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  1. ▼❚❆❚✳✵✺✳✶✵✺ ❚②♣❡ ❚❤❡♦r② ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❡♥❝❡

  2. ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❡♥❝❡ ❈✉rr②✲❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❡♥❝❡ ✭ ❡♥✳✇✐❦✐♣❡❞✐❛✳♦r❣ ✮ ❚❤❡ ❈✉rr②④❍♦✇❛r❞ ❝♦rr❡s♣♦♥❞❡♥❝❡ ✐s t❤❡ ❞✐r❡❝t r❡❧❛t✐♦♥s❤✐♣ ❜❡t✇❡❡♥ ❝♦♠♣✉t❡r ♣r♦❣r❛♠s ❛♥❞ ♣r♦♦❢s ✐♥ ❝♦♥str✉❝t✐✈❡ ♠❛t❤❡✲ ♠❛t✐❝s✳ ❆❧s♦ ❦♥♦✇♥ ❛s ❈✉rr②④❍♦✇❛r❞ ✐s♦♠♦r♣❤✐s♠✱ ♣r♦♦❢s✲❛s✲ ♣r♦❣r❛♠s ❝♦rr❡s♣♦♥❞❡♥❝❡ ❛♥❞ ❢♦r♠✉❧❛❡✲❛s✲t②♣❡s ❝♦rr❡s♣♦♥❞❡♥❝❡✱ ✐t r❡❢❡rs t♦ t❤❡ ❣❡♥❡r❛❧✐③❛t✐♦♥ ♦❢ ❛ s②♥t❛❝t✐❝ ❛♥❛❧♦❣② ❜❡t✇❡❡♥ s②s✲ t❡♠s ♦❢ ❢♦r♠❛❧ ❧♦❣✐❝ ❛♥❞ ❝♦♠♣✉t❛t✐♦♥❛❧ ❝❛❧❝✉❧✐ t❤❛t ✇❛s ☞rst ❞✐s❝♦✈❡r❡❞ ❜② t❤❡ ❆♠❡r✐❝❛♥ ♠❛t❤❡♠❛t✐❝✐❛♥ ❍❛s❦❡❧❧ ❈✉rr② ❛♥❞ ❧♦❣✐❝✐❛♥ ❲✐❧❧✐❛♠ ❆❧✈✐♥ ❍♦✇❛r❞✳

  3. ❈❧❛ss✐❝❛❧ ✈s✳ ❝♦♥str✉❝t✐✈❡ ❧♦❣✐❝ ❈❧❛ss✐❝❛❧ ❧♦❣✐❝ ❊✈❡r② ♣r♦♣♦s✐t✐♦♥ ✐s ❡✐t❤❡r tr✉❡ ♦r ❢❛❧s❡✳ ❈♦♥❝❡r♥❡❞ ✇✐t❤✿ ✧❲❤❡t❤❡r ❛ ❣✐✈❡♥ ♣r♦♣♦s✐t✐♦♥ ✐s tr✉❡ ♦r ♥♦t❄✧ ❈♦♥str✉❝t✐✈❡ ❧♦❣✐❝ Pr♦♣♦s✐t✐♦♥ ✐s tr✉❡ ♦♥❧② ✐❢ ✇❡ ❝❛♥ ♣r♦✈❡ ✐t✳ ❈♦♥❝❡r♥❡❞ ✇✐t❤✿ ✧❍♦✇ ❛ ❣✐✈❡♥ ♣r♦♣♦s✐t✐♦♥ ❜❡❝♦♠❡s tr✉❡❄✧ ❈❧❛ss✐❝❛❧ t❛✉t♦❧♦❣✐❡s ♥♦t ♣r♦✈❛❜❧❡ ❝♦♥str✉❝t✐✈❡❧② ❆ ❴ ✿ ❆ ✿✿ ❆ ✛ ❆ ✭✭ ❆ ✛ ❇ ✮ ✛ ❆ ✮ ✛ ❆

  4. ❈❧❛ss✐❝❛❧ ✈s✳ ❝♦♥str✉❝t✐✈❡ ❧♦❣✐❝ ❈❧❛ss✐❝❛❧ ❧♦❣✐❝ ❊✈❡r② ♣r♦♣♦s✐t✐♦♥ ✐s ❡✐t❤❡r tr✉❡ ♦r ❢❛❧s❡✳ ❈♦♥❝❡r♥❡❞ ✇✐t❤✿ ✧❲❤❡t❤❡r ❛ ❣✐✈❡♥ ♣r♦♣♦s✐t✐♦♥ ✐s tr✉❡ ♦r ♥♦t❄✧ ❈♦♥str✉❝t✐✈❡ ❧♦❣✐❝ Pr♦♣♦s✐t✐♦♥ ✐s tr✉❡ ♦♥❧② ✐❢ ✇❡ ❝❛♥ ♣r♦✈❡ ✐t✳ ❈♦♥❝❡r♥❡❞ ✇✐t❤✿ ✧❍♦✇ ❛ ❣✐✈❡♥ ♣r♦♣♦s✐t✐♦♥ ❜❡❝♦♠❡s tr✉❡❄✧ ❈❧❛ss✐❝❛❧ t❛✉t♦❧♦❣✐❡s ♥♦t ♣r♦✈❛❜❧❡ ❝♦♥str✉❝t✐✈❡❧② ❆ ❴ ✿ ❆ ✿✿ ❆ ✛ ❆ ✭✭ ❆ ✛ ❇ ✮ ✛ ❆ ✮ ✛ ❆

  5. ❈❧❛ss✐❝❛❧ ✈s✳ ❝♦♥str✉❝t✐✈❡ ❧♦❣✐❝ ❈❧❛ss✐❝❛❧ ❧♦❣✐❝ ❊✈❡r② ♣r♦♣♦s✐t✐♦♥ ✐s ❡✐t❤❡r tr✉❡ ♦r ❢❛❧s❡✳ ❈♦♥❝❡r♥❡❞ ✇✐t❤✿ ✧❲❤❡t❤❡r ❛ ❣✐✈❡♥ ♣r♦♣♦s✐t✐♦♥ ✐s tr✉❡ ♦r ♥♦t❄✧ ❈♦♥str✉❝t✐✈❡ ❧♦❣✐❝ Pr♦♣♦s✐t✐♦♥ ✐s tr✉❡ ♦♥❧② ✐❢ ✇❡ ❝❛♥ ♣r♦✈❡ ✐t✳ ❈♦♥❝❡r♥❡❞ ✇✐t❤✿ ✧❍♦✇ ❛ ❣✐✈❡♥ ♣r♦♣♦s✐t✐♦♥ ❜❡❝♦♠❡s tr✉❡❄✧ ❈❧❛ss✐❝❛❧ t❛✉t♦❧♦❣✐❡s ♥♦t ♣r♦✈❛❜❧❡ ❝♦♥str✉❝t✐✈❡❧② ❆ ❴ ✿ ❆ ✿✿ ❆ ✛ ❆ ✭✭ ❆ ✛ ❇ ✮ ✛ ❆ ✮ ✛ ❆

  6. ◆❛t✉r❛❧ ❞❡❞✉❝t✐♦♥ ●❡♥❡r❛❧ ❢♦r♠ ♦❢ ✐♥❢❡r❡♥❝❡ r✉❧❡s✿ P ✶ P ✷ ✿ ✿ ✿ P ♥ P ✵

  7. ◆❛t✉r❛❧ ❞❡❞✉❝t✐♦♥ ●❡♥❡r❛❧ ❢♦r♠ ♦❢ ✐♥❢❡r❡♥❝❡ r✉❧❡s✿ P ✶ P ✷ ✿ ✿ ✿ P ♥ P ✵ ④ P ✶ ✱ ✳ ✳ ✳ ✱ P ♥ ❛r❡ ♣r❡♠✐s❡s✱ P ✵ ✐s ❛ ❝♦♥❝❧✉s✐♦♥✳ ④ ■❢ ♥ ❂ ✵ ✭♥♦ ♣r❡♠✐s❡✮✱ t❤❡ ✐♥❢❡r❡♥❝❡ r✉❧❡ ✐s ❛♥ ❛①✐♦♠✳

  8. ◆❛t✉r❛❧ ❞❡❞✉❝t✐♦♥ ●❡♥❡r❛❧ ❢♦r♠ ♦❢ ✐♥❢❡r❡♥❝❡ r✉❧❡s✿ P ✶ P ✷ ✿ ✿ ✿ P ♥ P ✵ ❋♦r ❡❛❝❤ ❝♦♥♥❡❝t✐✈❡ ✭ ❫ ✱ ❴ ✱ ✳ ✳ ✳ ✮ t✇♦ ❦✐♥❞s ♦❢ r✉❧❡s✳ ■♥tr♦❞✉❝t✐♦♥ r✉❧❡s✿ ④ ❈♦♥♥❡❝t✐✈❡ ❛♣♣❡❛rs ✐♥ t❤❡ ❝♦♥❝❧✉s✐♦♥ P ✵ ✳ ④ ✧❍♦✇ t♦ ❡st❛❜✐s❤ ❛ ♣r♦♦❢❄✧ ❊❧✐♠✐♥❛t✐♦♥ r✉❧❡s✿ ④ ❈♦♥♥❡❝t✐✈❡ ❛♣♣❡❛rs ✐♥ ❛ ♣r❡♠✐s P ✐ ✳ ④ ✧❍♦✇ t♦ ❡①♣❧♦✐t ❛♥ ❡①✐st✐♥❣ ♣r♦♦❢❄✧ ◆♦t❡✿ ❯s✉❛❧❧② ❛ ❝♦♥♥❡❝t✐✈❡ ❤❛s ❛ s✐♥❣❧❡ ✐♥tr♦❞✉❝t✐♦♥ ❛♥❞ ❛ s✐♥❣❧❡ ❡❧✐♠✐♥❛t✐♦♥ r✉❧❡✱ ❜✉t s♦♠❡ ❝♦♥♥❡❝t✐✈❡s ♠❛② ❤❛✈❡ s❡✈❡r❛❧ r✉❧❡s ♦❢ t❤❡ s❛♠❡ ❦✐♥❞ ♦r ♥♦ r✉❧❡s ♦❢ ❝❡rt❛✐♥ ❦✐♥❞✳

  9. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P

  10. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r ✐♠♣❧✐❝❛t✐♦♥✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ ① P ✶ ✳ ✳ ✳ ✳ P ✷ ✛ I ① P ✶ ✛ P ✷ ④ ❊❧✐♠✐♥❛t✐♦♥✿ P ✶ ✛ P ✷ P ✶ ✛ E P ✷

  11. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r ❝♦♥❥✉♥❝t✐♦♥✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ P ✶ P ✷ ❫ I P ✶ ❫ P ✷ ④ ❊❧✐♠✐♥❛t✐♦♥✿ P ✶ ❫ P ✷ P ✶ ❫ P ✷ ❫ E ▲ ❫ E ❘ P ✶ P ✷

  12. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r ❞✐s❥✉♥❝t✐♦♥✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ P ✶ P ✷ ❴ I ▲ ❴ I ❘ P ✶ ❴ P ✷ P ✶ ❴ P ✷ ④ ❊❧✐♠✐♥❛t✐♦♥✿ ② ① P ✶ P ✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ P ✶ ❴ P ✷ P ✵ P ✵ ❴ E ①❀② P ✵

  13. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r tr✉t❤ ❛♥❞ ❢❛❧s❡❤♦♦❞✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ ❃ I ❃ ④ ❊❧✐♠✐♥❛t✐♦♥✿ ❄ ❄ E P

  14. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r tr✉t❤ ❛♥❞ ❢❛❧s❡❤♦♦❞✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ ❃ I ❃ ④ ❊❧✐♠✐♥❛t✐♦♥✿ ❄ ❄ E P ④ ❚r✉t❤ ❝❛♥ ❜❡ ❞❡☞♥❡❞ ❛s ❛ ✧s②♥t❛❝t✐❝ s✉❣❛r✧ ✿ ❃ ✑ ❄ ✛ ❄

  15. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r ♥❡❣❛t✐♦♥✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ ① P ✳ ✳ ✳ ✳ ❄ ✿ I ① ✿ P ④ ❊❧✐♠✐♥❛t✐♦♥✿ ✿ P P ✿ E ❄

  16. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P ■♥❢❡r❡♥❝❡ r✉❧❡s ❢♦r ♥❡❣❛t✐♦♥✿ ④ ■♥tr♦❞✉❝t✐♦♥✿ ① P ✳ ✳ ✳ ✳ ❄ ✿ I ① ✿ P ④ ❊❧✐♠✐♥❛t✐♦♥✿ ✿ P P ✿ E ❄ ④ ◆❡❣❛t✐♦♥ ❝❛♥ ❜❡ ❞❡☞♥❡❞ ❛s ❛ ✧s②♥t❛❝t✐❝ s✉❣❛r✧ ✿ ✿ P ✑ P ✛ ❄

  17. Pr♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❙②♥t❛①✿ P ✿✿❂ ❆ ❥ P ✛ P ❥ P ❫ P ❥ P ❴ P ❥ ❃ ❥ ❄ ❥ ✿ P Pr❡s❡♥t❡❞ r✉❧❡s ❣✐✈❡ ✐♥t✉✐t✐♦♥✐st✐❝ ♣r♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ IPC ✳ ❙♦♠❡t✐♠❡s ✇❡ ♠❛② ✉s❡ s♠❛❧❧❡r ❢r❛❣♠❡♥ts✿ ④ ❙②st❡♠ ✇✐t❤♦✉t t❤❡ ❄ E r✉❧❡ ✐s ♠✐♥✐♠❛❧ ♣r♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ◆❉ ✭ ✛ ❀ ❫ ❀ ❴ ✮✳ ④ ❙②st❡♠ ✇✐t❤ ♦♥❧② ✐♠♣❧✐❝❛t✐♦♥ r✉❧❡s ✭✐♠♣❧✐❝❛t✐♦♥❛❧ ❢r❛❣✲ ♠❡♥t✮ ◆❉ ✭ ✛ ✮✳ ❈❧❛ss✐❝❛❧ ♣r♦♣♦s✐t✐♦♥❛❧ ❧♦❣✐❝ ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ❜② ❛❞❞✐♥❣ t❤❡ ❞♦✉❜❧❡ ♥❡❣❛t✐♦♥ ❡❧✐♠✐♥❛t✐♦♥ r✉❧❡✿ ✿✿ P P

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