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By Christoph Meinel

One of many major difficulties in chip layout is the massive variety of attainable mixtures of person chip parts, resulting in a combinatorial explosion as chips turn into extra advanced. New key leads to theoretical computing device technological know-how and within the layout of knowledge buildings and effective algorithms, might be utilized fruitfully right here. the appliance of ordered binary selection diagrams (OBDDs) has resulted in dramatic functionality advancements in lots of computer-aided layout tasks. This textbook presents an advent to the principles of this interdisciplinary learn quarter with an emphasis on functions in computer-aided circuit layout and formal verification.

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S ✕✒✎✡✜❏✆➛✄✳✦✲✦✥✄❜s❖✑✥✤✡✽❑✦✲✜✧❱♦❱✻✭⑥✆➛✄✘✦✥✦✥✄❜s✰✓✩✜✧✭✘✓✒✑✥✦✲✴ ♥ ✞ ☛✶ ✡✪✡ ✩ ✧✾✠ ★ ✠ ✘❋✾ ✆✆☎ ✁ ★✰✦✵✺ ✁ ✙ ✭ ✪❋❊ ✱✍✦ ✙ ✭ ✯✰✶✕✏ ✌✞✛❀✎✒✛❃✓❉✌ ✧✖✠ ✵✠ ✍ ✴✩✬❅✛✑✣✏✯✖✱✍✢ ✥▲✶ ✙■★✟✯✧✯✖✱■✺ ✭ ③ ❁✞✩✱✑✔✕ ✥ ✾❙★✟✯✧✯ ✁ ✙ ✭ ✶✍★✰✪❃✥▲✶❋✾■❏ ✁ ✆✆☎ ✍ ✴✩✬✜✛✹✣✍✯✖✱✏✢ ✥▲✶❆✙✜★✟✯✧✯✖✱■✺ ✭ ③ ✙✦✓ ✡ ✆✞❇❃✶ ✎✒✶ ❯ ✥ ✾ ✣■✛✰✪❋❊ ✥▲✶ ✭ ✌❁❊ ★✟✬❅✺ ★✰✦✩✺ ✙ ✭ ✝ ❁✞✶✷✓✻✑✔☛ ✶ ✡☞✧✖✠ ✵✠ ✔ ✱✏✪ ✣■✱ ★✟✦ ✭ ✌✿✙■✛✰✢✝✴✩✯✖✱✍✪✫✱ ✴✵✬❅✛✹✣✍✯✖✱✍✢ ✘✵❊ ✱✍✦ ✪✧❊✒✱ ✾✏✛✟✯✧✯✖✛ ☛☎✥✧✦●✻ ❊✒✛✰✯✖✺✰✶ ✘❋✾ ✙ ✭ ✪✧❊✒✱✏✦✤✭ ✴ ✭ ✘❋✾ ✙ ✭ ✪✧❊✒✱✏✦✚★✟✯✧✯ ✭ ✌✿✙■✛✰✢✝✴✩✯✖✱✍✪ ✱ ✴✵✬❅✛✹✣✍✯✖✱✍✢✘✶ ✁ ✶✏★✟✪❁✥▲✶❋✾■❏ ✁ ✙ ✭ ✟ ✬❅✛❩✛ ✾ ❨❦✜✣✕ ✙ ✭✤❄✌ ✭✝✤✙✮♦✦✥✜€✕ ✁ ✬▲✜✰✭✝✤❑✭✝✁☎✬✡✑✲✕✒✁✪✭✝✁☎✴❘✗✡✁✒✄✳✬✡✦✥✜✣❱ ✑✥✤ ✭❑✞ ❯ ✓✼✑✥✤❑✗✙✭✝✁✒✕✒✑✔✺€✸✙✦✥✭✘✁ ✑✥✓ ❫ ✭ ✾❉✎✙✭✝✁✪✮❲❄✌ s✏✜❫✎✙✭❋✱✳✜ ✁ ✆✆☎ ✻✞✂★✩✎✡✜✧✤✫❨❦✜✧❱❑❱❑✭❑❃●✞①❊■✑✲❱❑✗✡✦✥✑✲✜☞✓ ✁ ✙ ❑✭ ✞ ❯ ✓ ✁ s✩✭✘✓ ✺✪✎✡✄❄✓✖✜✧✤r✭✘✁✒✬✡✑✲✕✒✁✪✭✝✁☎✑✥✦✲✴❑✆➛✁☎✄✘❱ ✭✤✙✌ s✏✜❏✎✙✭❋✱✳✜ ✭ ✴ ❑✭ ✞ ❣ ✄❜s ✦✲✜✣✕ ✙ ✭✤✡✌ ✭✝✤✙✮✻✦✥✜€✕ ✁ ✬✍✜❏✭✝✤ ❫ ✭ ✾❉✺✣✄✘❱❑✗✡✦✥✜€✕✒✜☛✗✡✁☎✄✘✬✡✦✥✜✣❱ s❖✑✲✕✒✎ ✁ ✙ ❑✭ ✞ ❯ ✺✧✺€✄✳✁☎✮❙✾ ✑✥✤✡✽❘✕✒✄❇✕✒✎✡✜ ✙❳ ✁☎✓✖✕✏✓✖✕☎✭✝✕✒✜✣❱❑✜✧✤✳✕❬✄✝✆ ✕✒✎✙✜✰✕✒✎✙✜✣✄✘✁☎✜✣❱ s✏✜✿✎✙✭❋✱✘✜ ✭ ✴ ✭✤❄✌ ✭✘✤✙✮❑✎✡✜✣✤✍✺€✜ ✙ ✭ ✝ ✂ ☛✞ ✁ ✂ ✂ ✁ ✂ ✁ ✡ ✂ ☛ ✠☛✡ ✂ ✒✓✡ ✂ ✁ ✁ ✁✞ ✡ ✡ ✁ ✂ ✡ ✂ ✂ ✡ ✂ ✁ ✡ ✒✓✡ ✁ ✡ ✂ ✠☛✡ ✂ ✂ ✂ ✁ ✂ ✁ ✁ ✂ ✁ ✁ ✂ ✂ ✁ ✑✥✤✛✺✣✄✘✤❄✕✒✁✪✭✘✮✡✑✥✺€✕✒✑✥✄✘✤✵✕☎✄❑✕✒✎✡✜■✭✳✓✒✓✒✸✡❱❑✗●✕☎✑✲✄✳✤❦✞ ✞ ✘★✩✎✡✖✜✻✩✧✡ s❬✜✣✆ ✑✥✽✘❇✢✶ ✎❄✕❘✧✖✄✝✠✢✟ ✆❬✖✕✒✠✎✡✜ ✗✖❡❩✸ ✾❶✕✒✎ ❯ ✤❙❱✻✸✡✽✘✭✘✽✳✤✢✜€✕❘✎✙✭✘✑✥✓ ✓✿✑✲✤❙✱✳✄✳✜✧✸✡✓✖✕✒✤✙✜✧✺✣✮ ✜✧✓✧✭✝✞✵✦✥✦❈❛✡✎✡✄✘✑✔✁■✓☛✓✒❱♦✑✥❱♦✄✳✤✡✗✙✜✣✦✲✑✔✴✛✺€✑✲✕✟✑✥✤✴✹✌❈❀✝s✏❥q✜✻✽✘✭✘✄✳✓☎✦✥✮✛✓✒✸✡✤❙❱❑✸✡✜⑥✽✳✽✘✕☎✜€✎✙✕✪✭❜✓✣✕ ✞ ✞ ✌✑ ✞ ❾ ✭ ✮ ❾ ✣✴✣✴✣ ❾ ✭✡✠ ✜ ✭ ★ ✚ ☞ ✔✌ ✘✭ ✁✒✜❬✤✙✭❜✕☎✸✡✁✪✭✝✦❄✤❄✸✙❱❇✬▲✜✣✁✪✓✣✞ ✎✡✜✣✤⑥✕✒✎✙✜❬❱✻✭✘✤♦✮●✑✥✜✧✓ ❜✎✡✑✔✓✶✦✥✭✳✓✟✕✶s❖✑✥✦✲✦✡✺✣✄✘✤❄✕☎✭✘✑✲✤✙✓ ✕✒✎✙✜✹✆➛✄✘✦✥✦✲✄❜s❖✑✥✤✡✽ ✺✣✄✘✤✙✮●✑✲✕✒✑✥✄✘✤✷♥✢❩❉✆❘✎✡✑✥✓q✁✒✑✔✺✪✎✡✜☞✓✻✺✣✭✝✤ ✬▲✜✢✓✒✗✡✦✲✑✲✕q✑✥✤❄✕✒✄ ✕✟s❬✄ ✗✙✭✝✁✒✕☎✓✻✄✘✆❘✜ ❄✸✙✭✝✦ s❬✜✣✑✥✽✘✎❄✕ ❜✕☎✎✡✜✣✤♦✜✧✭✳✺✪✎❇✄✘✆✙✎✡✑✔✓✼✮✡✭✝✸✡✽✳✎❄✕✒✜✣✁✪✓◗✓✖✎✡✄✳✸✡✦✔✮❇✄✳✬●✕☎✭✘✑✲✤⑥✄✘✤✡✜✩✄✝✆✙✕✒✎✡✜☞✓✖✜✩✗✙✭✘✁✖✕✪✓✣✞❈❩❉✆✍✑✥✤✙✓✟✕☎✜✧✭✳✮ ✕✒✎✙✜✣✁☎✜❘✑✥✓✩✤✡✄✵✓✒✸✙✺✪✎r✗✙✭✝✁✒✕✒✑✲✕✒✑✥✄✘✤ ❙✕✒✎✡✜✧✤✛✭✘✦✲✦➆✎✙✑✥✓❖✽✳✄✘✦✔✮✫✓✒✎✡✄✳✸✡✦✥✮✫✽✘✄♦✕☎✄⑥✕☎✎✡✜■✺✪✎❙✸✡✁✪✺✪✎❦✞ ★✩✎✡✜♦✽✘✜✧✤✡✜✣✁✪✭✝✦ ✳✸✙✜✧✓✖✕✒✑✥✄✘✤✹✕☎✎✡✜✣✁☎✜€✆➛✄✳✁✒✜⑥✑✥✓✧♥✰❩✟✓☛✑➀✕❏✗✍✄❄✓✒✓✒✑✥✬✡✦✲✜❇✕✒✄✛✮●✑✥✱❄✑✔✮●✜♦✭q✓✒✜€✕❏✄✝✆ ✂ ✤✙✭✝✕✒✸✡✁✪✭✝✦ ✤❙✸✡❱❇✬▲✜✣✁✪✓ ✎ ✭ ✞ ❾ ❾✳✭ ✠ ✖☛✑✥✤✻✕✟s❬✄❇✓✖✸✙✬✙✓✖✜✣✕☎✓❬✓✖✸✍✺✪✎✻✕✒✎✙✭✝✕♠✕☎✎✡✜☛✓✒✸✡❱✻✓♠✄❜✱✳✜✣✁✂✜☞✭✘✺✪✎✵✓✒✸✡✬✙✓✒✜€✕✩✭✝✁☎✜ ✜ ❄✸✙✭✘✆ ✦ ☛ ★✩✎✙✑✥✓♦✗✡✁☎✄✘✬✡✦✥✜✣❱ ✑✔✓✻✺✣✭✘✦✲✦✥✜✧✮ ✁ ✭✘✤✙✮ ✑✔✓ ✁ ❫✾❉✺✣✄✘❱❑✗✡✦✥✜€✕☎✜✘✞ ★✩✎✡✜ ✝ ✝ ✓✖✕✒✁✪✭✝✑✥✽✘✎❄✕✖✆➛✄✳✁✒s✩✭✝✁✪✮ ✕☎✁✒✑✔✭✝✦✲✾❁✭✝✤✙✮❙✾❉✜✣✁☎✁☎✄✘✁❑❱❑✜€✕✒✎✙✄❙✮ ✑✥✓✫✄✘✤✡✦✥✴◆✗✡✁☎✭✳✺❽✕☎✑✥✺✧✭✝✦❖✆➛✄✳✁✫✓✒❱❑✭✘✦✲✦ ✂ ✿✭✘✓q✑➀✕ ✁☎✜ ❄✸✡✑✥✁✒✜☞✓✂✕☎✜✧✓✖✕✒✑✥✤✡✽❇✄✘✆❈✭✝✦✥✦ ❃ ✠ ✗✍✄❄✓✒✓✒✑✥✬✡✑✲✦✥✑✲✕✒✑✥✜✧✓✏✑✲✤q✕✒✎✡✜❫s✏✄✳✁☎✓✖✕❬✺✧✭✘✓✒✜✘✞ ❣ ✄✘✕✒✜✰✕☎✎✙✭❜✕✩✑✲✆❈✓✖✄✳❱❑✜✣✄✘✤✙✜ ✽✘✑✥✱✘✜☞✓✩✴✘✄✳✸r✭❑✓✒✄✘✦✥✸●✕✒✑✥✄✘✤ ●✴✳✄✘✸✛✺✣✭✘✤✫✱✳✜✣✁☎✑➀✆➛✴✻✕☎✎✡✑✔✓✰✓✖✄✳✦✲✸✡✕✒✑✥✄✘✤r✱✘✜✣✁☎✴✻✜✧✭✳✓✖✑✥✦✥✴✘✞ ❃ ★✩✎✡✜❑✆➛✄✘✦✥✦✥✄❜s❖✑✲✤✡✽✹✗✙✁✒✄✳✬✡✦✲✜✧❱ ◗✺✧✭✝✦✥✦✲✜☞✌ ✮ ☞ ✁ ✝ ✝ ✁ ✁ ✚ ✝ ❈✑✔✓■✭✝✦✔✓✒✄ ✁ ❫✾❁✺€✄✘❱❑✗✡✦✥✜€✕☎✜✘✞⑥❍❫✑✥✱✘✜✧✤ ✭✘✤ ✸✡✤✍✮●✑✲✁☎✜✧✺€✕✒✜☞✮✢✽✘✁✪✭✝✗✙✎ s❖✑✲✕✒✎ ✂ ✤✡✄●✮●✜✧✓ ❦✮●✄❙✜✧✓☛✕☎✎✡✜✣✁☎✜⑥✜ ●✑✥✓✖✕■✭ ✺€✴●✺✣✦✲✑✔✺❇✗✍✭❜✕✒✎ ✄✝✆♠✦✥✜✣✤✙✽✝✕✒✎ ✂ ✕✒✎✡✁☎✄✘✸✙✽✘✎✹✕☎✎✡✜⑥✽✳✁☎✭✘✗✡✎✢s❖✎✡✑✔✺✪✎✢✕☎✁☎✭❋✱✳✜✣✁✪✓✖✜☞✓❖✜✧✭✳✺✪✎✢✤✡✄●✮●✜♦✑✲✤ ✕✒✎✡✜ ✽✘✁✪✭✝✗✙✎✫✜ ●✭✳✺❽✕☎✦✲✴✵✄✳✤✙✺€✜✍☛ ✺ ✭ ✔✌ ✔✓ ✔✓ ✗ ✑✸ ✭ ✓ ✣✴✣✴✣ ✌ ✭ ✌ ✍✎ ✔✓ ✽✌ ✖ ✄ ☛ ☛✒ ✭ ✖ ☛ ✣✒ ☛✩✖ ✔✁✌ ☛✩✄ ✁ ☛ ☎✌ ✌ ✍✎ ❼ ➓✩➁✣✇❁✉❄✈①➈❄❻ ➔❽→ ✯✰✶✕✏ ✌✞✛❀✎✒✛❃✓❉✌ ✧✖✠✢✟✡✟❉✠ ✘✵❊ ✱ ✙✦✓ ✡ ✆ ❇✢✶☛✡ ✶✷✌✏✎✒✩✫✑ ✥ ✴✩✬✜✛✹✣✍✯✖✱✏✢ ✛ ✾✝★❍✺✹✱■✙✏✥▲✶✭✥✮✛✟✦✘✴✵✬❅✛✹✣✍✯✖✱✍✢ ✬❅✱✏✶✭❂❄✯ ✪✮✶☎✾■✬❅✛✟✢ ✣✏❏ ✦✵✱❃✻❉★✰✪❃✥✧✦❉✻ ★✰✯✧✯ ★✰✦ ✶☞☛◗✱✍✬■✶ ✍ ✺✹✱■✙✍✥▲✶■✥✮✛✟✦❙✴✩✬❅✛✑✣✏✯ ✱✏✢ ✥▲✶ ✙■★✰✯✧✯ ✱✜✺ ✙✥✓✮③ ✭ ③ ✙✦✓ ✡ ✆ ❇✢✶ ✎✒✶ ❯✒✥ ✾ ✪❋❊ ✱☛✙■✛✰✢✝✴✩✯✖✱✍✢ ✱✏✦ ✪✫★✟✬✭❏✲✴✵✬❅✛✹✣ ✌ ✯✖✱✍✢ ✥▲✶ ✭ ✌✿✙■✛✟✢ ✴✵✯✖✱✏✪ ✱ ✘ ✖✧✩ ✡ ✆ ❇✢✶ ✧✖✠✢✟✫✧✾✠ ★✩✎✙✜❏✆➛✄✘✦✥✦✲✄❜s❖✑✥✤✡✽❑✗✡✁☎✄✘✬✡✦✥✜✣❱ ✑✔✓ ✙✦✓❥③ ✭❫✾❁✺€✄✳❱❑✗✡✦✲✜✣✕✒✜✳♥ ☛✍✌ ✆✞✗✘✎ ✔ ❯ ✤r✸✙✤✙✮●✑✥✁✒✜☞✺❽✕✒✜☞✮r✽✘✁✪✭✝✗✡✎✫s❖✑➀✕☎✎ ✂ ✤✡✄●✮●✜☞✓✣✞ ✒✿✗✘✎ ✆ ✗✘✎ ✔ ✆ ✜✧✓✞✝ ✍✌ ✑➀✆✼✕☎✎✡✜✣✁☎✜ ✺✑✛✔✱✏✶✘✦✵✛✰❖✪ ✜✏●✎ ✑✔✓✟✕❫✭✵✺€✴●✺€✦✥✑✔✺❘✗✙✭❜✕☎✎✢✄✝✆✼✦✥✜✣✤✡✽✘✕✒✎ ✂ s❖✎✡✑✔✺✪✎✛✕✒✁✪✭❜✺ ✾ ✱✘✜✧✁☎✓✒✜✧✓❬✜☞✭✘✺✪✎r✤✡✄●✮●✜❘✑✲✤r✕☎✎✡✜❘✽✘✁✪✭✝✗✡✎✫✜✏✡✎ ✭✘✺€✕✒✦✥✴✵✄✘✤✍✺€✜✘✞ ✆ ❣ ✄ ✝✒●✌ ✄✝✕☎✎✡✜✣✁☎s❖✑✥✓✒✜✘✞ ✂ ✂ ✂ ✂ ✂ ✡ ✁ ✁ ✡ ✁ ✞ ✁ ❛❝❜✄✂✆☎ r✧♥ ☛ ♦✕q ✛ ✩✫✪✜❁✘✛❃✌✘❄✘✠ ✹✌ ❁✘✩✻✪✒❁✞✛✢✌✞❄ ☞ ★✩✎✡✜❬✕☎✜✣✁☎❱ ✮●✜✣✤✡✄✘✕✒✜☞✓◗✮✙✭❜✕☎✭❏✓✖✕✒✄✳✁☎✭✘✽✘✜✏✭✘✤✙✮■✁☎✜€✕☎✁✒✑✥✜✣✱❜✭✘✦❄❱❑✜☞✺✪✎✙✭✝✤✡✑✔✓✒❱❑✓ s❖✎✡✑✔✺✪✎ ✺€✄✳❱♦✗✙✸●✕✒✜❑✕☎✎✡✜q✭✘✮✙✮●✁✒✜☞✓✒✓✒✜✧✓❏✄✘✆✩✕✒✎✡✜q✮✙✭❜✕☎✭✛✁☎✜✧✺✣✄✘✁✪✮✡✓☛✆➛✁✒✄✳❱➎✺✣✄✘✁☎✁✒✜☞✓✖✗▲✄✘✤✍✮●✑✲✤✙✽✫❚✳✜✣✴●✓✣✞ ❛✡✄✳✁✒❱✻✭✘✦✲✦✥✴ ✡✭♦✎✙✭✳✓✖✎✫✆➛✸✡✤✙✺€✕✒✑✥✄✘✤ ✝ ✏❳ ☎ ⑤ ♥✟✞ ✎✙✭✳✓❑✕✒✄ ✬▲✜✢✮●✜ ✙✤✙✜✧✮◆s❖✎✡✑✔✺✪✎◆❱✻✭✘✗✙✓♦✕✒✎✡✜✢✓✒✜€✕✵✄✘✆❫❚✳✜✣✴●✓✠✞ ✕☎✄ ✭ ✓✖✜✣✕✵✄✝✆❘✭✘✮✡✮●✁☎✜✧✓☎✓✒✜✧✓❇⑤■✞ ❯ ✮✡✭✝✕☎✭✛✁☎✜✧✺✣✄✘✁✪✮✢s❖✑✲✕✒✎ ✭✛❚✘✜✧✴ ✳✙ ✞ ✑✔✓❏✕☎✎✡✜✣✤ ✓✖✕✒✄✳✁✒✜☞✮ ✭✝✕❘✕✒✎✡✜q✭✳✮✡✮●✁☎✜✧✓☎✓ ✝ €✞✫❧♠✭✳✺✪✎ ✓✒✸✡✬✙✓✒✜ ❄✸✡✜✣✤❄✕✩✁✒✜✣✕✒✁☎✑✲✜✧✱❜✭✝✦✙✁☎✜ ❄✸✡✜☞✓✟✕✏✆➛✄✘✁✏✕✒✎✡✑✔✓✩✮✡✭❜✕✪✭■✁☎✜✧✺✣✄✘✁✪✮✻✺€✄✘✤✍✓✖✑✔✓✟✕✪✓✏✓✒✄✘✦✥✜✣✦✥✴❑✄✝✆✷✺✣✄✘❱❑✗✡✸●✕☎✑✲✤✡✽ ✕✒✎✙✜❘✎✙✭✘✓✒✎✛✱❋✭✘✦✲✸✙✜ ✝ ❖✭✝✤✍✮✫✓✒✜✧✭✘✁☎✺✪✎✡✑✥✤✡✽❑✭❜✕✩✕✒✎✙✑✥✓✰✭✳✮✡✮●✁☎✜✧✓☎✓✣✞ ❩❁✤⑥✕✒✎✡✜✩✮●✜✧✓✒✑✥✽✘✤❇✄✘✆✙✎✙✭✳✓✖✎❘✕☎✜✧✺✪✎✡✤✙✑ ❄✸✡✜☞✓✷✕✟s❬✄✿✑✥❱❑✗✍✄✳✁✖✕✪✭✝✤❄✕✼✭✘✓✒✗✍✜☞✺❽✕☎✓◗✎✙✭❋✱✳✜✂✕☎✄☛✬▲✜❬✺✣✄✘✤✙✓✒✑✔✮●✜✣✁☎✜✧✮➆♥ ✔✓ ✔✓ ✗ ✸ ✗ ✸ ✓ ✁ ✓❉❇❃❇✢✛❃✪✒✭✝✛❃✓❉✤✍✌✞✮q✪ ✑✔✔ ✮●✜✣❩❉✕☛✤❄✕☎✎✙✑✥✺✧✭✘✭✝✓✩✦❦✕☎✎✙✄✵✭✳✬▲✓✖✎r✜❇✱❜✮●✭✝✜€✦✥✕☎✸✡✜✣✜✁☎❱❑✑✲✗ ✤✡✜☞✸✲✮✛✴ ✎✡✄❜s➋✗ ✸❬✕✒✎✡✑✥✜❇✓✩✎✍✺✧✭✘✭✝✓✒✤✙✜❘✮●✦✥✄✝✜✧✆✶✮❦✕✟✞ s❬✄✻❚✘✜✣✴●✓ ✭✝✤✙✮ ✄ s❖✑➀✕☎✎ ✁✭✝✤✍❁✘✮✫✓✡✓✒✛✢✎✡✙✥✶✄✘✸✙✓✡✦✥✮r✸ ❁✘✮●✑✔✩✫✓✟✪✜✕☎✁✒❁ ✑✥✬✡✸✺✸●✗✘✕☎✌✞✜❏✙✚✕✒✎✜✎✡✛✢✜■✓✡✌ ✓✒✜€✔ ✕❖★✩✄✝✎✡✆◗✜☛❚✘✜✧ ✎✙✴❙✭✘✓ ✓✒✎❑✆➛✸✡✭✘✄✤✙✓❬✺€✜✣✕✒✱✳✑✥✄✘✜✣✤✤✛✭✝✤✙✓✖✮r✎✡✄✳✭✘✸✡✓✩✦✔✮❑✁✪✭✝✬✍✤✍✜☛✮●✄✘✜✧❱❑✭✘✓✒✦✥✴■✴✵✕☎✭✘✄❇✓✩✺€✗▲✄✳✄✳❱❑✓☎✗✡✓✖✑✥✸●✬✡✕✒✦✥✜✜ ✄✴ ✂ ✄ ✝ ✝ ✝ ✗➛✑✥✤✛✄✘✁✪✮●✜✣✁✩✕☎✄❑❚✘✜✣✜✧✗q✕☎✎✡✜❘✤❙✸✡❱❇✬▲✜✣✁✿✄✝✆◗✺✣✄✘✦✥✦✲✑✔✓✒✑✲✄✳✤✙✓❖✓✖❱✻✭✘✦✲✦✧✸❽✞ ✁ ✓❉❇❃❇✢✛❃✪✒✛❃✓❉✌ ❇❃✛✢✪✒✎✦✠ ❯ ✤ ✜✧✭✳✓✖✴✛s✩✭❋✴✫✕☎✄q✕☎✁✒✜☞✭❜✕❏✺€✄✘✦✥✦✥✑✥✓✒✑✲✄✳✤✙✌ ✓☛✕✒✑✥✎✡✓☛✜✹✕✒✄r✓✒✄✝✦✥✾❁✑✲✺✣✤✡✭✝❚✢✦✥✦✥✜✧✮✙✮ ✭❜✕☎✙✥✭✫✓❉✄✘❇❃❇✢✬ ✛✢❱✟✪✜✜✧✛✢✺❽✓✡✕✪✌✂✓❫s❖❇✢✛✢✑➀✪✒✕☎✎ ✎ ✞ ✑✔✮●✜✣✤❄✕✒✑✔✺✣✭✘✦❖✎✙✭✘✓✒✎ ✱❜✭✘✦✲✸✡✜☞✓♦✕✒✄✳✽✘✜€✕☎✎✡✜✣✁♦✑✥✤◆✭ ✦✥✑✲✤✡✜☞✭✝✁❑✦✥✑✥✓✖✕✔♠ ❲❙✜☞✭✝✁✪✺✪✎✡✑✲✤✙✽✛✆➛✄✘✁❇✭✢✮✙✭❜✕☎✭✛✁☎✜✧✺✣✄✘✁✪✮ s❖✑➀✕☎✎ ❚✘✜✣✴ ✕☎✎✡✜✣✤ ✁☎✜✔❄✓ ✸✡✑✥✁✒✜☞✓■✺€✄✳❱❑✗✡✸●✕✒✑✥✤✡✽ ✗ ✸✭✼✌ ✭✝✤✍✮ ✓✒✸✡✬✙✓✒✜✔❄✓ ✸✡✜✣✤❄✕☎✦✲✴ ✓✖✜☞✭✝✁✪✺✪✎✡✑✲✤✙✽r✓✒✜✔❄✓ ✸✡✜✧✤✳✕☎✑✥✭✘✦✲✦✥✴✹✆➛✄✳✁ ✑✲✤ ✕☎✎✡✜q✺€✄✳✦✲✦✥✑✔✓✖✑✥✄✘✤ ✦✲✑✔✓✖✕❇✺€✄✘✁☎✁☎✜✧✓✒✗✍✄✳✤✙✮●✑✥✤✡✽ ✕✒✄ ✗ ❽✸ ✞ ✘✭✻✖✓✖✕✒✧✩ ✁☎✡ ✑✲✤✡✽✆ ❇✢✶ ✴ ✧✖✠✢✟✱❆✖✣✒✠ ✣✴❨✷✣ ✜€✕✸ ✡✌ s❬✜❘✬✍✜✰✮●✜✏✕✒✎✡✍❳ ✜✰✤✡✜❏✓✒✜€✕✒✕✂✎✡✄✘✜■✆▲✺✣✭✝✄✘✦✥✁☎✦✙✁✒✓✖✜☞✕✒✓✖✁☎✗▲✑✲✤✙✄✘✽✳✤✍✓✔✮●✘✌ ✑✲✭✝✤✙✤✙✽⑥✮⑥✎✙✦✥✭✳✜€✓✖✕❍✎r⑤ ✱❜✭✝✴ ✦✥✸✡✎ ✜❏❥❥✬❙❾ ✴✣✴✣✒✣ ❾✒❢✘❢ ✖✳✞◗❛✡✄✘✁ ✟✞ ✸ ✗ ✲✸ ✴ ✗ ✟✞ ✣✴✣✴✣ ✸ ✶✸ ✴ ✭✘✓☎✺✟✗ ✑✚ ✸ ➑✗ ❱❑✄❙✮ ❡☞❥✘❥✑€✸ ❾ ✡✞ ✝ ✝ ☛✞ ✞ ✝ ✝ ☞ ✚✍✌✧✞ ❼❖➒◗➁✧✇❁✈①❷✪✇ 0 .

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