HAL Id: hal-01018427
https://hal-enac.archives-ouvertes.fr/hal-01018427
Submitted on 4 Jul 2014
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Reduction of air traffic congestion by genetic algorithms
Sofiane Oussedik, Daniel Delahaye
To cite this version:
Sofiane Oussedik, Daniel Delahaye. Reduction of air traffic congestion by genetic algorithms. Lecture Notes in Computer Science, Springer, 1998, Lecture Notes in Computer Science, 1498, pp 855-864.
�10.1007/BFb0056927�. �hal-01018427�
✒ ✓ ✔ ✁ ✟ ✁✆ ✝☎ ✡ ✕✏ ✞ ☛ ✝✆ ✖ ✗ ✑
✘✙✚ ✛✜ ✢ ✣ ✤✥✥✢✦✧★✩ ✛✜ ✦ ✪ ✛✜✧✢✫ ✪ ✢✫✛✬ ✛✭✢✮
✯ ✰ ✱ ✲ ✳ ✴ ✵✶✷✸✹✸✺✻✷✸✼ ✽ ✽ ✽
✾ ✿❀ ❁ ✴ ✰✵ ❂ ✲ ❃
❄
✸✶❅❅❆❇❈❉❊ ❇❆✼❋●❋❍❆■❏ ✹❑ ❋▲▼◆▲✸✼❍✻❆✹●✺❈❖✶❆◆P✷
✰ ❆✺✻✷❆ ❇❆ ✱ ❋✻●❆◗❑ ❋✻❈❖✶❆❅ ✲ ▲▲✼❈❖✶❆◗❆❅
✵✹✸✼❆ ✳✸✼❍✻❆✹●✺❈❖✶❆
❘❙❙❚❯
✳❋✼❋❈❅❆❋✶ ✰ ❆❇❆▼❊ ❱✷❋✺✹❆
❲ ❳❨❩❬❭❪❩❫ ❴
●❆ ❋✺✺✶❋✼ ✺✶❑❵ ❆✷ ✸P ❛❈❜●✻❅ ❈✺ ❝ ❆❅✻❆✷✺ ✵✶✷✸▲❆ ●❋❅ ❈✺❞
✹✷❆❋❅❆❇ P✷✸❑ ❋❵✸✶✻
❚❡❢
❑ ❈✼✼❈✸✺ ❈✺
❙❘❯❚
✻✸ ❋❵✸✶✻ ❣◆❤ ❑ ❈✼✼❈✸✺ ❈✺
❙❘❘❚
❊
❋✺ ❈✺✹✷❆❋❅❆ ✸P ✐❥❦ ◆ ✲ ✹✶✻❆ ✹✸✺❜❆❅✻❈✸✺ ✸P ✻●❆ ✲ ❈✷
❴
✷❋❧ ✹ ✰✸✺✻✷✸✼ ❅❍❅✻❆❑
●❋❅ ❵❆❆✺ ✻●❆ ✷❆❅✶✼✻◆ ❀✺❆ ♠ ❋❍ ✻✸ ✷❆❇✶✹❆ ✻●❈❅ ✹✸✺❜❆❅✻❈✸✺ ❈❅ ✻✸ ❑ ✸❇❈P❍ ✻●❆
❛❈❜●✻ ▲✼❋✺❅ ♥❅✼✸✻ ✸P ❇❆▲❋✷✻✶✷❆ ❋✺❇ ✷✸✶✻❆♦ ❈✺ ✸✷❇❆✷ ✻✸ ❋❇❋▲✻ ✻●❆ ❇❆❑ ❋✺❇
✻✸ ✻●❆ ❋♣❋❈✼❋❵✼❆ ✹❋▲❋✹❈✻❍◆
❴
●❈❅ ▲❋▲❆✷ ❋❇❇✷❆❅❅❆❅ ✻●❆ ❜❆✺❆✷❋✼ ✻❈❑ ❆❞✷✸✶✻❆ ❋❅❞
❅❈❜✺❑ ❆✺✻ ▲✷✸❵✼❆❑ ◆ ✲ ❅✻❋✻❆ ✸P ✻●❆ ❋✷✻ ✸P ✻●❆ ❆▼❈❅✻❈✺❜ ❑ ❆✻●✸❇❅ ❅●✸♠ ❅ ✻●❋✻
✻●❈❅ ▲✷✸❵✼❆❑ ❈❅ ✶❅✶❋✼✼❍ ▲❋✷✻❈❋✼✼❍ ✻✷❆❋✻❆❇ ❋✺❇ ✻●❆ ♠ ●✸✼❆ ▲✷✸❵✼❆❑ ✷❆❑ ❋❈✺❅
✶✺❅✸✼♣❆❇ ❇✶❆ ✻✸ ✻●❆ ✹✸❑ ▲✼❆▼❈✻❍ ❈✺❇✶✹❆❇◆
❝ ❆ ▲❆✷P✸✷❑ ✸✶✷ ✷❆❅❆❋✷✹● ✸✺ ✻●❆ ❋▲▲✼❈✹❋✻❈✸✺ ✸P ❅✻✸✹●❋❅✻❈✹ ❑ ❆✻●✸❇❅ ✸✺
✷❆❋✼ ✻✷❋❧ ✹ ❇❋✻❋❊ ❋✺❇ ♠ ❈✻●✸✶✻ ✶❅❈✺❜ ✻●❆ ❛✸♠ ✺❆✻♠✸✷❉ ✹✸✺✹❆▲✻❊ ❵✶✻ ❵❍
❅❈❑ ✶✼❋✻❈✺❜ ✻●❆ ❛❈❜●✻ ✸P ❆❋✹● ❋❈✷✹✷❋P✻◆
❴
●❆ q✷❅✻ ✷❆❅✶✼✻❅ ❅●✸♠ ❅ ✻●❋✻ ✸✶✷
❁ ❆✺❆✻❈✹ ✲ ✼❜✸✷❈✻●❑ ❅ ❵❋❅❆❇ ❑ ❆✻●✸❇ ❈❅ ❋❵✼❆ ✻✸ ✷❆❇✶✹❆ ✹✸✺❜❆❅✻❈✸✺ ✸P ✻●❆
P✷❆✺✹● ❋❈✷❅▲❋✹❆ ❵❍ ❋ P❋✹✻✸✷
❚
◆ r▲❆✹❈❋✼ ✹✸❇❈✺❜ ✻❆✹●✺❈❖✶❆❅ ❋✺❇ ✸▲ ❆✷❋✻✸✷❅
❋✷❆ ✶❅❆❇ ✻✸ ❈❑ ▲✷✸♣❆ ✻●❆ ❖✶❋✼❈✻❍ ✸P ✻●❆ ❜❆✺❆✻❈✹ ❅❆❋✷✹● ◆
s t✉✈✇① ② ③ ④✈⑤① ✉
⑥ ✥ ⑦✬✢⑧✢ ✛⑧✢ ⑨ ✛✜✭ ✛✧⑧⑩⑧✛❶⑦ ✥✧⑨ ✤ ✫⑦✛✜ ✢✙✤✥✫✭ ❷⑧✢✥✢✜⑦ ✧✜ ⑦✬✢ ✥★✭❸ ❷✧✫✙⑦✥ ⑨ ✤✥⑦ ❹ ✢
✬✢✫❷✢✦ ❹✭ ✛✜ ✛✧⑧ ⑦⑧✛❺ ⑩ ⑩✙✜⑦⑧✙✫✫✢⑧ ✙✜ ⑦✬✢ ❻⑧✙✤✜✦ ❼ ✬✙ ✬✛✥ ✛ ❻✫✙❹✛✫ ❽✧✢❼ ✙❶ ⑦✬ ✢
⑩✤⑧⑧✢✜⑦ ⑦⑧✛❺ ⑩ ✦ ✧✥⑦⑧✧❹✤⑦✧✙✜ ✧✜ ⑦✬✢ ✛✧⑧✥❷ ✛⑩✢ ✛✜ ✦ ⑩✛✜ ❻✧❽✢ ✙⑧✦✢⑧✥ ⑦✙ ⑦✬ ✢ ❷ ✧✫✙⑦✥ ⑦✙
✛❽✙✧✦ ⑩✙✫✫✧✥✧✙✜ ✥❾⑥ ✥✧✜ ❻✫✢ ⑩✙✜⑦⑧✙✫✫✢⑧ ✧✥ ✜✙⑦ ✛❹✫✢ ⑦✙ ⑨ ✛✜ ✛❻✢ ✛✫✫ ⑦✬✢ ✛✧⑧⑩⑧✛❶⑦❸ ⑦✬ ✛⑦❿✥
❼✬✭ ⑦✬✢ ✛✧⑧✥❷✛⑩✢ ✧✥ ❷✛⑧⑦✧⑦✧✙✜✢✦ ✧✜⑦✙ ✦✧➀✢⑧✢✜⑦ ✥✢⑩⑦✙⑧✥❸ ✢✛⑩✬ ✙❶ ⑦✬✢⑨ ❹ ✢✧✜❻ ✛✥✥✧❻✜✢✦
⑦✙ ✛ ⑩✙✜⑦⑧✙✫✫✢⑧❾
⑥ ✥ ✛✜✭ ✬✤ ⑨ ✛✜ ❹✢✧✜❻ ❸ ✛ ⑩✙✜⑦⑧✙✫✫✢⑧ ✬✛✥ ❼ ✙⑧★✧✜ ❻ ✫✧⑨ ✧⑦✥❸ ✛✜ ✦ ❼ ✬✢✜ ⑦✬✢ ✜✤⑨ ❹ ✢⑧
✙❶ ✛✧⑧⑩⑧✛❶⑦ ✧✜⑩⑧✢✛✥✢✥❸ ✥✙⑨ ✢ ❷ ✛⑧⑦✥ ✙❶ ⑦✬✢ ✛✧⑧✥❷ ✛⑩✢ ⑧✢✛⑩✬ ⑦✬ ✧✥ ✫✧⑨ ✧⑦ ✛✜✦ ❹✢⑩✙⑨ ✢
⑩✙✜❻✢✥⑦✢✦ ❾ ➁✜ ⑦✬✢ ❷✛✥⑦❸ ⑦✬ ✢ ✚⑧✥⑦ ❼ ✛✭ ⑦✙ ⑧✢✦✤ ⑩✢ ⑦✬✢✥✢ ⑩✙✜ ❻✢✥⑦✧✙✜✥ ❼ ✛✥ ⑦✙ ⑨ ✙✦✧❶✭
⑦✬ ✢ ✥⑦⑧✤⑩⑦✤ ⑧✢ ✙❶ ⑦✬✢ ✛✧⑧✥❷✛⑩✢ ✧✜ ✛ ❼ ✛✭ ⑦✬ ✛⑦ ✧✜⑩⑧✢✛✥✢✥ ⑦✬ ✢ ⑩✛❷ ✛⑩✧⑦✭ ➂✧✜⑩⑧✢✛✥✧✜❻
⑦✬ ✢ ✜✤ ⑨ ❹ ✢⑧ ✙❶ ⑧✤ ✜❼✛✭✥❸ ✧✜⑩⑧✢✛✥✧✜❻ ⑦✬ ✢ ✜✤⑨ ❹✢⑧ ✙❶ ✥✢⑩⑦✙⑧✥ ❹✭ ⑧✢✦✤ ⑩✧✜ ❻ ⑦✬ ✢✧⑧ ✥✧➃✢➄❾
➅✬ ✧✥ ✬✛✥ ✛ ✫✧⑨ ✧⑦ ✦✤✢ ⑦✙ ⑦✬✢ ⑩✙✥⑦ ✧✜❽✙✫❽✢✦ ❹✭ ✜ ✢❼ ⑧✤✜❼ ✛✭✥ ✛✜✦ ⑦✬ ✢ ❼✛✭ ⑦✙ ⑨ ✛✜✛❻✢
✽ ✽ ✽ ✵✶✷✸✹✸✺✻✷✸✼ ✵▼▲❆✷❈❑ ❆✺✻❋✼ ✰❆✺✻❆✷
⑦✙ ❹ ✢ ✛❹✫✢ ⑦✙ ✥✙✫❽✢ ⑩✙✜ ➇✧⑩⑦✥➄❾
➅
✬✢ ✙⑦✬✢⑧ ❼ ✛✭ ⑦✙ ⑧✢✦✤ ⑩✢ ⑩✙✜❻✢✥⑦✧✙✜ ✧✥ ⑦✙ ⑨ ✙✦✧❶✭
⑦✬ ✢ ➇✧❻✬⑦ ❷ ✫✛✜✥ ✧✜ ✛ ❼ ✛✭ ⑦✙ ✛✦ ✛❷⑦ ⑦✬✢ ✦✢⑨ ✛✜✦ ⑦✙ ⑦✬ ✢ ✛❽✛✧✫✛❹ ✫✢ ⑩✛❷✛⑩✧⑦✭❾
➅
✬✢✜
⑩✙✜❻✢✥⑦✧✙✜ ✧✥ ✢➈❷✢⑩⑦✢✦ ⑦✙ ❹ ✢ ⑧✢✦✤ ⑩✢✦ ❹✭ ⑨ ✙❽✧✜ ❻ ➂✧✜ ✛ ✫✧⑨ ✧⑦✢✦ ✦✙⑨ ✛✧✜➄ ⑦✬ ✢ ⑦✧⑨ ✢ ✙❶
✦✢❷ ✛⑧⑦✤⑧✢ ✙❶ ✛✧⑧⑩⑧✛❶⑦ ➂✧✜ ⑦✬✢ ❷✛✥⑦ ✛✜✦ ✧✜ ⑦✬ ✢ ❶✤ ⑦✤⑧✢➄ ✛✜✦ ❹✭ ⑩✬ ✛✜❻✧✜❻ ⑦✬✢ ⑩✤⑧⑧✢✜⑦
➇ ✧❻✬⑦ ❷ ✛⑦✬✥ ➂❼✧⑦✬ ✙✤ ⑦ ⑦✙✙ ⑨ ✤⑩✬ ✢➈⑦⑧✛✦✧✥⑦✛✜ ⑩✢➄❾
➅ ✬✧✥ ❷✛❷ ✢⑧ ✥✬✙❼ ✥ ✬✙❼ ❼✢✫✫ ✥⑦✙⑩✬ ✛✥⑦✧⑩ ✙❷⑦✧⑨ ✧➃✛⑦✧✙✜ ✧✥ ✛❹✫✢ ⑦✙ ⑨ ✛✜ ✛❻✢ ⑦✬✧✥
★✧✜✦ ✙❶ ❷⑧✙❹✫✢⑨ ❾
➉ ➊ ✇➋➌ ⑤① ③ ➍ ➎ ➋ ➏➐ ✈➋② ➑ ① ✇ ➒➍
➅⑧✛❺ ⑩ ✛✥✥✧❻✜⑨ ✢✜⑦ ⑦✢⑩✬✜ ✧➓✤✢✥ ✬ ✛❽✢ ❹✢✢✜ ✦ ✢❽✢✫✙❷ ✢✦ ✧✜ ✙⑧✦✢⑧ ⑦✙ ⑧✢✦✤⑩✢ ⑩✙✜❻✢✥⑦✧✙✜
✧✜ ⑦⑧✛✜✥❷ ✙⑧⑦✛⑦✧✙✜ ✜ ✢⑦❼✙⑧★✥ ❹✭ ✥❷⑧✢✛✦✧✜ ❻ ⑦✬✢ ⑦⑧✛❺ ⑩ ✦ ✢⑨ ✛✜✦ ✧✜ ⑦✧⑨ ✢ ✛✜✦ ✧✜ ✥❷✛⑩✢❾
✪ ✛❶✢⑧⑨ ✙✥ ✛✜✦ ✘❷ ✛⑧⑧✙❼ ➔→➣ ⑩✙✧✜✢✦ ⑦✬✢ ⑦✢⑧⑨ ✥ ↔↕➙➛➜➝➞➟➠➡ ➠➢➙➤ ✛✜ ✦ ↕➥↕➟➙➡ ➜➝➞ ➟➠➡ ➠➢➙➤
⑦⑧✛✜✥❷✙⑧⑦✛⑦✧✙✜ ✜✢⑦❼✙⑧★✥ ⑦✙ ✦✧✥⑦✧✜❻✤✧✥✬ ❹ ✢⑦❼✢✢✜ ⑦❼ ✙ ✦✧✥⑦✧✜ ⑩⑦ ✥✧⑦✤✛⑦✧✙✜✥ ✧✜ ❼✬ ✧⑩✬
✤✥✢⑧✥ ✛⑩⑦ ✤ ✜✧✫✛⑦✢⑧✛✫✫✭❸✧✜ ⑦✬✢✧⑧ ✙❼ ✜ ✥✢✫❶➦✧✜⑦✢⑧✢✥⑦❸ ✧✜ ✥✢✫✢⑩⑦✧✜ ❻ ⑦✬ ✢✧⑧ ⑧✙✤⑦✢✥❸ ✛✜✦ ✧✜
❼✬ ✧⑩✬ ✤✥✢⑧✥ ✥✢✫✢⑩⑦ ⑧✙✤ ⑦✢✥ ✛⑩⑩✙⑧✦✧✜❻ ⑦✙ ❼ ✬ ✛⑦ ✧✥ ✙❷ ⑦✧⑨ ✛✫ ❶⑧✙⑨ ⑦✬✢ ✥✙⑩✧✢⑦✛✫ ❷✙✧✜⑦ ✙❶
❽✧✢❼ ❸ ✧✜ ⑦✬✛⑦ ⑦✬✢ ⑦✙⑦✛✫ ⑩✙✥⑦✥ ✧✜ ⑦✬✢ ✥✭✥⑦✢⑨ ✛⑧✢ ⑨ ✧✜✧⑨ ✧➃✢✦ ❾ ➧ ✫✛✥✥✧⑩✛✫ ✛❷❷⑧✙✛⑩✬ ✢✥
✛⑧✢ ✛❷❷✫✧✢✦ ⑦✙ ✥⑦✛⑦✧⑩ ⑦⑧✛❺ ⑩ ✦✢⑨ ✛✜ ✦ ✛✜✦ ✛⑧✢ ⑨ ✛✧✜ ✫✭ ✤ ✥✢✦ ⑦✙ ✙❷⑦✧⑨ ✧➃✢ ⑦⑧✛❺ ⑩ ✙✜ ✛
✫✙✜ ❻ ⑦✧⑨ ✢ ❷✢⑧✧✙✦ ✛✜✦ ⑩✛✜ ✙✜ ✫✭ ⑩✛❷⑦✤⑧✢ ⑦✬ ✢ ⑨ ✛⑩⑧✙✥⑩✙❷✧⑩ ✢❽✢✜⑦✥❾
➨
✬ ✢✜ ✛ ⑨ ✙⑧✢ ❷⑧✢⑩✧✥✢ ⑨ ✛⑦⑩✬✧✜❻ ❹ ✢⑦❼✢✢✜ ⑦⑧✛❺ ⑩ ✦✢⑨ ✛✜✦ ✛✜✦ ⑩✛❷✛⑩✧⑦✭ ✬ ✛✥
⑦✙ ❹ ✢ ❶✙✤✜✦ ❸ ⑨ ✧⑩⑧✙✥⑩✙❷✧⑩ ✢❽✢✜⑦✥ ✬ ✛❽✢ ⑦✙ ❹✢ ⑦✛★✢✜ ✧✜⑦✙ ✛⑩⑩✙✤✜⑦❸ ✛✜✦ ✦✭✜ ✛⑨ ✧⑩
⑦⑧✛❺ ⑩ ✛✥✥✧❻✜⑨ ✢✜⑦ ⑦✢⑩✬✜✧➓✤✢✥ ✬ ✛❽✢ ⑦✙ ❹ ✢ ✤✥✢✦ ❸ ➂➔➩➫➣ ❻✧❽✢✥ ✛ ❻✙✙✦ ✦✢✥⑩⑧✧❷⑦✧✙✜ ✙❶
⑦✬ ✙✥✢ ⑦✢⑩✬✜✧➓✤✢✥➄❾
➅
✬✢ ⑨ ✛✧✜ ✙✜✢✥ ✛⑧✢ ⑦✬✢ ❶✙✫✫✙❼ ✧✜ ❻ ➭ ✘❷✛⑩✢➦⑦✧⑨ ✢ ✜✢⑦❼✙⑧★ ➔➩➯➣❸
➲✛⑧✧✛⑦✧✙✜✛✫ ➁✜ ✢➓✤ ✛✫✧⑦✭ ➔➳➣❸✣ ❷⑦✧⑨ ✛✫ ➧✙✜⑦⑧✙✫ ➔➵➣❸✘✧⑨ ✤✫✛⑦✧✙✜ ➔➸➣ ✛✜✦ ✪ ✭✜✛⑨ ✧⑩ ➺ ⑧✙➦
❻⑧✛⑨ ⑨ ✧✜ ❻ ➔➩➩❸➩➸❸➫➣❾
⑥ ✫✫ ⑦✬✢ ❷⑧✢❽✧✙✤✥ ✛❷❷ ⑧✙✛⑩✬✢✥ ✛⑧✢ ✜✙⑦ ✛❹✫✢ ⑦✙ ⑨ ✛✜✛❻✢ ⑦✬ ✢ ❼ ✬✙✫✢ ❷ ⑧✙❹✫✢⑨ ✦✤ ✢
⑦✙ ✧⑦✥ ⑩✙⑨ ❷ ✫✢➈✧⑦✭❾
⑥ ✚⑧✥⑦ ✛⑦⑦✢⑨ ❷⑦ ✙❶ ⑧✢✥✙✫✤ ⑦✧✙✜ ✙❶ ⑦✬✢ ❼ ✬✙✫✢ ❷⑧✙❹✫✢⑨ ⑩✛✜ ❹ ✢ ❶✙✤✜✦ ✧✜ ➔➻➣❾ ➅ ✬✧✥
❷✛❷ ✢⑧ ❷ ⑧✢✥✢✜⑦ ✛ ➇ ✙❼ ⑨ ✙✦✢✫✧✜❻ ✙❶ ⑦✬✢ ✛✧⑧ ⑦⑧✛❺ ⑩ ✜ ✢⑦❼✙⑧★ ✛✜✦ ❻✧❽✢ ✛ ⑧✢✥✙✫✤⑦✧✙✜
❷⑧✧✜⑩✧❷✫✢ ✙❶ ⑦✬✢ ⑧✙✤ ⑦✢➦⑦✧⑨ ✢ ❹✧➦✛✫✫✙⑩✛⑦✧✙✜ ❷ ⑧✙❹✫✢⑨ ❹✛✥✢✦ ✙✜ ✥⑦✙⑩✬✛✥⑦✧⑩ ✙❷ ⑦✧⑨ ✧➃✛➦
⑦✧✙✜ ❼ ✧⑦✬ ❽✢⑧✭ ❻✙✙✦ ⑧✢✥✤✫⑦✥❾ ➅ ✬✢ ❷⑧✢✥✢✜⑦ ✛❷❷⑧✙✛⑩✬ ✧✥ ⑦✬✢ ❶✙✫✫✙❼ ✧✜ ❻ ✙❶ ⑦✬✧✥ ❼ ✙⑧★ ❾
➅✬ ✢ ⑨ ✛➼✙⑧ ✦✧➀✢⑧✢✜⑩✢ ❹ ✢⑦❼✢✢✜ ⑦✬✢✥✢ ⑦❼✙ ✛❷❷⑧✙⑩✬✢✥ ⑧✢✫✧✢✥ ✙✜ ⑦✬ ✢ ✛✧⑧ ✜✢⑦❼ ✙⑧★
⑨ ✙✦ ✢✫✧✜❻ ❾➁✜ ⑦✬✢ ❶✙✫✫✙❼ ✧✜ ❻❸✛ ⑨ ✙✦ ✢✫ ✧✥ ❷⑧✙❷✙✥✢✦ ✛✜✦ ✛ ⑨ ✢⑦✬ ✙✦ ✧✥ ✦✢❽✢✫✙❷✢✦ ⑦✬ ✛⑦
✭✧✢✫✦ ➽❽✢⑧✭ ❻✙✙✦➾ ✥✙✫✤⑦✧✙✜✥ ❶✙⑧ ⑧✢✛✫✧✥⑦✧⑩ ✧✜✥⑦✛✜⑩✢✥ ✙❶ ⑦✬✢ ❼ ✬✙✫✢ ❷⑧✙❹✫✢⑨ ❾ ➁✜ ⑦✬✧✥
⑨ ✙✦ ✢✫❸❼ ✬ ✧⑩✬ ✧✥ ⑨ ✙⑧✢ ⑧✢✛✫✧✥⑦✧⑩ ❶✙⑧ ✛✧⑧ ⑦⑧✛❺ ⑩❸ ⑦✬ ✢ ⑩✙✜⑩✢❷⑦ ✙❶ ⑧✙✤⑦✢ ➇✙❼ ✧✥ ✜ ✙ ⑨ ✙⑧✢
❽✛✫✧✦ ✛✜ ✦ ⑦✬✧✥ ✧✜✦✤ ⑩✢ ✛ ⑩✙✜⑦⑧✙✫ ❼ ✙⑧★✫✙✛✦ ✥❷⑧✢✛✦✧✜❻ ✙❽✢⑧ ⑦✬ ✢ ✥❷ ✛⑩✢ ✛✜ ✦ ✛ ✥⑦⑧✙✜❻✢⑧
⑩✙⑨ ❷✫✢➈✧⑦✭❾
➚ ➪ ➶⑤➹ ➘ ➏⑤➴ ➋ ② ➷ ① ② ➋ ➏
➬➮➱ ✃❐❒❮❰ ÏÐ Ñ❒Ò❰❐
➧✙✜❻✢✥⑦✧✙✜ ✧✜ ⑦✬✢ ✛✧⑧✥❷ ✛⑩✢ ✧✥ ✦✤✢ ⑦✙ ✛✧⑧⑩⑧✛❶⑦ ❼ ✬✧⑩✬ ✬✛❽✢ ⑩✫✙✥✢ ❷ ✙✥✧⑦✧✙✜ ✥ ✧✜ ✛ ❶✙✤ ⑧➦