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  1. ▼❛r❦♦✈ ❝❤❛✐♥ ❛♣♣r♦①✐♠❛t✐♦♥s t♦ ♥♦♥✲s②♠♠❡tr✐❝ ❞✐☛✉s✐♦♥s ✇✐t❤ ❜♦✉♥❞❡❞ ❝♦❡✍❝✐❡♥ts ❏❡❛♥✲❉♦♠✐♥✐q✉❡ ❉❡✉s❝❤❡❧✱ ❚❯ ❇❡r❧✐♥ ❏♦✐♥t ✇♦r❦ ✇✐t❤ ❚❛❦❛s❤✐ ❑✉♠❛❣❛✐ ✭❑②♦t♦✮ ❤tt♣✿✴✴✇✇✇✳❦✉r✐♠s✳❦②♦t♦✲✉✳❛❝✳❥♣✴⑦❦✉♠❛❣❛✐ t♦ ❛♣♣❡❛r ✐♥ ❈♦♠♠✉♥✐❝❛t✐♦♥s P✉r❡ ❆♣♣❧✐❡❞ ▼❛t❤✳ ✷✵✶✷ ✺ ❉❡❝❡♠❜❡r ✷✵✶✶✱ ❑♦❝❤✐

  2. ✶ ■♥tr♦❞✉❝t✐♦♥ ❉✐☛✉s✐♦♥s ✐♥ ❞✐✈❡r❣❡♥❝❡ ❢♦r♠ ▲ ❣❡♥❡r❛t♦r ♦❢ ❞✐☛✉s✐♦♥ ✐♥ ❞✐✈❡r❣❡♥❝❡ ❢♦r♠ ❞ ✏ ✑ ❳ ❛ ✐❀❥ ✭ ① ✮ ❅ ① ❥ ❋ ✭ ① ✮ ▲ ❋ ✭ ① ✮ ❂ ❅ ① ✐ ✐❀❥ ❂✶ ❉✐r✐❝❤❧❡t ❢♦r♠ ❩ ❳ ❘ ❞ ❅ ① ✐ ❋ ✭ ① ✮ ❛ ✐❀❥ ✭ ① ✮ ❅ ① ❥ ● ✭ ① ✮ ❞① ✡ ☛ ❊ ✭ ❋❀ ● ✮ ❂ ✭ �▲ ❋ ✮ ❀ ● ❂ ✐❀❥ ❆❞❥♦✐♥t ▲ ✄ ✇✐t❤ ✭ ❛ ✐❀❥ ✭ ① ✮✮ ✄ ❂ ❛ ❥❀✐ ✭ ① ✮ ❀ ✭ �▲ ✄ ❋ ✮ ❀ ● ✡ ☛ ✡ ☛ ✿❂ ❋❀ ✭ �▲ ● ✮ ✳ ❇♦✉♥❞❡❞ ❛♥❞ ❯♥✐❢♦r♠ ❡❧❧✐♣t✐❝✿ ✾ ▼❀ ✍ ❃ ✵ s✳t✳ ❆ss✉♠♣t✐♦♥ ❳ ❥ ❛ ✐❀❥ ✭ ① ✮ ❥ ✔ ▼❀ ☛ ✐ ❛ ✐❀❥ ✭ ① ✮ ☛ ❥ ✕ ✍ ❀ ✽ ☛❀ ① ✷ ❘ ❞ ✿ ✡ ☛ ✡ ☛ ☛❀ ❛ ✭ ① ✮ ☛ ❂ ☛❀ ☛ ✐❀❥ ✮ ●❛✉ss✐❛♥✲t②♣❡ ❤❡❛t ❦❡r♥❡❧ ❡st✐♠❛t❡s ❛♥❞ ❍⑧ ♦❧❞❡r ❝♦♥t✳ ✭❆r♦♥s♦♥ ✬✻✼✮ ❛❧s♦ t❤❡ s❡❝t♦r ✑ ✷ ✏ ❝♦♥❞✐t✐♦♥ ❊ ✭ ❋❀ ● ✮ ✔ ❑ ❊ ✭ ❋❀ ❋ ✮ ❊ ✭ ●❀ ● ✮

  3. ▲❡t ❙ ♥ ❂ ♥ � ✶ ❩ ❞ ✳ ✭◗✶✮ ❘❛♥❞♦♠ ✇❛❧❦ ❛♣♣r♦①✐♠❛t✐♦♥ ♦❢ t❤❡ ❞✐✈✳ ❢♦r♠ ❜② ▼❈s✳ ✭◗✷✮ ●✐✈❡ ❝♦♥❞✐t✐♦♥ ❢♦r ▼❈s ❢ ❨ ✭ ♥ ✮ ❣ t ✕ ✵ ♦♥ ❙ ♥ t♦ ❝♦♥✈❡r❣❡ ✇❡❛❦❧② t♦ t❤❡ ❞✐✈✳ ❢♦r♠✳ t

  4. ❙②♠♠❡tr✐❝ ❝❛s❡ ❛ ✐❀❥ ✭ ① ✮ ❂ ❛ ❥❀✐ ✭ ① ✮ ✎ ✭◗✶✮ ✇❛s ❛♥s✇❡r❡❞ ❜② ❙tr♦♦❝❦✲❩❤❡♥❣ ✭✬✾✼✱ ❆■❍P✮ ❝♦♠♣❧❡t❡❧②✳ ◆❛♠❡❧②✱ t❤❡② ❝♦♥str✉❝t ✭ ❨ ✭ ♥ ✮ � ✁ ✮ t ✕ ✵ ♦♥ ❙ ♥ ✇✐t❤ ❣❡♥❡r❛t♦r ▲ ♥ ❋ ✭ ① ✮ ❂ P ② ✷❙ ♥ q ♥ ✭ ①❀ ② ✮ ❋ ✭ ② ✮ � ❋ ✭ ① ✮ s✳t✳ t ✮ ✭ ❳ t ✮ t ✷ ❬✵ ❀❚ ❪ ❀ ♣ ♥ ✭ t❀ ①❀ ② ✮ ❂ P ① ✭ ❨ ✭ ♥ ✮ ❂ ② ✮ ✭ ❨ ✭ ♥ ✮ t ✮ t ✷ ❬✵ ❀❚ ❪ ❂ ✦ ♣ ✭ t❀ ①❀ ② ✮ t ♥ � ❞ ✎ ✭◗✷✮ ✇❛s ❛♥s✇❡r❡❞ ❜② ❇❛ss✲❑ ✭✬✵✽✱ ❚❆▼❙✮ ❢♦r t❤❡ ✉♥❜♦✉♥❞❡❞ r❛♥❣❡ ❝❛s❡✳ ✭❇❛ss✲❑✲❯❡♠✉r❛ ✭✬✶✵✱ P❚❘❋✮ ❢♦r t❤❡ ❝♦♥✈❡r❣❡♥❝❡ t♦ ❞✐✈✳✰❥✉♠♣✮ ❖✉r ❣♦❛❧ ❚♦ ❛♥s✇❡r ✭◗✶✮ ❛♥❞ ✭◗✷✮ ❢♦r t❤❡ ❝❧❛ss ♦❢ ♥♦♥✲s②♠♠❡tr✐❝ ❞✐✈✳ ❢♦r♠s✳

  5. ✷ ❍❡❛t ❦❡r♥❡❧ ❡st✐♠❛t❡s ❢♦r ❝❡♥t❡r❡❞ ❘❛♥❞♦♠ ❲❛❧❦s ❈♦♥s✐❞❡r ☞rst ❛♥ ✐rr❡❞✉❝✐❜❧❡ ❝❤❛✐♥ ✭ ❳ ♥ ✮ ♦♥ ❛ ☞♥✐t❡ s❡t✳ ▲❡t ✗ ✭ ① ✮ ❃ ✵ ❜❡ t❤❡ ✉♥✐q✉❡ ✐♥✈❛r✐❛♥t ♠❡❛s✉r❡✳ ❚❤❡♥ ✇❡ ❤❛✈❡ ❛ ❝②❝❧❡ ❞❡❝♦♠♣♦s✐t✐♦♥ ♦❢ t❤❡ ❝❤❛✐♥ ❞✉❡ t♦ ❇✐r❦❤♦☛✿ � ✐s ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ ♦r✐❡♥t❡❞ ❝②❝❧❡s ✌ ❂ ✭ ① ✵ ❀ ① ✶ ❀ ✿✿✿❀ ① ❵ ✭ ✌ ✮ ❂ ① ✵ ✮ ❵ ✭ ✌ ✮ ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❝②❝❧❡ ❛♥❞ ☛ ✭ ✌ ✮ ✕ ✵ ✐s t❤❡ ✇❡✐❣❤t ♦❢ t❤❡ ❝②❝❧❡ ✌ s✉❝❤ t❤❛t ❛ ✭ ①❀ ② ✮ ✶ ❳ P ✭ ❳ ♥ ✰✶ ❂ ② ❥ ❳ ♥ ❂ ① ✮ ❂ ② ✿ ② ✻ ❂ ① ❛ ✭ ①❀ ② ✮ ❀ ✇❤❡r❡ ❛ ✭ ①❀ ② ✮ ✿❂ ☛ ✭ ✌ ✮✶ ❢ ✭ ①❀② ✮ ✷ ✌ ❣ ✿ P ✗ ✭ ① ✮ ✌ ❚❤❡ ❉✐r✐❝❤❧❡t ❢♦r♠ ❳ ✡ ☛ ❊ ✭ ❋❀ ● ✮ ❂ ✭ �▲ ❋ ✮ ❀ ● ✗ ❂ ☛ ✭ ✌ ✮ ❊ ✌ ✭ ❋❀ ● ✮ ✌

  6. ✇❤❡r❡ ❳ ❳ � ✁ � ✁� ✁ ❊ ✌ ✭ ❋❀ ● ✮ ❂ ❋ ✭ ① ✐ ✮ � ❋ ✭ ① ✐ ✰✶ ✮ ● ✭ ① ✐ ✮ ❂ ❋ ✭ ① ✐ ✮ � ❋ ✭ ① ✐ ✰✶ ✮ ● ✭ ① ✐ ✮ � ● ✭ ① ✵ ✮ ✿ ① ✐ ① ✐ ❚❤❡ ❛❞❥♦✐♥t ▲ ✐s ❞❡☞♥❡❞ ✇✐t❤ t❤❡ r❡✈❡rs❡❞ ❝②❝❧❡s✿ ✌ ✄ ❂ ✭ ① ❵ ❀ ① ❵ � ✶ ❀ ✿✿✿❀ ① ✵ ❂ ① ❵ ✮ ✿ ▲ ✄ ❂ ▲ ✐❢ ❛♥❞ ♦♥❧② ✐❢ ❵ ✭ ✌ ✮ ✔ ✷ ✿ ❋♦r ❡①❛♠♣❧❡ ❝♦♥s✐❞❡r t❤❡ r❛♥❞♦♠ ✇❛❧❦ ♦♥ t❤❡ t♦r✉s ❚ ◆ ♦❢ ❧❡♥❣t❤ ◆ ✿ P ✭ ❳ ✶ ❂ ① ✰ ✶ ❥ ❳ ✵ ❂ ① ✮ ❂ ♣❀ P ✭ ❳ ✶ ❂ ① � ✶ ❥ ❳ ✵ ❂ ① ✮ ❂ q ❆ss✉♠✐♥❣ ♣ ❃ q ✱ ✇❡ ❤❛✈❡ t❤❡ t✇♦ ❝②❝❧❡s ❢ ✌ ✭ ① ✮ ❂ ✭ ①❀ ① ✰✶ ❀ ① ✮ ❣ ❀ ① ✷ ❚ ◆ ✱ ✇✐t❤ ☛ ✭ ✌ ✭ ① ✮✮ ❂ q ❛♥❞ t❤❡ ◆ ❝②❝❧❡ ✖ ✌ ◆ ❂ ✭✵ ❀ ✶ ❀ ✷ ❀ ✿✿✿❀ ◆ � ✶✮ ✇✐t❤ ☛ ✭✖ ✌ ◆ ✮ ❂ ♣ � q✿

  7. ❖♥ t❤❡ ✐♥☞♥✐t❡ ❙ ♥ ✱ � ♥ ❛ ❝♦❧❧❡❝t✐♦♥ ♦❢ ✭♦r✐❡♥t❡❞✮ ☞♥✐t❡ ❝②❝❧❡s ✐♥ ❙ ♥ ✿ ✌ ♥ ❂ ✭ ① ✵ ❀ ① ✶ ❀ ✿✿✿❀ ① ❵ ✭ ✌ ♥ ✮ ❂ ① ✵ ✮ ☛ ♥ ✭ ✌ ♥ ✮ ✕ ✵ ✐s t❤❡ ✇❡✐❣❤t ♦❢ t❤❡ ❝②❝❧❡ ✌ ♥ ❉❡☞♥❡ t❤❡ ▼❛r❦♦✈ ❝❤❛✐♥ ❢ ❳ ✭ ♥ ✮ ✿ ❦ ❂ ✵ ❀ ✶ ❀ ✷ ❀ ✁ ✁ ✁ ❣ ❜② ❦ ❛ ♥ ✭ ①❀ ② ✮ P ① ✭ ❳ ✭ ♥ ✮ ❳ ❂ ② ✮ ❂ ② ✿ ② ✻ ❂ ① ❛ ♥ ✭ ①❀ ② ✮ ❀ ✇❤❡r❡ ❛ ♥ ✭ ①❀ ② ✮ ✿❂ ☛ ♥ ✭ ✌ ♥ ✮✶ ❢ ✭ ①❀② ✮ ✷ ✌ ♥ ❣ ✿ ✶ P ✌ ♥ ❚❤❡ ✭s❝❛❧❡❞✮ ❉✐r✐❝❤❧❡t ❢♦r♠ ✗ ♥ ❂ ♥ ✷ � ❞ ❳ ✭ �▲ ♥ ❋ ✮ ❀ ● ✡ ☛ ❊ ♥ ✭ ❋❀ ● ✮ ❂ ☛ ♥ ✭ ✌ ♥ ✮ ❊ ✌ ♥ ✭ ❋❀ ● ✮ ✌ ♥ ✇❤❡r❡ ✗ ♥ ✭ ① ✮ ✿❂ ♥ � ❞ ✭❢♦r s✐♠♣❧✐❝✐t②✮ ❛♥❞ ❳ � ✁� ✁ ❊ ✌ ♥ ✭ ❋❀ ● ✮ ❂ ❋ ✭ ① ✐ ✮ � ❋ ✭ ① ✐ ✰✶ ✮ ● ✭ ① ✐ ✮ � ● ✭ ① ✵ ✮ ✿ ① ✐ ❢ ❨ ✭ ♥ ✮ ✿ t ✕ ✵ ❣ ❝♦rr❡s♣♦♥❞✐♥❣ ✭❝♦♥t✳ t✐♠❡✱ s❝❛❧❡❞✮ ▼❈✳ t ▲❡t ❘❛♥❣❡✭ ✌ ♥ ✮ ❂ ♠❛① ❢❥ ① ✐ � ① ✐ ✰✶ ❥ ✿ ① ✐ ✷ ✌ ♥ ❣ ❜❡ t❤❡ r❛♥❣❡ ♦❢ t❤❡ ❝②❝❧❡ ✌ ♥ ✳

  8. ❆ss✉♠♣t✐♦♥ ❆ ✐✮ ❇♦✉♥❞❡❞ ❧❡♥❣t❤✱ ❜♦✉♥❞❡❞ ✇❡✐❣❤ts ❛♥❞ ❜♦✉♥❞❡❞ r❛♥❣❡✿ ❵ ✭ ✌ ♥ ✮ ✔ ▼❀ ☛ ♥ ✭ ✌ ♥ ✮ ✔ ▼❀ ❘❛♥❣❡✭ ✌ ♥ ✮ ✔ ❘❂♥✿ ✐✐✮ ❯♥✐❢♦r♠ ✐rr❡❞✉❝✐❜✐❧✐t②✿ ✾ ◆❀ ✍ ✶ ❀ ✍ ✷ s✳t✳ ✽ ① ✷ ❙ ♥ ❀ ❡ ✷ ❩ ❞ ✇✐t❤ ❥ ❡ ❥ ❂ ✶✱ P ① ✭ ❳ ✭ ♥ ✮ ❳ ❂ ① ✝ ❡❂♥ ✮ ✕ ✍ ✶ ❢♦r ✾ ❦ ❂ ❦ ✭ ①❀ ✝ ❡ ✮ ✔ ◆❀ ❛ ♥ ✭ ①❀ ② ✮ ✕ ✍ ✷ ✿ ❦ ② ✿ ② ✻ ❂ ① ✮ t❤❡ s❡❝t♦r ❝♦♥❞✐t✐♦♥ ✑ ✷ ✏ ❊ ♥ ✭ ❋❀ ● ✮ ✔ ❑ ❊ ♥ ✭ ❋❀ ❋ ✮ ❊ ♥ ✭ ●❀ ● ✮

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