By Christoph Meinel
One of many major difficulties in chip layout is the massive variety of attainable mixtures of person chip components, resulting in a combinatorial explosion as chips turn into extra advanced. New key leads to theoretical laptop technological know-how and within the layout of information buildings and effective algorithms, could be utilized fruitfully right here. the appliance of ordered binary determination diagrams (OBDDs) has resulted in dramatic functionality advancements in lots of computer-aided layout initiatives. This textbook offers 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 .
17 18 . .