❍➁■❑✯❂✐❄③✾✬✰⑦✗❸❄✻✾❋❧✻➓■❑③❛✲❂✽❑③❧✯✧✯✑✐P✽❀①❣✲❼❊✑✻❥❋❧①❣③❏❃❼✲❂✽❑✽
❱❥❁P❍❧❝❯✯❂➐➑❫❄✻✾✺✼✻✾✐P❫❄✻✾✐❄❱❥✻❂✬✹➽✮✯✑❋t❍❏❸❄■❑③✹✯✑✿❄③❧✻✾❋❾❊❂✲✕✿❄✽❑✻❭✲❂✐❄❫❣✲✕❍✹❍➁❸P■❑③✹✻✾✐❄✻❥❋❏✱❂①⑤❍❏❸❄✻❭❱❳❸❄■❑❋❏✲❂✽✙✻❩➒✛✺✮✲❂✐P③❏■❑✯❂✐❣③❧✻✾✻✾❃✤③✹❍➁✯
✿✼✻➅❱✾✯✑✐✜❊❂✻✾❋❏✱❂✻✾❫✢✬➇⑦✗❸❄✻➅✐❄❫➔❱✾❋❧✯✑③❏③✹③❏✻❥❱❥❍❏■❑✯✑✐➔❃✤■❑✐❄■❀❃→❁❄❃➪✲✕❇❍ ☞❃➓
✟ ❢❻✻❥✈◗✱✑✻❩❍➁③✰✲✄❊✪■❑③❏■❀✿❄✽❑✻❉❱✾✯✑✐✜❍➁❋❧■❑✿❄❁✛❍➁■❑✯❂✐✧❜➃❋❏✯✑❃
✭❛✭❉✁❽ →✬✒➽✮✯✑❋♠❍❏❸❄❈
✻ ✸❉✹➾✲✕✐❄❊
❫ ✸✺❀➍❊✕✲❂✽❀❁❄✻✾③→✯❂✿P❍❳✲❂■❀✐❄✻✾❫➶✿❨①➏❍➁❸❄❋
✻ ✝P❍✵✴✌❍➁❸P✻⑤✺❄❋❏✻❥❫❄■❑❱❩❍➁■❑✯❂✐❄③➓✲✕❍→✭❉✭❉❽✁ ✲❂❋❏✻➊■❀✐
✲❂✱❂❋❏✻✾✻❥❃❼✻❥✐✜❍✄➀✹■❀❍❏❸➏❍❏❸❄✻✧❫✮✲✆❍❳✲➡✲✕✐❄❫➶❍➁❸P✻●✂➛❫❄✻✾✺✼✻✾✐❄❫P✻✾✐❄❱❥✻⑤■❑③❭③❏❃❼✲❂✽❑✽✦✬✧⑦✗❸❄■❀③✄■❑✐P❫❄■❑❱✾✲✕❍➁✻❥③❭❍❏❸✮✲✕❍❭❍➁❸❄✻❼❱✾❋❏✯❂③❏③
③❧✻✾❱❥❍❏■❑✯✑✐➏■❑③❭❱✾✯✑✐✜❊❂✻✾❋❏✱❂✻✾❫➫✲✕❍❭❍➁❸P■❑③❙✯✑❋❏❫P✻✾❋✾✬⑤➄④✐✜❍❏✻✾❋❏✻❥③❧❍❏■❑✐❄✱✑✽▼①✑✴❿❍➁❸❄✻❼✲❂✱✑❋❧✻✾✻❥❃❼✻❥✐❨❍❭➀✹■❀❍❏❸➏❍❏❸❄✻❼❫❄✲✕❍❳✲⑤❊✕✲❂✐❄■❑③❧❸❄✻✾③❥✴
➀✹❸❄✻❥✐➎❱❳❸✮✲✕✐❄✱✑■❑✐P✱➑❍❏❍
✯ ✸❉✹■✳❏❅❛✽↕ ✼ ✕ ❜➃✯❂❑
❋ ✂▲✳▼✟ ✕◆✕ ❢❻✻❥✈→✴✌➀✹❸P■❑✽❑✻⑤❫P✻❥❍➁✻❥❋❏❃✤■❑✐❄■❀✐❄✱✎✸❁❀ ✿✜① ✪
✲ ✝❄❍➓❍❏✯➣❍❏❸❄✻
↕✑✭ qt✸✗✬✇⑦✗❸❄■❑③✤③❏❸❄✯❷➀✹③✤❍➁❸❄✻❣③❏✻✾✐P③❏■❀❍❏■❀❊✪■❀❍④①✎✯✕❜❉❍➁❸P✻➡❱✾❋❧✯✑③❏③✤③❏✻❥❱❥❍❏■❑✯✑✐➋❃✤■❑✐P■❑❃→❁❄❃ ❍➁✯➣❍➁❸❄✻❻❫❄✻❩❍❳✲❂■❀✽❑③❆✯❂❜⑨❍❏❸❄✻
↕✑✭❛➽❺✬✢➄❯❍❙✲✕✽❑③❏✯⑤■❀✐❄❫❄■❀❱✵✲✕❍❏✻✾③❉❍❏❸✮✲✕❍⑨❍❏❸❄✻➓❋❏✻❥❫❄❁❄❱✾✻❥❫➏❱❥✯✑✐✜❍➁❋❧■❑✿❄❁P❍❏■❑✯✑✐➡✯❂❜✠❍➁❸❄✻➓③❧❁❄✿❄✽❑✻✾✲❂❫❄■❀✐❄✱❻➺✆➻✎✻❩➒✛❱❳❸✮✲✕✐❄✱✑✻❆③❧❍❏■❑✽❑✽
↕
✽❑✻✾✲❂❫❄③❛❍❏✯⑤✲➊❱✾✯❂✐❄③❏■❀③❧❍➁✻❥✐✜❍⑨❍➁❸❄✻❥✯✑❋❧①❣✯❂❜✒❍❏❸❄✻➓✐❨❁❄❱✾✽❀✻✵✲❂❋❛■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❑✯❂✐✢✬⑨➄④✐➨❱✾✯❂✐❨❍❏❋➁✲❂③❾❍✵✴✞❍❏❸❄✻➓✲❂✐❄✲❂✽❀①✪⑥✾■❀✐❄✱✧✺✼✯❷➀❺✻❥❋
✂✁❙❜➃✯✑❋✰✐❄❫➡③❧❱✵✲✕❍❧❍➁✻❥❋❏■❑✐P✱⑤✲✕❍❉↕➊❢❣✻❩✈➲❱❳❸✮✲❂✐P✱✑✻✾③❥✴✞➀✹❸❄✻✾✐➨■❀✐❄❱✾❋❧✻✵✲❂③❧■❑✐❄✱❆❍➁❸P✻✄✯✑❋❧❫❄✻✾❋✰❜➃❋❏✯✑❃ ✭❛✮❽ ❍❏✯➊✭❉✭❛✁❽ ➓✬
⑦✗❸❄✻✄✺P❋❏✻✾❫P■❑❱❥❍❏■❑✯✑✐➡✲✕❍➅✭❛✭❉✁❽ ❫❄✯✪✻✾③➅✲✕✽❑③❏✯❼✐❄✯❂❍❉✲❂✱✑❋❧✻✾✻♠➀✹■▼❍➁❸➡❍❏❸❄✻✄✻◆➒✛✺➆✻❥❋❏■❑❃✤✻✾✐✜❍✾✬⑨❶✛❁P❋❏✺❄❋❧■❑③❏■❀✐❄✱✑✽▼①✑✴✮❜➃✯✑❋✹❍➁❸❄■❀③
✯✑✿❄③❧✻✾❋❧❊✕✲❂✿P✽❑✻❂✴✛❍➁❸❄✻❙❱❳❸❄■❀❋➁✲❂✽✙✻◆➒P✺❄✲❂✐❄③❏■❀✯✑✐❻■❑③✗✐❄✯❂❍✹❱❥✯✑✐✜❊✑✻❥❋❏✱✑✻❥❫✢✬
⑨✐❄❱❥✻⑤❍➁❸❄✻➔↕✑✭❛➽➾❸✮✲❂③➓✿✼✻✾✻✾✐ ❫❄✻❩❍➁✻✾❋❧❃❼■❀✐❄✻✾❫✞✴✠❍❏❸❄✻ ➯ ✭ qt✸ ■❑③➓✲➨❱✾✯❂❃❼✺❄✽❀✻❥❍❏✻➊✺❄❋❏✻❥❫❄■❑❱❩❍➁■❀✯✑✐✎✲✕❍✤✭❉✭❛✁❽ ➓✴
✿➆✻❥❱✵✲❂❁P③❏✻⑤✐❄✯ ➯ ✭ ❜➃✯❂❋❏❱✾✻⑤✯✪❱✾❱❥❁❄❋❏③❆✲✆❍→❍➁❸❄■❀③→✯✑❋❧❫❄✻✾❋❥✬➏❖➏✻⑤✯✑✿P❍❳✲✕■❑✐ ➯ ✭ q❺✏✸ ✡ ③➓✿✼✻❥❍④➀➇✻✾✻✾✐➋◆➺ ✒P✾✬ ✟➨❢❣✻❥✈ ✲✕✐❄❫
↕ ✕ ✬ ✕ ❢❣✻❥✈ ❫❄✻❥✺➆✻❥✐❄❫❄■❀✐❄✱❣✯❂❍
✐ ✂❛✬➓⑦✗❸❄■❑③➅✐P■❑❱✾✻❥✽❀①➌✲❂✱✑❋❏✻❥✻✾③➅➀✹■❀❍❏❸➨❍➁❸❄✻❆❱✾✯❂❋❏❋❏✻❥❱❥❍❏✻✾❫➣✻❩➒✛✺➆✻❥❋❏■❀❃❼✻❥✐❨❍➁✲❂✽✌❊✕✲❂✽❑❁P✻→✯❂❜
◆➺ ✒P✓✬ ✧
✑ ❢❻✻❥✈→✬✼⑦✗❸❄✻❭❱✾❁P❍❾❝④✯❂➐➣❫❄✻❥✺➆✻❥✐❄❫❄✻❥✐❄❱✾✻→■❀③ ✟ ✕✶✕ ❲✕✻❥✈ ✯✑❋ ✬ ✍☎✄➭✯❂❜✌❍❏❸❄✻✄q❺✸✹✬✼❬✰✯❹➀➇✻❥❊❂✻✾❋❥✴✢❱✵✲❂✽❀❱✾❁❄✽❑✲✕❍➁■❀✯✑✐❄③
✿✮✲❂③❧✻✾❫⑤✯✑✐➊❍❏❋➁✲❂❫❄■▼❍➁■❀✯✑✐✮✲❂✽✮❜➃✯✑❋❧❱✾✻✾③❺❸✮✲✵❊✑✻❙③❏❸❄✯❷➀✹✐⑤❍➁❸❄✲✕❍t❍➁❸P✻➅↕✑✭✥✲❂✐P❫ ➯ ✭✥qt✸ ✲❂❋❏✻❉❱✾✯✑❋❧❋❏✻✾✽❑✲✕❍➁✻❥❫➑✠➳ ✍✆➸☛✬✒⑦✗❸P✻✾❋❏✻◆❝
❜➃✯✑❋❏✻✕✴⑩q❺✸✥❋❏✻✾③❧❁❄✽❀❍❏③❭❜➃✯❂❋❭✽❀■❑✱✑❸✜❍❙✐❨❁❄❱❥✽❑✻✾■✇✲❂❋❧✻❆✐❄✻✾❱❥✻✾③❏③❏✲❂❋❧①➣❍➁✯❣✱✜✲❂■❀✐➣❃✤✯✑❋❧✻✤❱❥✯✑✽✐ ✝✮❫P✻✾✐❄❱❥✻➊■❑✐➨❍➁❸P✻❼✻◆➒P✺❄✲❂✐❄③❏■❀✯✑✐
❜➃✯✑❋✗✿✼✯✑❁❄✐❄❫➔③❧❍➁✲✕❍➁✻❥③❉✲✕✐❄❫➔■❑✐⑤❍➁❸❄✻❙③❾❍➁❋❏❁P❱❥❍➁❁P❋❏✻❭✯❂❜✩❍❏❸❄✻❙✺❄❋❏✻❥❫❄■❑❱❩❍➁✻❥❫➡↕✑✭❛➽❺✬
✜✢➝✧➠✙✘✛✚ ✝➙ ✆✟✞ ✧✩★✪✧✢➠✙✚ ✫
➁➙ ❽❿■✼■❑③❺✯✲ ✮✝ ❋❧③❧❍✗✻◆➒P✲❂❃❼✺P✽❑✻❂✬✒➂t✲❂✽❑❱❥❁❄✽❞✲✕❍❏■❑✯✑✐P③✇✿❄✲❂③❏✻❥❫➊✯✑✐✧❍❏❋➁✲❂❫❄■▼❍➁■❀✯✑✐✮✲❂✽❄❜➃✯✑❋❧❱✾✻❥③❺❸✮✲✵❊✑✻➅③❧❸❄✯❷➀✹✐➊❍➁❸✮✲✆❍➇❍❏❸❄✻➅qt✸
✯❂❜✌❍❏❸❄✻ ↔ ✱✑❋❏✯❂❁❄✐❄❫➌③❾❍❳✲✕❍❏✻→✲❂✐❄❫❣❍➁❸❄✻♠✻❩➒✛❱✾■▼❍❳✲✕❍❏■❑✯✑✐❣✻✾✐❄✻❥❋❏✱❂①❣✯❂❜✌❍❏❸❄✻→↕ ↔ ✝✮❋❏③❾❍➅✻❩➒✛❱❥■❀❍➁✻❥❫➌③❧❍➁✲✕❍➁✻♠❫❄✻✾✺✼✻✾✐P❫➨✯✑✐
❍➁❸❄✻→↕✑✭❉➽➋❃✤✯✛❫P✻✾✽☛✴✼✻❥❊❂✻✾✐➣■❀❜✒❍❏❸❄✻➓↕✑✭➲q❺✸ ■❑③❛❱✾✯✑❋❧❋❏✻❥❱❥❍➁✽▼①➌✺❄❋❧✻✾❫❄■❀❱❥❍❏✻✾❫ ✌➳ ✑P✾✴ ✒✆➸☛✬❙⑦✗❸❄✻➓✐❨❁❄❱❥✽❑✻✾❁P③❭✺P❋❏✯✑❃✤■❑③❧✻✾③❛❍❏✯
✿➆✻❙✲❆✱✑✯✪✯✛❫⑤✽❑✲❂✿✼✯✑❋➁✲✕❍❏✯✑❋❧①✤❍➁✯❆✺❄❋❧✯✑✿✼✻❙❍❏❸❄✻❙❱❳❸❄■❑❋❏✲❂✽✙↕✑✭❛➽❺✬
⑦✗❸P✻➓❱❳❸❄■❑❋❏✲❂✽✩❜➃✯✑❋❧❱✾✻❥③❙✲❂❋❏✻→✐P✯✑✐✛❝④✽❀✯✛❱✾✲❂✽❿✿➆✻❥❱✵✲❂❁P③❏✻➓✯❂❜✠❍➁❸P✻✾■❑❋❉❋❏✻✾✱❂❁❄✽❞✲❂❋❧■❑⑥✾✲✕❍➁■❀✯✑✐✢✬❉⑦✗❸P■❑③⑨■❀❃❼✺❄✽❀■❑✻❥③✰❍❏❸✮✲✕❍⑨✯❂✐❄✽❀①
✲→❊✑✻✾❋❾①➔✽❑■❀❃❼■▼❍➁✻✾❫❼✐❨❁❄❃→✿✼✻✾❋✹✯❂❜✩❃❼✻❩❍➁❸❄✯✪❫❄③✹✻❩➒✛■❑③❾❍✗❍➁✯❆③❏✯❂✽❀❊✑✻➅❍❏❸❄✠✻ ✳ ☞❆✐❨❁❄❱❥✽❑✻✾✲❂❋✗✿➆✯❂❁❄✐❄❫❻③❧❍❳✲✆❍➁✻❙✺❄❋❏✯❂✿❄✽❑✻❥❃❣✬
❬❛✻❥❋❏✻❛➀➇✻❉✻❥❃❼✺P✽❑✯❷①➓❍➁❸❄✻❛✐❄✯✕❝❯❱✾✯✑❋❧✻❛③❧❸❄✻✾✽❀✽➆❃✤✯✛❫P✻✾✽✩➈✦✭❉➂✗❶❄❢➌➉❉➳ ✑ ✴ ➺✆➸✦✬✒➽✮✯✑❋➇✭⑨➂✗❶❄❢➣✴❄✲❂✽❀✽✮✐✪❁P❱✾✽❑✻❥✯✑✐❄③➇❋❏✻✾❃❼✲❂■❀✐
✲❂❱❥❍❏■❀❊❂✻➑✲❂✐❄❫ ✐❄✯ ■❀✐❄✻✾❋❾❍➔❱✾✯✑❋❧✻➑■❑③➔✲❂③❧③❏❁❄❃✤✻✾❫✢✬➪⑦✗❸❄✻❥❋❏✻❩❜➃✯✑❋❏✻✕✴❙✲✎③❾①✪③❧❍➁✻❥❃✧✲✆❍➁■❑❱➑✺❄❋❧✯✛❱❥✻✾❫❄❁P❋❏✻➣✻❩➒✛■❀❍❏③✾✴❛➀✹❸P■❑❱❳❸
✻✾✐✮✲✕✿❄✽❑✻❥③➊❍➁✯➫❱✵✲✕✽❑❱✾❁P✽❞✲✕❍❏✻➡✻❥➐➆✻✾❱❩❍➁■▼❊✑✻➑■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❀✯✑✐❄③✧❜➃❋❧✯✑❃ ✿✮✲✕❋❏✻➣➺❂✭ ✲✕✐❄❫ ↕✑✭ ❜➃✯✑❋❧❱✾✻✾③➏➈➃③❏✻✾✻ ✌➳ ✒✕➸❞➉❩✬ ⑦✗❸❄✻
✻❥➐➆✻✾❱❩❍➁■❀❊❂✻➨■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❀✯✑✐❄③➊③❧✺➆✻❥✻✾❫ ❁❄✺➍❱✾✯✑✐✜❊❂✻✾❋❏✱❂✻✾✐❄❱❥✻➶③❏☛❁ ✡❼❱❥■❑✻❥✐❨❍❏✽❀① ❍➁✯➫✯✑✿P❍➁✲❂■❑✐➎❋❏✻✵✲✕✽❑■❑③❾❍➁■❀❱➡❋❏✻❥③❏❁❄✽▼❍➁③❥✬ ❖➏✻
➀❺✻❥❋❏✻✤✲❂✿❄✽❀✻→❍➁✯➔✺✼✻✾❋❧❜➃✯❂❋❏❃ ❱✾✲❂✽❑❱❥❁❄✽❞✲✕❍❏■❑✯✑✐P③❉❁❄✺➑❍➁✯➔③❏❸P✻✾✽❑✽✒✻◆➒✛❱✾■❀❍➁✲✕❍➁■❀✯✑✐❄③⑨✯✕❜✌☞ ✳ ☞P✴✢➀✹❸❄■❀❱❳❸➏❃✤✻✵✲❂✐P③❭❃✤✯✪❫❄✻✾✽
③❏✺✮✲✕❱✾✻✗③❏■❀⑥✾✻❥③✌❜➃✯✑❋✌➙❳❽✙■P✯✕❜✎✍❑✳ ✒❃✍ ✑✜➺✑➺✛✬❈⑦✗❸❄✻✗✿✮✲❂❋❧✻✹↕✑✭❉➽ ✡s③✌❋❧✻✆☎❨❁❄■❀❋❏✻t❍➁❸P✻✗❁❄③➁✲❂✱❂✻t✯❂❜✼✻❥➐➆✻✾❱❩❍➁■❀❊❂✻✗❍➁❸❄❋❧✻✾✻❩❝❯✿➆✯✪❫P①
❜➃✯✑❋❏❱❥✻✾③❥✴❄➀✹❸❄■❑❱❳❸⑤➀➇✻✾❋❏✻❭✯✑✿P❍➁✲❂■❑✐P✻✾❫⑤❜➃❋❏✯✑❃ ③❏✯✑✽❀❁P❍➁■❀✯✑✐❄③t✯✕❜✌↕✑✭✥❱❥✽❑❁❄③❾❍➁✻❥❋✗✻✆☎❨❁✮✲✕❍❏■❑✯✑✐❄③❥✬✠✫❉✽❑✽➆❱✵✲❂✽❀❱✾❁❄✽❑✲✕❍➁■❀✯✑✐❄③❺➀➇✻✾❋❧✻
✺➆✻❥❋❧❜➃✯✑❋❧❃❼✻❥❫⑤❜➃✯✑❋✹✲❂✐➔❸✮✲❂❋❧❃❼✯✑✐P■❑❱⑨✯✑③❧❱✾■❀✽❑✽❞✲✆❍➁✯✑❋✇❜➃❋❏✆✻ ☎❨❁❄✻❥✐❄❱❥①❻✯❂❜ ↕✤❢❣✻❩✈→✬
➽✩■❑✱❄✬ ③❧❸❄✯❷➀✹③✤❍❏❸❄✻⑤❱✾✯❂✐❨❊❂✻✾❋❧✱✑✻✾✐❄❱❥✻➡✯❂❜✰❍➁❸P✻❣q❺✏✸ ✡ ③➓❜➃✯✑❋➓❫❄■▼➐✞✻❥❋❏✻✾✐✜❍❆❱❳❸❄■❀❋➁✲❂✽❺■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❑✯❂✐❄③✾✬➶❖♥■▼❍➁❸➫❍➁❸P✻
✻❩➒✛❱✾✻❥✺P❍➁■❀✯✑✐➩✯❂❜✰✭❛❽✁ ❜➃✯❂❋ ✂■✳ ✟ ✕◆✕ ❢❣✻❥✈✄✴✩❍❏❸❄✻ ✝✮✱❂❁❄❋❏✻➊■❀✐❄❫❄■❀❱✵✲✕❍❏✻✾③❭❱✾✯✑✐✜❊✑✻❥❋❏✱✑✻❥✐❄❱✾✻➔✯❂❜✗❍❏❸❄✻➊q❺✏✸ ✡ ③✄❍❏✯➨✲
✽❑✻❩❊✑✻✾✽✦✴❄➀✹❸❄■❑❱❳❸❻➀✹■❑✽❀✽✢✿➆✻❙③❧✏❁ ✤
✡ ❱✾■❑✻❥✐✜❍❉❍➁✯✤③❧❍❏❁❄❫P①⑤❍❏❸❄✙
✻ ♥
✂ ❫❄✻❥✺➆✻❥✐❄❫❄✻❥✐❄❱✾✻→✯✕❜⑩❍➁❸P✻❭❋❧✻✾③❧❁❄✽❀❍❏③✾✬➇❖➏✻❭✯✑✿❄③❏✻❥❋❧❊❂✻✾❫➌❍➁❸P✻
③➁✲❂❃✤✻❆✿➆✻❥❸✮✲✵❊✪■❑✯✑❋➅❜➃✯✑❋➅❍➁❸P✻❼✻◆➒P❱❥■❀❍➁✲✕❍➁■❀✯✑✐➑✻✾✐❄✻❥❋❏✱❂①❂✴✩➀✹❸❄✻❥❋❏✻❼❍❏❸❄✻❼✭❉✁❽ ❋❏✻❥③❏❁❄✽▼❍♠❜➃✯❂✯❋ ✂❆✳ ✟ ✕✶✕ ❢❣✻❥✈ ❃→❁❄③❾❍
✲❂✽❑③❧✯➓✿➆✻➅❍➁✲❂❲❂✻❥✐❻➀✹■▼❍➁❸❻❱✵✲❂❋❧✻❂✬
➽✮✯✑❋❆❍➁❸P✻➌qt✞✸ ✡ ③❼❍➁❸P❂
✻ ✂➭❫P✻✾✺✼✻✾✐❄❫❄✻❥✐❄❱✾✻➨■❀③❼③❧❸❄✯❷➀✹✐➍■❑✐➎➽⑩■❑✱❄✬✇➺✪✬ ⑦❈✯➩✱✑■▼❊✑✻❣✲❂✐➋■❀❫❄✻✵✲➣✯❂❜⑨❍➁❸P✻❂❨☎ ❁✮✲❂✽❀■❀❍④①
✯❂❜✰❍➁❸❄✻➔❫❄✻❥③❏❱✾❋❧■❑✺P❍❏■❑✯✑✐✞✴✠➀➇✻❣✲❂✽❑③❧✯➣③❧❸❄✯❷➀➭❍❏❸❄✻➔✻❩➒✛✺➆✻❥❋❏■❀❃❼✻❥✐❨❍➁✲❂✽✹qt✸➲✲✕✐❄❫➎✲✕✐ ✻❥③❧❍❏■❑❃❼✲✕❍➁✻❥❫ ❱❥✯✑❋❏❋❧✻✾❱❩❍➁■❑✯❂✐ ❜➃✯✑❋
❍➁❸❄✻✄❃❼■❀③❏③❏■❀✐❄✱➔➂❺➄❡q❉✴➆➀✹❸❄■❑❱❳❸➨➀➇✻➓✯✑✿P❍❳✲✕■❑✐❄✻❥❫➨✿❨①➡③❏■❀❃❼✺❄✽▼①❻③❏❱✵✲✕✽❑■❑✐P✱✧❍➁❸❄✻✄❲✪✐P✯❹➀✹✐➣❱✾✯❂❋❏❋❏✻❥❱❥❍❏■❑✯✑✐➨■❀✐ ✰ ❬♠✬➆⑦✗❸❄✻
➂❺✯✑❁❄✽❀✯✑❃→✿➊❜➃✯✑❋❧❱✾✻⑨➀❺✲❂③✹■❑✐❄❱❥✽❑❁❄❫❄✻❥❫➔■❑✐✜❍➁✯→❍❏❸❄✻❙❱✵✲❂✽❀❱✾❁❄✽❑✲✕❍➁■❀✯✑✐❄③✾✬ ⑨✐❄✻✬✝✮✐❄❫❄③✗❍➁❸❄✲✕❍✗❍➁❸❄✻➅✻◆➒✛✺➆✻❥❋❏■❑❃✤✻✾✐✜❍➁✲❂✽✢❊✕✲❂✽❑❁❄✻
■❑③➊➀✹■▼❍➁❸❄■❀✐ ❍❏❸❄✻➑✿✮✲❂✐❄❫❄③❥✬ ❘➅✯✑■❑✐❄✱➫❜➃❋❧✯✑❃ ✭❉✁❽ ❍❏✯➎✭❛✭❉✁❽ ✯✑✐P✻➏✯✑✿P③❏✻✾❋❾❊✑✻❥③➌✲✎❋❏✻✾❫P❁❄❱❥❍❏■❑✯✑✐ ✯❂❜✄❍❏❸❄✻ ✂
❫❄✻✾✺✼✻✾✐P❫❄✻✾✐❄❱❥✻❂✬❼✫t❍→✭❛✭❉❽✁ ■▼❍❙■❑③ ✓✬ ✑❣❢❻✻❥✈ ✯✑❋✯✛✟ ✬✾✑
✍ ✄ ✯✕❜➇❍❏❸❄✻✧q❺✸✹✬❿✭✰✯❂❍➁✻➓❍❏❸✮✲✕❍❙❍➁❸❄✷
✻ ✂◗❫❄✻❥✺➆✻❥✐❄❫❄✻✾✐P❱✾✻
✯❂❜✇❍➁❸❄✻✤✭❉❽✁➪❋❏✻✾③❧❁❄✽❀❍❏③❙❃❼■❀✱✑❸✜❍➅✿➆✻❆✽❑✲❂❋❏✱✑✻❥❋⑨❍➁❸✮✲✕✐➣■❀✐❄❫❄■❀❱✵✲✕❍❏✻✾❫✢✴✙✿✼✻✾❱✾✲❂❁❄③❏✻✤✯❂❜➇❍➁❸❄✻❆③❏✽❀✯❷➀ ❱❥✯✑✐✜❊✑✻✾❋❧✱✑✻✾✐P❱✾✻✧❜➃✯✑❋
✭❉❽✁➭✲✕❍ ✂❆✳ ✟ ✕✶✕ ❢❣✻❥✈✄✬❿⑦✗❸❄✻❼③❏✲❂❃✤✻✤❸P✯✑✽❑❫❄③➅❍❏❋❏❁❄✻➓❜➃✯✑❋➅❍➁❸P✻✤✻◆➒✛❱✾■❀❍➁✲✕❍➁■❀✯✑✐➑✻✾✐❄✻❥❋❏✱❂①➣③❧❸❄✯❷➀✹✐➶■❑✐➣➽⑩■❀✱❄✬✙↕P✬
✫t❍✰✭❉✭❛✮❽ →✴P❍❏❸❄✻ ✂➍❫❄✻✾✺✼✻✾✐P❫❄✻✾✐❄❱❥✻✄❋❧✻✾❃❼✲❂■❑✐❄③t✲✕❍ ✍ ✕ ❲✕✻❥✈ ✯✑✏❋ ✍✛✬✓☎
☞ ✄ ✯❂❜❿❍➁❸❄✻❙✻◆➒P❱❥■❀❍➁✲✕❍➁■❀✯✑✐⑤✻✾✐❄✻❥❋❏✱❂①❂✬➇✫❛✽❑③❧✯
❸❄✻✾❋❧✻❂✴✷❍➁❸❄✻♠✻❩➒✛✺✼✻✾❋❏■❀❃❼✻❥✐✜❍❳✲❂✽❿❊✕✲❂✽❑❁❄✻❭■❑③✹➀✹■❀❍❏❸❄■❑✐➔❍➁❸P✻✄✿✮✲❂✐P❫✢✬✹⑦✗❸❄✻→✺❄❋❧✻✾❫❄■❀❱❥❍➁■❀✯✑✐➔❜➃✯✑❋✰❍❏❸❄✻✄✻◆➒✛❱✾■❀❍➁✲✕❍➁■❀✯✑✐❻✱✑✯✑■❑✐P✱
❜➃❋❏✯✑❃ ✭❉❽✁➲❍➁✯❻✭❉✭❛✁❽ ➪❱❳❸✮✲✕✐❄✱✑✻✾③➅❊✪■❑③❧■❑✿❄✽▼①✑✴✢③❧❸❄✯❷➀✹■❑✐❄✱⑤❍❏❸❄✻➓■❑❃✤✺➆✯❂❋❧❍❳✲✕✐❄❱✾✻♠✯❂❜➇✭❉✭❉✁❽ ❍➁✻✾❋❧❃❼③❥✬→➽✮✯✑❋✰❍➁❸❄■❀③
❃❼✯✪❫❄✻❥✽☛✴✞➀✹❸❄✻❥❋❏✻❆❍➁❸❄✻❆③❧❁❄✿❄✽❑✻✾✲❂❫❄■❀✐❄✱➌➺❹➻ ✻◆➒✛❱❳❸✮✲❂✐❄✱✑✻❼■❑③➅❋❧✻✾❫❄❁❄❱❥✻✾❫➏■❑✐➑③❧❍❏❋❏✻✾✐P✱❂❍➁❸✢✴❈❍➁❸❄✻❆❫❄✻❥③❏❱❥❋❏■❑✺✛❍➁■❑✯❂✐➣✯✕❜❺❍➁❸P✻
➯
◆✻ ➒P✺✼✻✾❋❧■❑❃✤✻✾✐✜❍❳✲✕✽➇❊✕✲❂✽❑❁P✻✧■❑❃✤✺❄❋❧✯❹❊❂✻✾③❥✬➑➽✷✯❂❋✄❂
✲ ✝✮✐❄✲❂✽❺✲✕③❏③❏✻❥③❏③❧❃❼✻❥✐❨❍✾✴✇❍❏❸❄✻➊✻❩➐✞✻❥❱❥❍➁③➓✯✕❜✗❍➁❸❄■❀③✄❋❏✻❥❫❄❁❄❱❩❍➁■❑✯❂✐➫❸✮✲✵❊✑✻
❍❏✯❣✿✼✻❆❁❄✐❄❫❄✻❥❋❏③❧❍❏✯✛✯✪❫➣■❑✐➑❃❼✯❂❋❏✻➓❫❄✻❩❍❳✲❂■❀✽☛✬→⑦✗❸❄✻❼✲❂✺❄✺P✽❑■❑❱✾✲✕❍➁■❀✯✑✐➌✯❂❜➇❱❳❸❄■❀❋➁✲❂✽✌■❀✐✜❍➁✻✾❋❏✲❂❱❥❍❏■❑✯✑✐P③➅✿✮✲❂③❏✻❥❫➶✯✑✐➏✲⑤✐❄✻❥➀
❋❧✻✾✱✑❁❄✽❑✲❂❋❏■❀⑥✵✲✕❍❏■❑✯✑✐➑③❧❱❳❸❄✻✾❃✤✻✧➀✹■❑✽❀✽✒✿➆✻✤❊✑✻❥❋❧①➏■❑❃✤✺➆✯✑❋❾❍❳✲❂✐✜❍❙■❀✐➏❍➁❸P■❑③❭❋❏✻✾③❧✺➆✻❥❱❥❍❻➳ ➯ ➸✦✬➔⑦✗❸❄✻➊③❏■❀⑥✾✻✤✯❂❜t❍❏❸❄✻✧✿✮✲✕✐❄❫❄③
■❀✐❄❫❄■❑❱✾✲✕❍➁✻➓❍❏❸✮✲✕❍♠❸❄■❑✱✑❸P✻✾❋❙✯✑❋❏❫P✻✾❋❏③❭❃✤■❑✱✑❸✜❍❙✿✼✻❼✐❄✻❥❱✾✻❥③❏③➁✲✕❋❧①➣❍➁✯➡✺P❋❏✻✾❫P■❑❱❥❍❙❍❏❸❄✻✾③❧✻✧✯✑✿❄③❧✻✾❋❾❊❂✲✕✿❄✽❑✻❥③✄✯✑✐➑❍➁❸❄✻
✽❀✻❥❊✑✻❥✽☛✬
➽⑩■❑✐✮✲✕✽❑✽❀①❂✴✑➀❺✻⑨➀➇✯✑❁❄✽❀❫➊✽❑■❀❲❂✻✹❍➁✯→❁P③❏✻⑨❍➁❸P✻⑨✐❄✻❥➀ ➄④❫✮✲✕❸❄✯➓✭❉↕❂✮❽ ✥■❀✐❨❍❏✻✾❋❏✲❂❱❥❍❏■❑✯✑✐➌➳ ↕✆➸✞■❀✐➊❱✾✯✑❃✄✿❄■❑✐✮✲✆❍➁■❑✯❂✐✤➀✹■▼❍➁❸
❍❏❸❄✻✧✭❛✭❉✁❽ ↕✑✭❛➽♥❍❏✯❣■❀✐❨❊❂✻✾③❾❍➁■❑✱✑✲✕❍➁✻➓❍➁❸P✻❼③❧✻✾✐❄③❧■❀❍➁■▼❊✪■❀❍④①➑✯❂❜➇❍➁❸❄✻ ➙ ❽✙■✒③❧①✪③❧❍❏✻✾❃ ❍➁✯➔❍➁❸❄✻✤❱❳❸❄✯✑■❀❱✾✻❆✯❂❜ ✸❉✹ ✲❂✐❄❫
✸❁❀✒✬➓❖➶✻❆❫❄✻❩❍➁✻✾❋❧❃❼■❀✐❄✻✾❫➑❍④➀➇✯❣❫❄■▼➐✞✻❥❋❏✻❥✐❨❍❭③❧✻❥❍➁③❭✯❂❜ ✸❉✹ ✲❂✐❄❫ ✸❁❀✌✴✙➀✹❸❄■❑❱❳❸➏❫❄✻✾③❧❱✾❋❏■❀✿➆✻❆✿✜①➑❱✾✯❂✐❄③❧❍❏❋❏❁❄❱❩❍➁■❑✯❂✐➣❍❏❸❄✻
✻◆➒P✺✼✻✾❋❧■❑❃✤✻✾✐✜❍❳✲✕✽✽ ❳✰ ❬ ✲❂✐❄❫✁◆❬✰✻✗qt✞✸ ✡s③✩❜➃✯✑❋✮✂ ✳ ✟ ✕✶✕ ❢❣✻❩✈→✬✕⑦✗❸❄✻❺❍④➀➇✯➅③❏✻❥❍❏③✒✲❂❋❧✻ ✸✺✹✻✳ ❅ ✼ ✑ ✓✴ ✸❁❀✎✳❆❅ ✕ ✼✓☞✶☞
➈✓↕✑✭❉➽❈❝❯✫➅➉✗✲❂✐❄❂
❫ ✸❉✹✻✳ ✑✽✼ ➯ ✓✴ ✸✺❀✪✳■❅❉✿➺ ✼ ✕ ➺❻➈✦↕✑✭❛➽❈❝❡q✗➉◆✴✮❋❏✻❥③❏✺✼✻✾❱❥❍❏■❀❊❂✻✾✽❀①❂✬✗➽⑩■❀✱❄✬ ➯ ③❏❸❄✯❷➀✹③❛❍❏❸❄✻❭❱✾✯✑✐✜❊✑✻❥❋❏✱✑✻❥✐❄❱✾✻
✯❂❜❛✯✑❁❄❋✄❋❏✻✾③❧❁❄✽❀❍❏③→➀✹■❀❍❏❸➫❋❏✻✾③❧✺➆✻❥❱❥❍❆❍➁✯ ❜➃✯✑❋♠❍➁❸❄✻⑤❫❄■▼➐✞✻❥❋❏✻❥✐❨❍❆❱✾✲❂③❏✻❥③✾✴✠➀✹❸❄■❑❱❳❸✎■❀③➓✲❂❱✾❱❥✻✾✺P❍➁✲❂✿❄✽❀✻⑤✻❩➒✛❱✾✻❥✺P❍❆❜➃✯✑❋
➄④❫✮✲✕❸❄✯➑✭❉↕✑✁❽ ✲❂✐❄❫➩↕✑✭❉➽❈❝④q❉✬✩✭❛✻❥❊❂✻✾❋❾❍➁❸❄✻❥✽❑✻✾③❧③✾✴✒➀➇✻⑤❱✵✲❂✐➩✯❂✿❄③❏✻❥❋❧❊✑✻➔✲❣③❧❍➁❋❧✯✑✐❄✱➌❫P✻✾✺✼✻✾✐❄❫❄✻❥✐❄❱✾✻➔✯❂❜✗❍❏❸❄✻⑤qt✸
✯✑✐➊❍❏❸❄✻⑨❱❳❸❄✯❂③❏✻✾✐❻↕✑✭❛➽✄✂✛✲❂✐⑤✯✑✿❄③❧✻✾❋❧❊✕✲✕❍❏■❑✯✑✐✞✴✪➀✹❸❄■❀❱❳❸➊➀❺✻➅❱❥✯✑❁❄✽❀❫⑤✲❂✽❑③❧✯✄❃❼✲❂❲❂✻❛❜➃✯✑❋➇❍❏❸❄✻⑨✻❩➒✛❱❥■❀❍❳✲✆❍➁■❑✯❂✐✧✻✾✐P✻✾❋❏✱❂■❑✻✾③❥✬
⑦✗❸❄✻❥③❏✻✬✝✮❋❧③❧❍t❋❧✻✾③❧❁❄✽❀❍❏③t❱✾✯✑✿✐ ✝✮❋❏❃➪❍➁❸❄✻❉■❑❃✤✺➆✯✑❋❾❍❳✲❂✐P❱✾✻✰✯❂❜✢❍➁❸P✻⑨③❏❸❄✯❂❋❧❍➁✻❥❋❾❝❯❋➁✲❂✐❄✱❂✻❛❍➁✻❥❋❏❃✤③t✯❂❜✢❍❏❸❄✻➅↕✑✭❛➽➏❜➃✯✑❋➇✽❑■❑✱❂❸❨❍
✐❨❁❄❱❥✽❑✻✾■✦✬
✄
☞
➦ ✧✞➞❹➤✤✎
❂
➟ ✧ ✣⑤➟➡➥ ➤✤➦➔➠ ➤➊➤✆☎
➂❺❸❄■❑❋❏✲❂✽✗✺➆✻❥❋❧❍❏❁❄❋❏✿✮✲✆❍➁■❑✯❂✐ ❍➁❸P✻✾✯✑❋❾①✎✺❄❋❏✯✑❃✤■❑③❧✻✾③❼✲➣❃✄❁❄❱❳❸➋✿✼✻❥❍❏❍❏✻✾❋✤❁❄✐❄❫❄✻❥❋❏③❾❍❳✲❂✐❄❫P■❑✐❄✱➩✯✕❜⑨✐❨❁❄❱✾✽❀✻✵✲❂❋❆❜➃✯✑❋❧❱✾✻✾③❥✬
⑦✗❸❄✻♠③❧❍❏❋❏❁❄❱❩❍➁❁❄❋❧✻✄✯❂❜✩❍➁❸❄✻♠↕✑✭❉➽✎➀✹■❑✽❀✽✢✿➆✻♠✲❂✐❣■❑❃✤✺➆✯✑❋❾❍❳✲❂✐✜❍✹✲✕③❏✺✼✻✾❱❥❍✾✴➆✿✼✻✾❱✾✲❂❁❄③❧✻✄■❀❍✰■❀③✰✐P✯❂❍❛➀➇✻✾✽❀✽❿❁❄✐❄❫❄✻❥❋❏③❧❍❏✯✛✯✪❫
✺❄❸P✻✾✐❄✯✑❃✤✻✾✐P✯✑✽❑✯✑✱❂■❑❱✵✲✕✽❑✽❀①→✲❂✐❄❫➊✿✼✻✾❱✾✲❂❁❄③❧✻➅■❀❍❺✲❂✽❑✽❀✯❹➀✹③✒❍❏✯→③❧❍❏❁❄❫P①✤❍➁❸❄✻⑨③❧❁❄✿❄✽❀✻✵✲❂❫❄■❀✐❄✱✄❱❥✯✑✐✜❍➁❋❧■❑✿❄❁P❍❏■❑✯✑✐P③✾✴❨➀✹❸❄■❑❱❳❸➊■❀③
❱❥❋❏❁❄❱❥■❞✲❂✽✞❍❏✯➓❱✾✯✑✐✿✝✮❋❏❃ ❍➁❸❄✻❙✲❂✺P✺❄❋❏✯✜✲✕❱❳❸✢✬✒➄④✐⑤❍➁❸❄■❀③t❋❏✻❥③❏✺✼✻✾❱❥❍✰■▼❍❺➀✹■❑✽❀✽➆✿✼✻⑨❊✑✻❥❋❧①⑤■❀✐✜❍➁✻✾❋❧✻✾③❾❍➁■❑✐P✱→❍➁✯❆✲❂✺❄✺P✽❀①✤❜➃✯✑❋❏❱❥✻✾③
✿✮✲✕③❏✻✾❫✤✯✑✐➓❫❄■▼➐✞✻❥❋❏✻❥✐❨❍✌❋❏✻✾✱❂❁❄✽❞✲❂❋❧■❑⑥✾✲✕❍➁■❀✯✑✐✄③❧❱❳❸❄✻✾❃✤✻✾③❛➳ ➯ ➸P❍❏✯❙➽✌✭➎③❧①✪③❾❍➁✻✾❃✤③✾✬✠✭✰✻❥➀ ❫❄✻❥❊❂✻✾✽❀✯✑✺❄❃✤✻✾✐✜❍➁③✠③❏❸P✯❹➀ ❍➁❸❄✲✕❍
➂❺➄❡q➍✲❂✐P❫➊❱❳❸✮✲❂❋❧✱✑✻❩❝❯③❧①✪❃❼❃✤✻❥❍❏❋❧①❼✿❄❋❏✻✾✲❂❲❨■❑✐❄✱✄❱✵✲❂✐➊✿✼✻⑨■❀✐❄❱✾✽❀❁❄❫❄✻✾❫❼✯✑✐✧❍❏❸❄✻⑨③➁✲✕❃❼✻✰❜➃✯✛✯❂❍❏■❑✐❄✱P✬⑩⑦✗❸❄✻❥✐⑤■❀❍✇➀✹■❑✽❑✽✷✿✼✻
❊❂✻✾❋❧①➊■❑✐✜❍➁✻❥❋❏✻✾③❾❍➁■❀✐❄✱✄❍➁✯✄✻❩➒✪❍➁✻❥✐❄❫⑤❍➁❸❄✻⑨❱✾✲❂✽❑❱❥❁❄✽❞✲✆❍➁■❑✯❂✐❄③✇❍❏✯→✐❄✻❥❁P❍➁❋❧✯✑✐⑤❋❏■❀❱❳❸➊✐❨❁❄❱✾✽❀✻✾■✢✲✕✐❄❫⑤✻❩➒✛✺❄✽❀■❑❱✾■▼❍➁✽▼①❆✺❄❋❏✯✑✿✼✻❉❍❏❸❄✻
■❀③❏✯✑③❧✺❄■❑✐➔❫❄✻❥✺➆✻❥✐❄❫❄✻✾✐P❱✾✻✄✯✕❜✩❍❏❸❄✻❭↕✑✭❉➽ ✡ ③✾✬
➄④❃❼✺❄❋❧✯❷❊✑✻✾❃✤✻✾✐✜❍❏③→■❑✐➣❍➁❸❄✻✧✲❂✽❑✱✑✯❂❋❏■❀❍❏❸❄❃✤③❉❜➃✯✑❋♠✭⑨➂✗❶❄❢ ✲❂❋❧✻✧❱❥❁❄❋❏❋❧✻✾✐✜❍➁✽▼①➏❫P✻❥❊✑✻❥✽❑✯✑✺✼✻✾❫✞✬❣⑦✗❸❄✻❩①➏➀✹■❀✽❑✽✇✲❂✽❀✽❑✯❷➀
❜➃✯✑❋✹✽❑✲❂❋❏✱✑✻❥❋t③❏✺❄✲❂❱✾✻❥③❉✲❂✐P❫❻❜➃❁❄❋❾❍➁❸❄✻❥❋✹❋❏✻✾❃✤✯❷❊✑✻➅❍➁❸P✻❭❁P✐❄❱✾✻❥❋❧❍❳✲✕■❑✐✜❍➁■❀✻✾③✹✯❂❜ ✞✝ ➯ ❱✵✲❂✽❀❱✾❁❄✽❑✲✕❍➁■❀✯✑✐❄③✾✬
⑦✗❸❄■❑③✠➀❺✯❂❋❏❲➓➀t✲✕③❺③❏❁P✺❄✺➆✯❂❋❧❍➁✻❥❫⑤■❑✐✤✺✮✲❂❋❾❍❺✿✜①✤✱✑❋➁✲✕✐❨❍❏③✇❜➃❋❧✯✑❃➲❍➁❸P✻⑨❵♠✬Ý❶➆✬✪✭❉✲✆❍➁■❑✯❂✐✮✲❂✽✼❶✛❱❥■❑✻✾✐P❱✾✻⑨➽✮✯✑❁P✐❄❫✮✲✕❍❏■❑✯✑✐✢✴
❍❏❸❄✻✗❵♠✬Ý❶➆✬✠✟⑨✻✾✺✮✲✕❋❧❍➁❃✤✻✾✐✜❍⑩✯❂❜✼✸✒✐❄✻✾❋❧✱❂①→✲✕✐❄❫✄❍➁❸P✻✡✟⑨✻✾❁✛❍➁③❏❱❳❸P✻✹➽✷✯❂❋❏③❏❱❳❸❨❁❄✐P✱✑③❏✱✑✻❥❃❼✻❥■❑✐❄③❧❱❳❸✮✲✕❜❰❍✾✬✌⑦✗❸❄✻t✐❨❁❄❃✤✻✾❋❧■❑❱✵✲✕✽
❱✾✲❂✽❑❱❥❁❄✽❞✲✕❍❏■❑✯✑✐P③✇➀➇✻✾❋❧✻➅✺➆✻❥❋❧❜➃✯✑❋❧❃❼✻❥❫➊✯✑✐✧❍❏❸❄✻⑨➄❡q✗❢➚❶P❇ ✲✕❍t✭❉✸✠r❉❶P➂♥■❀✐➊q❺✻❥❋❏❲❨✽❑✻❩①⑤✲❂✐❄❫❼❍➁❸❄✻❙➂❺❋❏✲✵①✧❱❥✯✑❃❼✺P✽❑✻❩➒
✯❂❜✩❍➁❸❄✻❭✭✰➄❾➂ ■❑✐❣✉➆❁❄❚ ✽❀■❑❱❳❸✢✴❄❘❙✻❥❋❏❃❼✲❂✐✜①✑✬
✥❿➝❻➧❆➤✤➟➨➧
✆
✆
➢❋✚☞☛ ✚⑨❋
➢ ✚➅➟➨➧ ✚✯✧
✬➲✸✹✬❿✸✒✺✼✻✾✽❀✿✮✲❂❁❄❃❻✴❿❬♠✬✙❪❙✲❂❃❼✲❂❫✮✲✛✴✙✫✄✬✙✭✰✯✑✱✑✱✜✲P✴❿❬❭✬✞❖♥■❀❍➁✲✕♦✽❞✲✛✴✞❖◗✬❿❘➅✽④✯✑❚ ❱❳❲❨✽❑✻✕✴❿❵♠✬ ❝❾❘➓✬✙❢❣✻❥■❑❤✑✐P✻✾❋✾✴❈❇✒❸✜①✪③✾✬
r✰✻❩❊➆✬✼❽✙✻❥❍❧❍✵✬ ✑◆❣
☞ ➈✦➺ ✕✶✕P ➉ ➯ ✍◆✑❃✍✛✬
➺✛✬➲✸✹✬✌✸✠✺✼✻✾✽❀✿✮✲❂❁❄❃❻✴✌✫♠✬✌✭❛✯❂✱✑✱✜✲P✴✌❖◗✬✌❘❙✽❯✯✑❚ ❱❳❲❨✽❑✻❂✴✌❬♠✬✌❪❙✲❂❃❼✲❂❫✮✲✛✴✒❵♠✬ ❝❾❘➓✬✌❢❻✻✾■❑❤❂✐❄✻✾❋❥✴✠❬♠✬✩❖♥■▼❍❳✲✕♦✽❑✲P✴✌✸✒❁❄❋❥✬
❇✠❸✜①✪③✾✬✞✉P✬✮✫ ✟➔➈☛➺ ✕✶✕ ➺✑✞➉ ✟ ➯ ↕P✬
↕P✬➲✸✹✬❿✸✒✺✼✻✾✽❀✿✮✲❂❁❄❃❻✴✙✫✄✬✙✭✰✯✑✱✑✱✜✲✛✴✢❖◗✬❈❘❙✽❯✯✑❚ ❱❳❲❨✽❑✻❂✴✢❬♠✬❿❪❙✲❂❃❼✲❂❫✮✲P✴✙❵❭✬ ❝❡❘❆✬✙❢❣✻✾■❀❤✑✐❄✻✾❋❥✴❿❬♠✬✢❖♥■▼❍❳✲✕♦✽❑✲P✴✢❇✒❸✜①✪③✾✬
r✰✻❩❊➆✬➆➂ ☞✶☞❻➈☛➺ ✕✶✕ ➺✑➉ ✕ ☞ ➯ ✕✶✕P ✬
✬➯ ➲✸✹✬✷✸✒✺✼✻✾✽❀✿✮✲❂❁❄❃❻✴❄✻❥❍❛✲❂✽✦✬❀✴P❱✾✯✑✐✜❍➁❋❧■❑✿❄❁✛❍➁■❑✯❂✐➊❍➁✯➓❍➁❸❄■❀③✹❱✾✯✑✐P❜➃✻❥❋❏✻❥✐❄❱✾✻✕✬
✟✛✬➲✸✹✬✷✸✒✺✼✻✾✽❀✿✮✲❂❁❄❃❻✴P❖◗✬✼❘➅✽④✯✑❚ ❱❳❲❨✽❑✻✕✴✮❵♠✬ ❝❾❘➓✬✷❢❣✻❥■❑❤✑✐P✻✾❋✾✴❄✭❛❁❄❱❥✽☛✬✷❇✒❸✜①✛③❥✬✷✫ ☞❃✍ ➈✦➺ ✕✶✕✶✕ ➉✗➺ ✒❃✟✛✬
☞P✬➲❵♠✬❄❊✕✲❂✐❣❪❙✯❂✽❑❱❳❲✷✴✮❇✒❸✜①✛③❥✬✞r✹✻❥❊✼✬✼➂ ➯ ✒❻➈ ✒✶✒ ➯ ➉t◆➺ ✒✑↕✑➺✛✬
✍✛✬ ✫✄✬✷✭❛✯❂✱✑✱✜✲P✴✮❬❭✬✷❪❙✲❂❃✧✲✕❫✮✲P✴✛❖◗✬✼❘➅✽④✯❂❚ ❱❳❲✪✽❀✻❂✴Pq❉✬✷r❭✬✷q❺✲❂❋❏❋❧✻❥❍❏❍✾✴✮❇✒❸✜①✛③❥✬✞r✹✻❥❊✼✬✼➂ ☞❃✟➔➈☛➺ ✕✶✕ ➺✑➉ ✕ ✟ ➯ ✕✶✕ ↕P✬
✟
⑩➽ ■❑✱❂❁❄❋❏✻ ✬⑩q❺■❀✐❄❫❄■❀✐❄✱✗✻✾✐❄✻❥❋❏✱✑■❀✻✾③❿✯❂❜ ➙ ❽✙■❂❜➃✯✑❋✙❫❄■▼➐✞✻❥❋❾❝
✻✾✐✜❍✗❱❳❸❄■❀❋➁✲❂✽➆■❑✐✜❍➁✻❥❋➁✲❂❱❩❍➁■❀✯✑✐❄③✾✬⑩⑦✗❸❄✻❭✭⑨➂✗❶❄❢ ❃✤✯✛❫❄✻❥✽
③❏✺✮✲✕❱✾✻❺③❧■❑⑥❥✻✾③✩➀➇✻✾❋❧✻➇❍❏❋❏❁❄✐❄❱✾✲✕❍➁✻❥❫→✿✜①❙❍➁❸❄✻✇❃✧✲❹➒P■❀❃✧✲✕✽
✻❩➒✛❱✾■▼❍❳✲✕❍❏■❑✯✑✐➊❍❏✯☎☞ ✳ ✁➺ ➯ ✯✑✏❋ ☞P✬
➽✩■❑✱✑❁❄❋❧✻⑨➺✪✬✒q❺■❑✐P❫❄■❑✐❄✱❙✻❥✐❄✻✾❋❧✱✑■❑✻❥③❺✯❂❜ ➙ ❽❿■✮❜➃✯✑❋➇✭❉❽✁
✲✕✐❄❫♥✭❉✭❛✮❽ ❱❥✯✑❃❼✺❄✲❂❋❏✻❥❫➎❍➁✯➶❍❏❸❄✻➌✻◆➒P✺✼✻✾❋❧■❑❃✤✻✾✐✛❝
❍➁✲❂✽➅❊✕✲❂✽❑❁❄✻✕✬➭⑦✗❸❄✻➶✲❂❋❏❋❧✯❷➀➚■❑✐❄❫P■❑❱✵✲✆❍➁✻✾③❻✲✎❋❏✯✑❁P✱✑❸
✻❥③❧❍❏■❑❃❼✲✕❍➁✻➓✯❂❜❺➂❺➄❡q❉✬✙⑦✗❸P✻❼✿✮✲✕✐❄❫❄③❭✲❂❋❏✻➓✱❂■❀❊✑✻❥✐➑✿❨①
❊✕✲❂❋❧■❞✲✕❍❏■❑✯✑✐P③⑩✯❂❄❜ ✂➩✿✼✻❥❍④➀➇✻✾✻❥✄
✐ ✟ ✕◆✕ ✲❂✐❄✲
❫ ☞ ✕✶✕ ❢❣✻❥✈✄✬
⑩➽ ■❑✱❂❁❄❋❏✻➇↕P✬✒❶✛✲❂❃❼✻❺✲❂③✌➽✩■❑✱❄✬✕➺✰❜➃✯✑❋❈❍➁❸❄✻❺✻❩➒✛❱✾■▼❍❳✲✕❍❏■❑✯✑✐
✻✾✐❄✻❥❋❏✱❂①✧❍➁❸❄✻❭↕ ↔ ③❧❍➁✲✕❍➁✻✕✬
✩➽ ■❑✱✑❁❄❋❧✻ ➯ ✬✒❶P✲❂❃✤✻t✲✕③✌➽⑩■❀✱❄✬ ❜➃✯✑❋✩❫❄■❀➐➆✻✾❋❧✻✾✐✜❍✌❱❥✯✑❃❆❝
✿P■❑✐✮✲✕❍❏■❑✯✑✐P③t➀✹■❀❍➁❸➔➄④❫✮✲✕❸❄✯✤✭❉↕✑❽✁→✬
✑P✬
❶✼✬❨➂❉✬✜❇✒■❑✻❥✺➆✻❥❋✾✴✑✈→✬✑r❭✬❂❇⑩✲❂✐❄❫P❸✮✲❂❋❏■❀✺✮✲❂✐❄❫P✻❂✴❨r❙✬✜q❉✬✕❖♥■❀❋❏■❀✐❄✱✜✲P✴✑✉P✬❨➂t✲❂❋❏✽❀③❏✯✑✐✞✴❨❇✠❸✜①✪③✾✬❨r✹✻❥❊✼✬❨❊
➂ ☞ ➯ ➈✦➺ ✕✶✕P ➉
✬
✒P✬➲❇❈✬✷✭❉✲✵❊✪❋✮✕●✲ ❍❏■❑✽✦✴✛❖◗✬✷✸✗✬ ⑨❋❏❃❼✲❂✐❄❫❻✭❛❁❄❱❥✽▼❝☛❍➁✄❸ ✂ ✕ ↕ ✕ ✟ ✕ ✒ ✕ ✬
✖✕ ✬✙❬❭✬❺❖♥■❀❍➁✲✕♦✽❞✲✛✴❺❖◗✬✗❘➅✽④✯✑❚ ❱❳❲❨✽❀✻❂✴✰✉P✬✗❘➅✯✑✽❑✲❂❲✷✴✗✫✄✬t✭✰✯✑✱✑✱✜✲✛✴❛❬❭✬t❪❙✲❂❃❼✲❂❫✮✲P✴✹r❙✬✗❶✪❲✪■❀✿❄■✕❄●✐ ③❧❲❨■☛✴✹✉P✬❺❪❙❁P❋❏✯❿③❡● ❝
⑧✞☎ ✯✕♦✽❑✐❄■❀✻✾❋❏❱❥⑥✾❁❄❲✷✴✮❇✒❸✜①✪③✾✬➆r✰✻❩❊✼✬✼➂ ☞✑↕❻➈☛➺ ✕✶✕P ➉ ✕ ➺ ➯ ✕✶✕ ✍✛✬
✑ ✬✙❇❈✬✷✭❉✲✵❊✪❋✮✕●✲ ❍❏■❑✽✦✴✮✉P✬✷❇✩✬❄✈✇✲✕❋❧①➔✲❂✐P❫❣q❛✬✷r❭✬✮q❺✲❂❋❏❋❧✻❥❍❏❍✾✴✷❇✒❸❨①✪③❥✬➆r✹✻❥❊✼✬➆➂ ☞✑➺❻➈✦➺ ✕✶✕✶✕ ➉ ✕ ✟ ➯ ↕ ✑ ✬
➺✛✬✙❇❈✬✷✭❉✲✵❊✪❋✮✕●✲ ❍❏■❑✽✦✴✛❖◗✬✷✸✗✬ ⑨❋❏❃❼✲❂✐❄❫✢✴✮❇✒❸✜①✪③✾✬➆r✰✻❩❊✼✬✷❽❿✻❩❍❏❍✾❄✬ ✑✶✑❻➈☛➺ ✕✶✕ ➺✑➉ ✟✑◆➺ ✟ ✕ ➺✛✬
↕P✬ →✬✷r❙✬✮✸✒✐✜❍➁✻❥❃❣✴✷r❙✬✷❢➡✲❂❱❳❸P✽❑✻✾■❀❫P❍✵✴✮✐❨❁❄❱❥✽▼❝☛❍➁✄❸ ✂ ✕ ↕ ✕ ➯ ✕P ✑P✬
✟
✕✛ ➯ ✶✕ ✕P
Auspices Statement
This work was performed under the auspices of the U.S. Department of Energy by University
of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.