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r trs r tr ts t t t tt t t r t r r r ts r r

  1. ▲✐♥❡❛r ❋✐❧t❡rs ✎ ❆ ❧✐♥❡❛r ☞❧t❡r t❛❦❡s ✐♥♣✉t ① t ✐♥t♦ ♦✉t♣✉t ② t ✿ ✶ ❳ ② t ❂ ❛ r ① t � r r ❂ �✶ ❢♦r ❝♦❡✍❝✐❡♥ts ❛ r ❀ �✶ ❁ r ❁ ✶ ✳ ✎ ■❢ t❤❡ ✐♥♣✉t ✐s ❛ ✉♥✐t ✐♠♣✉❧s❡ ❛t t ❂ ✵✱ ✽ ✶ t ❂ ✵ ❁ ① t ❂ ✵ t ✻ ❂ ✵ ❀ ✿ t❤❡ ♦✉t♣✉t ✐s ② t ❂ ❛ t ✱ s♦ t❤❡ ❝♦❡✍❝✐❡♥ts ❛r❡ ❝❛❧❧❡❞ t❤❡ ✐♠♣✉❧s❡ r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ☞❧t❡r✳ ✶

  2. ✎ ❋♦r ❡①❛♠♣❧❡✱ ✇✐t❤ ❛ ✶ ❂ ✶ ❀ ❛ ✷ ❂ ✵ ✿ ✺ ❀ ❛ ✸ ❂ � ✵ ✿ ✷ ❛♥❞ ❛ r ❂ ✵ ♦t❤❡r✇✐s❡✿ ♣❛r✭♠❢r♦✇ ❂ ❝✭✷✱ ✶✮✮ ① ❂ ts✭r❡♣✭✵✱ ✷✵✮✱ st❛rt ❂ ✲✺✮ ①❬t✐♠❡✭①✮ ❂❂ ✵❪ ❂ ✶ ♣❧♦t✭①✱ t②♣❡ ❂ ✧❜✧✮ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❝♦❧ ❂ ✧r❡❞✧✱ ❧t② ❂ ✷✮ ② ❂ ❢✐❧t❡r✭①✱ ❝✭✵✱ ✶✱ ✵✳✺✱ ✲✵✳✷✮✱ s✐❞❡s ❂ ✶✮ ♣❧♦t✭②✱ t②♣❡ ❂ ✧❜✧✮ ❛❜❧✐♥❡✭❤ ❂ ✵✱ ❝♦❧ ❂ ✧r❡❞✧✱ ❧t② ❂ ✷✮ ✎ ■❢✱ ❛s ❤❡r❡✱ ❛ r ❂ ✵ ❢♦r r ❁ ✵✱ t❤❡ ☞❧t❡r ✐s r❡❛❧✲t✐♠❡ ✱ ♦r ❝❛✉s❛❧ ✱ ♦r r❡❛❧✐③❛❜❧❡ ✳ ✷

  3. ✎ ■❢ t❤❡ ✐♥♣✉t ✐s ❛ ✭❝♦♠♣❧❡①✮ ❝♦s✐♥❡ ✇❛✈❡✱ ① t ❂ ❘❡ ✐ ✭✷ ✙✦t ✰ ✣ ✮ ❀ t❤❡ ♦✉t♣✉t ✐s ✶ ❛ r ❘❡ ✐ ❬✷ ✙✦ ✭ t � r ✮✰ ✣ ❪ ❳ ② t ❂ r ❂ �✶ ✶ ❛ r ❡ � ✷ ✙✐✦r ❳ ❂ ① t r ❂ �✶ ❂ ① t ❆ ✭ ✦ ✮ ❀ ✇❤❡r❡ ✶ ❛ r ❡ � ✷ ✙✐✦r ❳ ❆ ✭ ✦ ✮ ❂ r ❂ �✶ ✐s ❝❛❧❧❡❞ t❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ♦❢ t❤❡ ☞❧t❡r✳ ✸

  4. ✎ ❙❛♠❡ ❡①❛♠♣❧❡✿ ★ ❢✐❧t❡r✭✮ ❞♦❡s ♥♦t ✇♦r❦ ❢♦r ❝♦♠♣❧❡① ✐♥♣✉t✿ ❢✐❧t❡r✳❝♦♠♣❧❡① ❂ ❢✉♥❝t✐♦♥✭①✱ ✳✳✳✮ ④ ❝♦♠♣❧❡①✭r❡❛❧ ❂ ❢✐❧t❡r✭❘❡✭①✮✱ ✳✳✳✮✱ ✐♠❛❣ ❂ ❢✐❧t❡r✭■♠✭①✮✱ ✳✳✳✮✮ ⑥ ❘ ❂ ✷ ♦♠❡❣❛ ❂ ✵✳✷ ♣❤✐ ❂ ✶ ① ❂ ❘ ✯ ❡①♣✭✶✐ ✯ ✭✷ ✯ ♣✐ ✯ ♦♠❡❣❛ ✯ t✐♠❡✭①✮ ✰ ♣❤✐✮✮ ② ❂ ❢✐❧t❡r✳❝♦♠♣❧❡①✭①✱ ❝✭✵✱ ✶✱ ✵✳✺✱ ✲✵✳✷✮✱ s✐❞❡s ❂ ✶✮ ② ✴ ① ✎ ❙♦ ❆ ✭✵ ✿ ✷✮ ❂ ✵ ✿ ✵✻✻✸✶✷ � ✶ ✿ ✸✻✷✺✵✻ ✐ ✳ ✹

  5. ❇❛❝❦s❤✐❢t ❖♣❡r❛t♦r ✎ ❚❤❡ ☞❧t❡r ❝❛♥ ❜❡ ✇r✐tt❡♥ ✶ ✶ ❛ r ❇ r ① t ❳ ❳ ② t ❂ ❛ r ① t � r ❂ r ❂ �✶ r ❂ �✶ ❂ ❛ ✭ ❇ ✮ ① t ❀ ✇❤❡r❡ ✶ ❛ r ❇ r ✿ ❳ ❛ ✭ ❇ ✮ ❂ r ❂ �✶ ✎ ❚❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✐s ✏ ❡ � ✷ ✙✐✦ ✑ ❆ ✭ ✦ ✮ ❂ ❛ ✿ ✺

  6. ●❛✐♥ ❛♥❞ P❤❛s❡ ✎ ❚❤❡ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✐♥ ♣♦❧❛r ❝♦♦r❞✐♥❛t❡s✿ ❆ ✭ ✦ ✮ ❂ ❥ ❆ ✭ ✦ ✮ ❥ ❡①♣ ❢� ✐✣ ✭ ✦ ✮ ❣ ✿ ✎ ❥ ❆ ✭ ✦ ✮ ❥ ✐s t❤❡ ❣❛✐♥ ❢✉♥❝t✐♦♥ ✭♦r ❛♠♣❧✐t✉❞❡✮✳ ✎ ✣ ✭ ✦ ✮ ✐s t❤❡ ♣❤❛s❡ ❢✉♥❝t✐♦♥ ✳ ✎ ❊✳❣✳ ❞❡❧❛②✿ ② t ❂ ❆① t � ❉ ❀ ❆ ❃ ✵ ❀ ✮ ❆ ✭ ✦ ✮ ❂ ❆❡ � ✷ ✙✐❉✦ ✱ s♦ ④ ❣❛✐♥ ❂ ❆ ✱ ❝♦♥st❛♥t✱ ④ ♣❤❛s❡ ❂ ✷ ✙❉✦ ✱ ❧✐♥❡❛r ✐♥ ✦ ✇✐t❤ s❧♦♣❡ ✷ ✙❉ ✳ ✻

  7. ❚②♣❡s ♦❢ ❋✐❧t❡r ✎ ■❢ ♠ ❳ ② t ❂ ❛ r ① t � r r ❂✵ t❤❡ ☞❧t❡r ✐s ❛ ❋✐♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡ ✭❋■❘✮ ☞❧t❡r✳ ✎ ■❢ ♠ ❂ ✶ ✐t ✐s ❛♥ ■♥☞♥✐t❡ ■♠♣✉❧s❡ ❘❡s♣♦♥s❡ ✭■■❘✮ ☞❧t❡r✳ ✎ ❙♦♠❡ ■■❘ ☞❧t❡rs ❛r❡ r❡❝✉rs✐✈❡ ✿ ♠ ❳ ② t ❂ ❛ ✵ ① t ✰ ❜ r ② t � r ✿ r ❂✶ ✼

  8. ❆❘▼❆ ♠♦❞❡❧s ✎ ■❢ ① t ✐s ✇❤✐t❡ ♥♦✐s❡ ❛♥❞ t❤❡ ☞❧t❡r ✐s ❋■❘✱ ② t ✐s ▼❆✭ ♠ ✮✳ ✎ ■❢ ① t ✐s ✇❤✐t❡ ♥♦✐s❡ ❛♥❞ t❤❡ ☞❧t❡r ✐s r❡❝✉rs✐✈❡✱ ② t ✐s ❆❘✭ ♠ ✮✳ ✎ ●❡♥❡r❛❧ ❆❘▼❆ ✐s t❤❡ ♦✉t♣✉t ♦❢ ❛ ❝♦♠❜✐♥❡❞ ☞❧t❡r ❛♣♣❧✐❡❞ t♦ ✇❤✐t❡ ♥♦✐s❡✱ ✇✐t❤ ❛♥ ❋■❘ ☞❧t❡r ❢♦❧❧♦✇❡❞ ❜② ❛ r❡❝✉rs✐✈❡ ☞❧t❡r✳ ✽

  9. ❖✉t♣✉t ❙♣❡❝tr✉♠ ✎ ■❢ t❤❡ ✐♥♣✉t ✐s ❛♥② st❛t✐♦♥❛r② ♣r♦❝❡ss ✇✐t❤ ❛✉t♦❝♦✈❛r✐❛♥❝❡s ✌ ①① ✭ ❤ ✮✱ t❤❡ ❝♦✈❛r✐❛♥❝❡s ♦❢ t❤❡ ♦✉t♣✉t ❛r❡ ✥❳ ✦ ✏ ✑ ❳ ❝♦✈ ② t ✰ ❤ ❀ ② t ❂ ❝♦✈ ❛ r ① t ✰ ❤ � r ❀ ❛ s ① t � s r s ✏ ✑ ❳ ❳ ❂ ❛ r ❛ s ❝♦✈ ① t ✰ ❤ � r ❀ ① t � s r s ❳ ❳ ❂ ❛ r ❛ s ✌ ①① ✭ ❤ � r ✰ s ✮ ✿ r s ✎ ❚❤✐s ❞♦❡s ♥♦t ❞❡♣❡♥❞ ♦♥ t ✱ s♦ ❢ ② t ❣ ✐s ✇❡❛❦❧② st❛t✐♦♥❛r② ✇✐t❤ ❳ ❳ ✌ ②② ✭ ❤ ✮ ❂ ❛ r ❛ s ✌ ①① ✭ ❤ � r ✰ s ✮ ✿ r s ✾

  10. ✎ ❙♦ t❤❡ ♣♦✇❡r s♣❡❝tr❛❧ ❞❡♥s✐t② ♦❢ ❢ ② t ❣ ✐s ✌ ②② ✭ ❤ ✮ ❡ � ✷ ✙✐✦❤ ❳ ❢ ②② ✭ ✦ ✮ ❂ ❤ ❛ r ❛ s ✌ ①① ✭ ❤ � r ✰ s ✮ ❡ � ✷ ✙✐✦❤ ❳ ❳ ❳ ❂ r s ❤ ✥❳ ✦ ✥❳ ✦ ❛ r ❡ � ✷ ✙✐✦r ❛ s ❡ ✰✷ ✙✐✦s ❂ r s ✷ ✸ ✌ ①① ✭ ❤ � r ✰ s ✮ ❡ � ✷ ✙✐✦ ✭ ❤ � r ✰ s ✮ ✹❳ ✂ ✺ ❤ ❂ ❥ ❆ ✭ ✦ ✮ ❥ ✷ ❢ ①① ✭ ✦ ✮ ✿ ✎ ■♥ ✇♦r❞s✱ ♦✉t♣✉t s♣❡❝tr✉♠ ❂ ✐♥♣✉t s♣❡❝tr✉♠ ✂ sq✉❛r❡❞ ❣❛✐♥ ✿ ✶✵

  11. ✎ ❲❡ ❝❛♥ ❛❧s♦ ❝♦♠♣✉t❡ t❤❡ ❝r♦ss ❝♦✈❛r✐❛♥❝❡ ✌ ①② ✭ ❤ ✮✿ ✥ ✦ ✏ ✑ ❳ ❝♦✈ ① t ✰ ❤ ❀ ② t ❂ ❝♦✈ ① t ✰ ❤ ❀ ❛ s ① t � s s ✏ ✑ ❳ ❂ ❛ s ❝♦✈ ① t ✰ ❤ ❀ ① t � s s ❳ ❂ ❛ s ✌ ①① ✭ ❤ ✰ s ✮ ✿ s ✎ ❚❤✐s t♦♦ ❞♦❡s ♥♦t ❞❡♣❡♥❞ ♦♥ t ✱ s♦ ❢ ① t ❣ ❛♥❞ ❢ ② t ❣ ❛r❡ ❥♦✐♥t❧② st❛t✐♦♥❛r② ✇✐t❤ ❳ ✌ ①② ✭ ❤ ✮ ❂ ❛ s ✌ ①① ✭ ❤ ✰ s ✮ ✿ s ✶✶

  12. ✎ ❙♦ t❤❡ ❝r♦ss s♣❡❝tr❛❧ ❞❡♥s✐t② ✐s ✌ ①② ✭ ❤ ✮ ❡ � ✷ ✙✐✦❤ ❳ ❢ ①② ✭ ✦ ✮ ❂ ❤ ❛ s ✌ ①① ✭ ❤ ✰ s ✮ ❡ � ✷ ✙✐✦❤ ❳ ❳ ❂ s ❤ ✷ ✸ ✧❳ ★ ❛ s ❡ ✷ ✙✐✦s ✌ ①① ✭ ❤ ✰ s ✮ ❡ � ✷ ✙✐✦ ✭ ❤ ✰ s ✮ ✹❳ ❂ ✂ ✺ s ❤ ❂ ❆ ✭ ✦ ✮ ❢ ①① ✭ ✦ ✮ ✿ ✎ ❙✐♠✐❧❛r❧②✱ ❢ ②① ✭ ✦ ✮ ❂ ❆ ✭ ✦ ✮ ❢ ①① ✭ ✦ ✮✱ ♦r ✐♥ ✇♦r❞s✱ ❝r♦ss s♣❡❝tr✉♠ ❂ ✐♥♣✉t s♣❡❝tr✉♠ ✂ ❢r❡q✉❡♥❝② r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥ ✿ ✶✷

  13. ✎ ◆♦t❡ t❤❛t t❤❡ sq✉❛r❡❞ ❝♦❤❡r❡♥❝② ✐s ❥ ❢ ②① ✭ ✦ ✮ ❥ ✷ ✚ ✷ ②✿① ✭ ✦ ✮ ❂ ❢ ①① ✭ ✦ ✮ ❢ ②② ✭ ✦ ✮ ❥ ❆ ✭ ✦ ✮ ❢ ①① ✭ ✦ ✮ ❥ ✷ ❂ ❢ ①① ✭ ✦ ✮ ❥ ❆ ✭ ✦ ✮ ❥ ✷ ❢ ①① ✭ ✦ ✮ ❂ ✶ ❢♦r ❡✈❡r② ❢r❡q✉❡♥❝② ✦ ✳ ✎ ❚❤❛t ✐s✱ ✐❢ ♦♥❡ s❡r✐❡s ✐s ❛ ☞❧t❡r❡❞ ✈❡rs✐♦♥ ♦❢ ❛♥♦t❤❡r✱ t❤❡✐r sq✉❛r❡❞ ❝♦❤❡r❡♥❝② ✐s ✶ ❛t ❛❧❧ ❢r❡q✉❡♥❝✐❡s✳ ✎ ❚❤❡ ❝♦♥✈❡rs❡ ✐s ❛❧s♦ tr✉❡✳ ✶✸

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