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  1. ▲♦❝❛t✐♦♥✲❞♦♠✐♥❛t✐♦♥ ❛♥❞ ♠❡tr✐❝ ❞✐♠❡♥s✐♦♥ ✐♥ ✐♥t❡r✈❛❧ ❛♥❞ ♣❡r♠✉t❛t✐♦♥ ❣r❛♣❤s ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ✭❯♥✐✈✳ ❇❧❛✐s❡ P❛s❝❛❧✱ ❈❧❡r♠♦♥t✲❋❡rr❛♥❞✱ ❋r❛♥❝❡✮ ❥♦✐♥t ✇♦r❦ ✇✐t❤✿ ●❡♦r❣❡ ❇✳ ▼❡rt③✐♦s ✭❉✉r❤❛♠✱ ❯❑✮✱ ❘❡③❛ ◆❛s❡r❛sr ✭P❛r✐s✱ ❋r❛♥❝❡✮✱ ❆❧✐♥❡ P❛rr❡❛✉ ✭▲②♦♥✱ ❋r❛♥❝❡✮✱ P❡tr✉ ❱❛❧✐❝♦✈ ✭▼❛rs❡✐❧❧❡✱ ❋r❛♥❝❡✮ ❆♣r✐❧ ✷✵✶✺

  2. PARIS L YON BORDEAUX MARSEILLE ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✷ ✴ ✷✹

  3. PARIS CLERMONT-FERRAND L YON BORDEAUX MARSEILLE ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✷ ✴ ✷✹

  4. ▲♦❝❛t✐♦♥✲❞♦♠✐♥❛t✐♦♥ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✸ ✴ ✷✹

  5. ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  6. ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  7. ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  8. ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  9. ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  10. ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  11. ❋✐r❡ ❞❡t❡❝t✐♦♥ ✐♥ ❛ ❜✉✐❧❞✐♥❣ ❉❡t❡❝t♦r ❝❛♥ ❞❡t❡❝t ✜r❡ ✐♥ ✐ts r♦♦♠ ❛♥❞ ✐ts ♥❡✐❣❤❜♦r❤♦♦❞ ✭t❤r♦✉❣❤ ❛ ❞♦♦r✮✳ ❊❛❝❤ r♦♦♠ ♠✉st ❝♦♥t❛✐♥ ❛ ❞❡t❡❝t♦r ♦r ❤❛✈❡ ♦♥❡ ✐♥ ❛♥ ❛❞❥❛❝❡♥t r♦♦♠✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✹ ✴ ✷✹

  12. ❙❡t ♦❢ ❞❡t❡❝t♦rs ❞♦♠✐♥❛t✐♥❣ s❡t ❉ ❱ ✿ ✉ ❱ ◆ ✉ ❉ ❉♦♠✐♥❛t✐♦♥ ♥✉♠❜❡r ● ✿ s♠❛❧❧❡st s✐③❡ ♦❢ ❛ ❞♦♠✐♥❛t✐♥❣ s❡t ♦❢ ● ▼♦❞❡❧✐s❛t✐♦♥ ✇✐t❤ ❛ ❣r❛♣❤ ●r❛♣❤ ● = ( ❱ , ❊ ) ✳ ❱❡rt✐❝❡s✿ r♦♦♠s✳ ❊❞❣❡s✿ ❜❡t✇❡❡♥ ❛♥② t✇♦ r♦♦♠s ❝♦♥♥❡❝t❡❞ ❜② ❛ ❞♦♦r ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✺ ✴ ✷✹

  13. ❙❡t ♦❢ ❞❡t❡❝t♦rs ❞♦♠✐♥❛t✐♥❣ s❡t ❉ ❱ ✿ ✉ ❱ ◆ ✉ ❉ ❉♦♠✐♥❛t✐♦♥ ♥✉♠❜❡r ● ✿ s♠❛❧❧❡st s✐③❡ ♦❢ ❛ ❞♦♠✐♥❛t✐♥❣ s❡t ♦❢ ● ▼♦❞❡❧✐s❛t✐♦♥ ✇✐t❤ ❛ ❣r❛♣❤ ●r❛♣❤ ● = ( ❱ , ❊ ) ✳ ❱❡rt✐❝❡s✿ r♦♦♠s✳ ❊❞❣❡s✿ ❜❡t✇❡❡♥ ❛♥② t✇♦ r♦♦♠s ❝♦♥♥❡❝t❡❞ ❜② ❛ ❞♦♦r ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✺ ✴ ✷✹

  14. ❉♦♠✐♥❛t✐♦♥ ♥✉♠❜❡r ● ✿ s♠❛❧❧❡st s✐③❡ ♦❢ ❛ ❞♦♠✐♥❛t✐♥❣ s❡t ♦❢ ● ▼♦❞❡❧✐s❛t✐♦♥ ✇✐t❤ ❛ ❣r❛♣❤ ●r❛♣❤ ● = ( ❱ , ❊ ) ✳ ❱❡rt✐❝❡s✿ r♦♦♠s✳ ❊❞❣❡s✿ ❜❡t✇❡❡♥ ❛♥② t✇♦ r♦♦♠s ❝♦♥♥❡❝t❡❞ ❜② ❛ ❞♦♦r ❙❡t ♦❢ ❞❡t❡❝t♦rs = ❞♦♠✐♥❛t✐♥❣ s❡t ❉ ⊆ ❱ ✿ ∀ ✉ ∈ ❱ , ◆ [ ✉ ] ∩ ❉ � = / 0 ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✺ ✴ ✷✹

  15. ▼♦❞❡❧✐s❛t✐♦♥ ✇✐t❤ ❛ ❣r❛♣❤ ●r❛♣❤ ● = ( ❱ , ❊ ) ✳ ❱❡rt✐❝❡s✿ r♦♦♠s✳ ❊❞❣❡s✿ ❜❡t✇❡❡♥ ❛♥② t✇♦ r♦♦♠s ❝♦♥♥❡❝t❡❞ ❜② ❛ ❞♦♦r ❙❡t ♦❢ ❞❡t❡❝t♦rs = ❞♦♠✐♥❛t✐♥❣ s❡t ❉ ⊆ ❱ ✿ ∀ ✉ ∈ ❱ , ◆ [ ✉ ] ∩ ❉ � = / 0 ❉♦♠✐♥❛t✐♦♥ ♥✉♠❜❡r γ ( ● ) ✿ s♠❛❧❧❡st s✐③❡ ♦❢ ❛ ❞♦♠✐♥❛t✐♥❣ s❡t ♦❢ ● ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✺ ✴ ✷✹

  16. ❛ ❝ ❄ ❝ ❜ ❄ ❜✱❝ ❜ ❇❛❝❦ t♦ t❤❡ ❜✉✐❧❞✐♥❣ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✻ ✴ ✷✹

  17. ❛ ❝ ❄ ❝ ❜ ❄ ❜✱❝ ❜ ❚♦ ❧♦❝❛t❡ t❤❡ ✜r❡✱ ✇❡ ♥❡❡❞ ♠♦r❡ ❞❡t❡❝t♦rs✳ ❇❛❝❦ t♦ t❤❡ ❜✉✐❧❞✐♥❣ ❲❤❡r❡ ✐s t❤❡ ✜r❡ ❄ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✻ ✴ ✷✹

  18. ❛ ❝ ❄ ❝ ❜ ❄ ❜✱❝ ❜ ❚♦ ❧♦❝❛t❡ t❤❡ ✜r❡✱ ✇❡ ♥❡❡❞ ♠♦r❡ ❞❡t❡❝t♦rs✳ ❇❛❝❦ t♦ t❤❡ ❜✉✐❧❞✐♥❣ ❲❤❡r❡ ✐s t❤❡ ✜r❡ ❄ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✻ ✴ ✷✹

  19. ❛ ❝ ❄ ❝ ❜ ❄ ❜✱❝ ❜ ❚♦ ❧♦❝❛t❡ t❤❡ ✜r❡✱ ✇❡ ♥❡❡❞ ♠♦r❡ ❞❡t❡❝t♦rs✳ ❇❛❝❦ t♦ t❤❡ ❜✉✐❧❞✐♥❣ ❲❤❡r❡ ✐s t❤❡ ✜r❡ ❄ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✻ ✴ ✷✹

  20. ❛ ❝ ❝ ❜ ❜✱❝ ❜ ❇❛❝❦ t♦ t❤❡ ❜✉✐❧❞✐♥❣ ❄ ❄ ❲❤❡r❡ ✐s t❤❡ ✜r❡ ❄ ❚♦ ❧♦❝❛t❡ t❤❡ ✜r❡✱ ✇❡ ♥❡❡❞ ♠♦r❡ ❞❡t❡❝t♦rs✳ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✻ ✴ ✷✹

  21. ❄ ❝ ❄ ❜✱❝ ❜ ▲♦❝❛t✐♥❣ t❤❡ ✜r❡ ❛ ❝ ❜ ❋❧♦r❡♥t ❋♦✉❝❛✉❞ ■❞❡♥t✐✜❝❛t✐♦♥ ♣r♦❜❧❡♠s ✐♥ ❣r❛♣❤s ✻ ✴ ✷✹

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