✢✣✁✤☛✦✥✧✄★✥✧✩✕✥☞✪✫✍☎✞✔✬✭✄✎✮✡✁☎✯✡✄✰✏✒☛✲✱✴✳✤✏✵✥✧✏✶☛
✷✸✞✡✹✑✏✒✠✺✥✻✏✒✼✫✞✡✁✽✥✌✪✙✍☎✞✔✬✭✄✝✮✾✁☎✯✿✄❀✏❁✍✑✏❂✬❃✪✽✼✫✹✤✩❄✥✻✏✒❅✾❆✵✪
❇❉❈✡❊●❋■❍❑❏▼▲◆❏P❖❘◗❃❙❯❚❱❙✕❊✵❲❨❳❩❏❬❍❑❏▼❭❂❈❱❏❘❍❑❪
❫❴❙✤❈●❵■❲❜❛❑❝❡❞✲❪❢❚❤❣✺❪❢❲✐❊❱❏❡❥❧❦♠❛■❲❜❖♥❏
♦■❙✑♣■❲q❙✤❛■❏▼▲✙❋❑◗r❪❢❚❤❊❱❲❜❛■❏❡s❁❏❯❊❱❪❢t❜❵■❏
✉✈✞✡✖✝✪①✇②✪✽✠✦✄✎③✿✪✟✁✽✥✌✞
✂☎✄✝✆✟✞✡✠☞☛ ✌✍☛✏✎ ✑✓✒✕✔✖✒✕✆✘✗✚✙✛☛ ✠☞☛ ✜✢✄✝☛ ✠☞✣
✤✥✒✦✄✘✧☞✗✩★☞✪ ✫✬✣✭✔✯✮✰✣✱✗✲✆✘☛ ✳ ✴✵★✡✗✵✎ ☛
✶✸✷✺✹✻✹✽✼✩✾✽✿❁❀❃❂❅❄❇❆❈❀❇❉❊✾✻✼✵✹✻✼✩❋●✿❁❀❃❍■❀❏❀❃❆❏❑▼▲❊✾✻✹✽❆◆❍❊✼✓❖◗P❘✹❚❙
❯
✾❁❀❃❍❱▲■❀❃❂❅❄❇❆❲✼✵❳ ❑▼✷❩❨✵❋❊❬✩✷❩❀✥❍❊❀❭❑▼❆❘❳❪❉❊▲❱✿❁❀❃❂❅❄❇❆
❍■❀❏❫❴❋❱✷✺❵❘✼✵✾✻✹✽✷❩❍■❀❃❍❱✼❜❛■✼✵❍❊✼✩✾✻❀❃❝✭❍❊✼❜❞❜✷✺❋■❀❃✹
❯
✼✵✾❁❀❃✷✺✹✩❡
❬✵❆❘❳❢❆❜✾✻✼✵❣❤▲❱✷❩✹✻✷✐✿❁❆✓❉■❀❃✾✽❬✩✷❥❀❇❝❦❉■❀❃✾❁❀❜❀❜❆❘❧♠✿❁✼✩❋❱❂❅❄❃❆❜❍❊❆
♥
✾✻❀❃▲✛❍❊✼✭❞❜✼✩✹♦✿❁✾✽✼✭✼✩❳♣❑▼✷❩❨✵❋❊❬✩✷❩❀❴❍■❀q❑▼❆❘❳❢❉❱▲❱✿r❀❃❂✩❄❃❆❊s
✉✈✞✡✖✝✪①✇②✪✽✠✦✄✎③✿✪✟✁✽✥✌✞
④✒⑤
✍✕✞⑥✁☎✪✾✆✽✞✡✼✙⑦☎✠✦✪⑧✍✕✞
❫❴❳❢❀☞☛▲❊❋❊❂❅❄❇❆✍✌✏✎✒✑✓✌ ❉ ✼✩✾✔☛ ✼✵✷✺✿❁❀ ❳✖✕❩❋❱✷❩❳❢❀✡✗ ▲❊❳❢❀☞☛▲❊❋❊❂❅❄❇❆ ❧❱✷✙✘✽✼✵✿✻❆❘✾❁❀ ❣ ▲❊✼◆❳❢❀❃❉ ✼✵✷❥❀ ▲❊❳ ❬✩❆❘❋✒✘✽▲❱❋ ✿✻❆
✼✩✹♦✿✓✚❇✿✻✷❩❬✵❆ ❍❊✼
n
❬✓✛■❀❅❵❘✼✵✹❜✼✵❳ ▲❊❳❢❀❈✿r❀❇❧ ✼✵❝❥❀✜✌✏✎✒✑✓✌❏❍❊✼ ✿❁❀❃❳ ❀❇❋✢✛❊❆n
s ❫❴❳❢❀ ❵❇❀❃❋●✿r❀♥
✼✩❳ ❍■❀❃✹✂☛ ▲❊❋❊❂✤✣♠✼✵✹
✌✏✎✒✑✓✌ ❉ ✼✵✾✔☛ ✼✩✷✐✿r❀❃✹ ❳✖✕❩❋❊✷✺❳ ❀❇✹✏✼✩❳ ✿❁✼✩✾✽❳❢❆❃✹❪❍❱✼✓✼✵❬✩❆❘❋❱❆❘❳❢✷❩❀ ❍❊✼✡✼✩✹✻❉❊❀❃❂✩❆✡✗✓❣ ▲❊✼✓❋■❄❃❆✥✛✦✚◆❋❊✼✩❬✵✼✩✹✽✹✻✷❩❍❊❀❃❍❊✼✓❍❊✼
❀❃✾✽❳ ❀★✧✵✼✩❋■❀❇✾✏❀❃✹✦❬✓✛■❀❅❵❘✼✵✹✩❡ ❀❃❉ ✼✵❋■❀❃✹✏❀✩☛ ▲❊❋❊❂✩❄❃❆✪✗ ✹✽▲✏✫■❬✵✷❩✼✩❋●✿✻✼ ❉■❀❃✾✻❀ ❬❅❀❃❝✺❬✩▲❊❝❩❀❃✾ ▲❊❳❢❀❜✼✩❋●✿✻✾❁❀❃❍■❀❜❋■❀❜✿r❀❇❧ ✼✵❝❥❀❱s
✬❦✹✽✿❁❀◆❍❱✷❩✹✻✹✽✼✩✾♦✿r❀❃❂✩❄❃❆❏❀❃❉❊✾✻✼✵✹✻✼✵❋ ✿❁❀❈▲❊❳ ✼✩✹♦✿❁▲❊❍❊❆❏❬✩❆❃❳❢❉■❀❇✾❁❀❇✿✻✷✺❵❘❆ ❍❊❆❘✹ ❉❊✾✻✷✺❋❊❬✩✷✺❉■❀❃✷✺✹✛❀❃❝
♥
❆❘✾✻✷✐✿❁❳❪❆❘✹ ❉■❀❃✾❁❀
♥
✼✩✾❁❀❇✾
☛ ▲❊❋❊❂✤✣♠✼✵✹✭✌✏✎✒✑✓✌q❉ ✼✵✾✔☛ ✼✵✷✺✿r❀❇✹ ❳✖✕❩❋❱✷❩❳❢❀❃✹✯❍❊✷✺✹✻❉ ❆❘❋✢✕✐❵❘✼✩✷✺✹ ❋■❀✦❝✺✷✺✿❁✼✵✾❁❀❇✿✻▲❊✾❁❀♠s✟✮❴❝✯✗✩❳ ❍❊✷❩✹✽✹✻❆❊❡ ❬✩❆❃❳❢❉■❀❇✾❁❀❃❳❪❆❘✹✰☛ ▲❊❋❊❂✤✣♠✼✵✹
✌✏✎✒✑✓✌ ❉ ✼✩✾✔☛✼✵✷✺✿❁❀❃✹▼❳✖✕❩❋❊✷✺❳ ❀❇✹ ❬✵❆❘❳ ❆✏✿❁✾✻❀❃❍❊✷❩❬✵✷❩❆❘❋❊❀❃❝ ❳✱✗✲✿❁❆❤❍❊❆✏✼✵❋❊❍❊✼✩✾✽✼✩❂✩❀❃❳❢✼✵❋●✿❁❆❪❀❃❧ ✼✩✾✽✿✻❆✛❣ ▲❊✼q✿❁✾✻❀❇✿r❀✦❬✩❆❘❝✺✷❩✹✲✣❤✼✩✹
❉ ❆❘✾✖✌✏✎✒✑✓✌☎✳✵✴☎✶❢❝✺✷❩❋❊✼✩❀❃✾✩s✷✮ ✿❁❀✒✸❱❀ ❍❊✼ ❆❤❬✩▲❱❉■❀❃❂❅❄❇❆ ❆❘▲✹☛❀❇✿✻❆❘✾✏❍❱✼ ❬❅❀❇✾
♥
❀✪✗ ❍❊✼✤✫■❋❱✷❩❍■❀ ❉ ✼✩❝❩❀❜✾✻❀★✧❅❄❃❆ ✼✩❋●✿❁✾✽✼ ❆
❋✻✺❊❳❪✼✩✾✻❆✡❍❊✼ ✾✽✼
♥
✷✺✹✽✿❁✾✽❆❘✹✕❀❃✾✽❳ ❀✼✧✩✼✩❋❊❀❃❍❊❆❘✹✕❋■❀ ✿❁❀❃❧ ✼✵❝❥❀ ✼ ❆✡✹✻✼✵▲❏✿❁❀❃❳❢❀❃❋✢✛❊❆❊s✏❫❴❳✢✾✽✼✩✹✽▲❊❝✺✿❁❀❃❍❊❆☞✷❩❋●✿✻✼✩✾✻✼✵✹✻✹✻❀❃❋●✿❁✼
❍❊✼✵✹✽✿❁✼❴✼✩✹♦✿❁▲❊❍❊❆✽✗❴❣ ▲❊✼✸❀✦❀❅❵❇❀❃❝✺✷❥❀❃❂✩❄❃❆✕❍■❀✾☛▲❱❋❊❂❅❄❃❆✿✌✏✎✒✑✓✌✕❉ ✼✩✾❀☛ ✼✩✷✐✿r❀ ❳✱✕✺❋❊✷❩❳❢❀✸❉■❀❃✾✻❀ ✼✵❋❊❬✩❆❃❋ ✿✻✾❁❀❃✾ ▲❊❳❢❀ ❉ ❆❘✹✽✷❩❂❅❄❇❆
❍■❀✡✿r❀❃❧ ✼✩❝❩❀❁✌✏✎✒✑✓✌❂✗❢❳ ❀❇✷❩✹ ✾❃✚❃❉❱✷❩❍■❀✓❍❊❆ ❣ ▲❊✼❢❆ ❳✱✗✲✿❁❆❤❍❊❆✓✼✩❋❊❍❊✼✵✾✻✼✵❂❅❀❃❳❪✼✩❋●✿❁❆◆❀❇❧ ✼✵✾✽✿❁❆❜❉■❀❃✾✻❀❜❆❤❬✩▲❊❉■❀❇❂❅❄❃❆❜❍■❀
✿r❀❇❧ ✼✵❝❥❀ ❀❃❬✩✷✺❳ ❀✕❍❊✼
40%
s✰✮❴✹✻✹✽✷❩❳✓❡❤❉❊❀❃✾❁❀ ❣ ▲❊✼✸❆ ❳✱✗✲✿❁❆❤❍❊❆ ✼✩❋❊❍❊✼✵✾✻✼✵❂❅❀❃❳❪✼✩❋●✿❁❆✛❀❃❧ ✼✵✾✽✿✻❆ ✿✻✼✩❋✢✛■❀ ❍❊✼✩✹✽✼✩❳❪❉ ✼✵❋✢✛❊❆ ❳❪✼✩❝✯✛❱❆❘✾✦❍❱❆ ❣ ▲❊✼✂☛ ▲❊❋❊❂✤✣♠✼✵✹✱✌✏✎✒✑✓✌✡❉ ✼✩✾✔☛✼✵✷✺✿❁❀❃✹✏❳✖✕❩❋❊✷✺❳ ❀❇✹✾✗❢❋❊✼✩❬✵✼✩✹✽✹❃✚❃✾✽✷❩❆ ❳❢❀❃❋●✿❁✼✩✾✏❉ ✼✵❝❩❆ ❳❪✼✩❋❱❆❘✹60%
❍❊❀❃✹✮ ❳❪✷❩❋❊✷✺❳ ❀❇❝❱❉ ✼✩✾✔☛✼✵❬✵✿ ✛■❀❃✹✲✛✱☛ ▲❊❋❊❬✵✿✻✷❩❆❘❋❪✷❩✹ ❀✦❧❱✷✙✘✽✼✩❬✲✿❁✷✺❆❘❋✱☛▲❊❋❱❬✵✿❁✷✺❆❘❋ ✿❃✛■❀❇✿ ❳❢❀❃❉❊✹ ❀✏✹✽✿❁❀❇✿❁✷✺❬ ✹✽✼✵✿▼❆★☛
n
☞ ✼☎✌❤✹✷❩❋●✿✻❆❴❀✭✛■❀❃✹✔✛ ✿❁❀❃❧❊❝✺✼❦❆★☛❱✹✽✷✯✧✵✼
n
s ✮❴❋✏❀❃❍♠❵❃❀❇❋ ✿❁❀♥
✼ ❆★☛♠❳❢✷✺❋❊✷❩❳❢❀❃❝ ❉ ✼✩✾✔☛✼✵❬✵✿✟✛■❀❃✹✔✛✾☛▲❊❋❱❬✵✿❁✷✺❆❘❋❊✹✘✷❩❋✕✿✻✼✩✾✻❳❪✹✘❆★☛♠✹✻❉■❀❃❬✵✼
✷❩✹ ✿❃✛❊❀❇✿❴✿✲✛❊✼✩✾✽✼✏✷✺✹ ❋❱❆ ❋❊✼✩✼✵❍ ✿❁❆❢✹✽✿✻❆❘✾✻✼ ✿❃✛❊✼✦✹✻✼✲✿q❆★☛
☞
✼☎✌❤✹✩❡ ✘✽▲❊✹✽✿❴✿❃✛❊✼✾☛▲❊❋❊❬✲✿❁✷❩❆❃❋❜✷✺✹❴✹✽▲✎✍❪❬✩✷❩✼✵❋●✿✸✿❁❆❢❬❅❀❃❝✺❬✩▲❊❝❩❀❇✿❁✼
✿❃✛❱✼✷✛❊❀❃✹✲✛ ✿r❀❃❧❱❝❩✼☞✼✩❋●✿✻✾✏✌❘s✒✑ ✛❊✷✺✹ ✿✲✛❊✼✩✹✽✷❩✹ ❉❊✾✽✼✩✹✻✼✵❋●✿❁✹ ❀◆❬✩❆❃❳❢❉■❀❇✾❁❀❇✿✻✷✺❵❘✼ ✹✽✿❁▲❱❍✎✌ ❆★☛✸✿✲✛❊✼✡❳ ❀❇✷❩❋ ❀❃❝
♥
❆❘✾✻✷✐✿❃✛❊❳❪✹
✷❩❋ ✿❃✛❱✼✓❝✺✷✺✿✻✼✩✾❁❀✰✿❁▲❊✾✽✼✂☛❆❘✾
♥
✼✩❋❊✼✵✾❁❀❇✿✻✷❩❋
♥
❳❪✷❩❋❊✷✺❳ ❀❇❝ ❉ ✼✩✾❀☛ ✼✩❬✵✿✱✛■❀❃✹✔✛✜☛ ▲❊❋❱❬✵✿❁✷✺❆❘❋❊✹✵s ❞❜❆❘✾✽✼✩❆ ❵❘✼✵✾✩❡✔✓ ✼✓❬✩❆❘❳❪❉■❀❃✾✽✼
❳❪✷❩❋❊✷✺❳ ❀❃❝✝❉ ✼✩✾❀☛ ✼✩❬✲✿ ✛■❀❃✹✔✛❁☛ ▲❱❋❊❬✵✿✻✷❩❆❘❋❊✹✕✓ ✷✺✿❃✛❜✿❃✛❊✼✛✿✻✾❁❀❃❍❊✷✐✿❁✷✺❆❘❋■❀❃❝✝❆❘❉ ✼✩❋◆❀❇❍❊❍❊✾✻✼✵✹✻✹✽✷❩❋
♥
❳❪✼✵✿❃✛❱❆♠❍ ▲❱✹✻✷❩❋
♥
❝❩✷❩❋❱✼❅❀❃✾
✛■❀❃✹✔✛❊✷❩❋
♥
✿❁❆✦✾✻✼✵✹✻❆❘❝✐❵❘✼✸❬✵❆❘❝❩❝✺✷❩✹✽✷❩❆❘❋❊✹✵s✖✑ ✛❊✼q❝❩❆❘❀❃❍✖☛ ❀❇❬✵✿❁❆❃✾ ✷✺✹ ❍❱✼✤✫■❋❊✼✵❍✡❀❃✹ ✿❃✛❊✼❴✾❁❀❇✿✻✷❩❆ ❧ ✼✲✿✗✓▼✼✵✼✩❋ ✿❃✛❱✼✸❋ ▲❊❳✛❧ ✼✩✾ ❆★☛
✾✻✼✵❬✩❆❘✾✽❍❊✹✱✹✽✿✻❆❘✾✻✼✵❍☞✷❩❋ ✿✲✛❊✼q✿r❀❇❧❊❝❩✼✸❀❃❋❊❍☞✷✺✿✻✹▼✹✽✷✯✧✩✼❇s ✮✸❋✡✷❩❋●✿✻✼✩✾✻✼✵✹✽✿✻✷❩❋
♥
✾✽✼✩✹✽▲❊❝✺✿✱❆✼☛✝✿❃✛❊✷✺✹✭✹✽✿✻▲❊❍✎✌ ✷✺✹ ✿✲✛■❀❇✿✭✿✲✛❊✼✸✿❁✷✺❳❢✼
✿❁❆✡❬✩❀❃❝❩❬✵▲❊❝❥❀❇✿✻✼ ❀❂✛■❀❃✹✲✛◆✿r❀❇❧❊❝❩✼ ✼✵❋ ✿✻✾✏✌◆❧✘✌ ✿✲✛❊✼ ❳❢✷✺❋❊✷❩❳❢❀❃❝✟❉ ✼✵✾✔☛ ✼✩❬✲✿✾✛■❀❃✹✲✛❁☛▲❊❋❊❬✲✿❁✷✺❆❘❋◆✷❩✹✕✹✻❳❢❀❃❝✺❝❩✼✩✾❴✿❃✛■❀❃❋◆✿❃✛❱✼
✿❁✷✺❳❢✼ ☛❆❘✾ ✿❃✛❱✼✏❆❘❉ ✼✩❋ ❀❇❍❊❍❊✾✻✼✵✹✻✹✽✷❩❋
♥
❳❪✼✵✿✲✛❊❆❤❍✙✓✭✛❊✼✵❋ ✿❃✛❊✼✦❝❩❆●❀❃❍ ☛ ❀❃❬✲✿❁❆❘✾ ✷❩✹❴❀❃❧ ❆ ❵❃✼
40%
s✚✑ ✛ ▲❊✹✵❡ ✿❃✛❊✼✦❆❘❉ ✼✩❋ ❀❃❍❊❍❱✾✻✼✩✹✽✹✻✷✺❋♥
❳❢✼✲✿❃✛❊❆❤❍ ✷❩✹✰☛ ❀❃✹♦✿❁✼✵✾✖✿❃✛■❀❃❋ ❳❪✷❩❋❊✷✺❳ ❀❇❝●❉ ✼✵✾✔☛ ✼✩❬✲✿ ✛■❀❃✹✲✛✿☛▲❊❋❱❬✵✿❁✷✺❆❘❋❊✹❦❆❘❋❱❝✛✌✜✓✭✛❊✼✩❋❪❳❢❆❃✾✻✼▼✿✲✛■❀❃❋
60%
❆★☛✟✿❃✛❊✼ ✛■❀❇✹✲✛✡✿r❀❃❧❊❝✺✼✕✼✩❋●✿❁✾✽✷❩✼✵✹❴❀❇✾✻✼
☞
✬❦❳ ❉❱✾✻✷❩❳❪✼✩✷✺✾✻❆ ❝❩▲
♥
❀❃✾
♥
❆❘✹✽✿❁❀❃✾✻✷❩❀✦❍❊✼✕❀
♥
✾❁❀❃❍❱✼✩❬✩✼✵✾✱❀✛✶✸✼✵▲❊✹✱❉ ❆❘✾ ✿✻✼✩✾▼❬✵❆❘❋❊❬✵✼✩❍❊✷✺❍❊❆ ❀✏❳❪✷❩❳ ❵❤✷❩❍■❀✦✼q✹❁❀❃❧ ✼✩❍❱❆❘✾✻✷❩❀
❉■❀❃✾✻❀ ✾✻✼❅❀❇❝❩✷✯✧✩❀❃✾✭▲❊❳ ✹✻❆❘❋✢✛❱❆❢❍❊✼ ✷✺❋✏☛✗✖❃❋❊❬✵✷❥❀❱s
❯ ❆❃✹✽✿r❀❇✾✻✷❥❀ ❍❊✼✱❀
♥
✾❁❀❃❍❊✼✵❬✩✼✵✾✖❀❃❆❘✹◗❳❢✼✵▲❊✹✖❣ ▲❊✼✵✾✻✷❩❍❱❆❘✹✖❉■❀❃✷✺✹✖❞❜❀❃✾✻✷❩❀✙✘ ✺❊❬✩✷❩❀❴❍❊✼✚✘✝✷✺❳ ❀✜✛▼❆❃✿✻✼✩❝✯✛❱❆q✼✚✢❃❆❘✹✔✗✤✣q✷✐✿❁❆❘✾
✛▼❆❃✿✻✼✩❝✛❊❆ ❉ ✼✵❝❩❆❘✹▼✹❁❀❃❬✵✾✻✷☛✕✺❬✩✷✺❆❘✹▼✾✽✼❅❀❃❝✺✷✯✧❅❀❇❍❊❆❘✹✭❉■❀❇✾❁❀ ✼✩✹♦✿r❀ ❬✩❆❘❋❱❣❤▲❱✷❩✹✽✿❁❀❱s
❯
❆❘✹✽✿❁❀❃✾✻✷❩❀✏❍❊✼ ❀
♥
✾✻❀❃❍❊✼✩❬✵✼✩✾✭✿❁❀❃❳✛❧ ✗✩❳ ❀❇✹
❳❪✷❩❋✢✛■❀❇✹ ❣ ▲❊✼✵✾✻✷✺❍■❀❃✹ ✷❩✾✻❳❢❄❃✹ ❑▼✾✽✷❩✹✽✿✻✷❥❀❃❋❱✼ ❑▼▲❱❉ ✼✵✾✽✿❁✷✺❋❊❆✥✛ ❆❃✿❁✼✵❝✯✛❊❆✓✼
❯
❝❩✼✵✷❩❬✵✷❥❀❃❋❊✼❪❑▼▲❱❉ ✼✵✾✽✿❁✷✺❋❊❆✦✛▼❆❃✿❁✼✵❝✯✛❊❆❱❡◗❉ ✼✩❝✺❆
❬❅❀❇✾✻✷❩❋✏✛❊❆ ✼✦❀❇❳❢❆❘✾▼❍■❀❃✹ ❍❊▲■❀❃✹ ❳❪✼✩❝✛❊❆❘✾✻✼✵✹✱✷❩✾✽❳ ❄❃✹▼❍❊❆ ❳✛▲❊❋❊❍❊❆❱s
✑✯❀❇❳✛❧ ✗✵❳
♥
❆❘✹♦✿r❀❃✾✽✷❥❀ ❍❊✼❜❀
♥
✾❁❀❇❍❊✼✩❬✵✼✩✾❢❀❏❳❪✷❩❋✢✛❊❀◆❋❱❆❘✷✺❵❇❀◆✼✷☛▲❱✿✻▲❊✾❁❀◆✼✩✹✽❉ ❆❃✹❁❀✧✢❘❀❇❋■❀★✕❩❋❊❀❈❞❜❀❃✾✻❬✵❆❘❋ ❞ ❀ ❙
❬✓✛■❀❃❍❱❆☞❉ ✼✵❝❩❆ ❀❇❳❢❆❘✾✵❡ ❬✵❆❘❳❪❉❊✾✻✼✵✼✩❋❊✹✻❄❃❆❊❡ ❬✵❆❘❳❢❉❊❀❃❋✢✛❊✼✵✷❩✾✻✷✺✹✻❳❪❆❢✼✦✷❩❋❊❬✵✼✩❋●✿❁✷✐❵❘❆☞❍❊▲❱✾❁❀❃❋●✿❁✼✏❳❢❆❘❳❪✼✩❋●✿✻❆❘✹❴❋❱❆❘✹q❣ ▲■❀❃✷✺✹
✿❁✷✐❵❘✼❪❵❘❆❘❋●✿r❀❇❍❊✼ ❍❊✼❢❍❊✼✩✹✽✷❩✹♦✿❁✷❩✾ ❍❊✼❪✿❁▲❊❍❊❆❱s✥★q❧❊✾✽✷
♥
❀❃❍❱❆✥✢❘❀❃❋❊❀❱❡✯❬✵❆❘❳❲❀
♥
✾✻❀❃❂❅❀✓❍❊✼ ✶✸✼✵▲❊✹✛✼✵❳❲❋❱❆❘✹✻✹✻❀❃✹✏❵❤✷❩❍■❀❇✹
❬✩❆❃❋ ✿✻✷❩❋ ▲■❀❃✾✽✼✩❳❪❆❘✹ ❀ ✹✻✼✩✾ ❳✛▲❱✷✺✿❁❆ ☛✼✵❝❩✷✧✩✼✩✹✵s
✢❘❀❃❳❢❀❃✷❩✹q❉ ❆❤❍❊✼✩✾✽✷❥❀ ✼✩✹✽❣ ▲❊✼✩❬✵✼✩✾✏❍❱✼❢❀
♥
✾❁❀❃❍❱✼✩❬✩✼✵✾ ❀❃❆❘✹ ❳❢✼✵▲❊✹✕❣ ▲❊✼✩✾✽✷❩❍❊❆❃✹ ✿✻✷❩❆❘✹✪✩❤▲❊❍✦✚❃✾✽✷❩❆ ✮✸❝✐❵❘✼✩✹ ✼❢❞✪✚❃✾✽❬✩✷❩❀
✫❴❆ ❵❇❀❃✼✵✹ ✮✸❝✐❵❘✼✵✹✩❡❤❆❘✹ ❣ ▲■❀❇✷❩✹ ❳❢✼❴❀❃❬✩❆❃❝✯✛❊✼✵✾❁❀❃❳ ❬✵❆❘❳ ✿❁❆❤❍❊❆ ❬❅❀❃✾✽✷❩❋✢✛❊❆ ✼✭☛ ❆❘✾❁❀❃❳ ❵❃✼✩✾✽❍■❀❃❍❊✼✵✷❩✾✻❆❃✹ ❉■❀❇✷❩✹ ❉■❀❃✾❁❀ ❳❪✷❩❳
❍❊▲❊✾✻❀❃❋●✿❁✼ ❆❘✹✭✬✯✮✛❳❪✼✩✹✻✼✵✹ ❍❊✼✦❳❪✼✩✹♦✿❁✾✻❀❃❍❊❆❊s
❯
❆❃✹✽✿r❀❇✾✻✷❥❀ ❍❊✼✏❀
♥
✾❁❀❇❍❊✼✩❬✵✼✩✾q❀❇❆ ❳❪✼✩▲ ❆❘✾✽✷❩✼✵❋ ✿❁❀❃❍❊❆❘✾ ❖❦✾✻❆✼☛❚s✰✫ ✷✺❵❤✷❩❆✲✱ ✷✺❵❤✷❥❀❇❋❊✷ ❡❊❉ ❆❘✾ ✿❁✼✵✾✸✹✻✷✺❍❊❆ ❳✏▲❊✷✺✿✻❆❢❳❢❀❃✷❩✹
❍❊❆❜❣❤▲❱✼❢▲❊❳ ❆❃✾✻✷❩✼✵❋●✿r❀❃❍❊❆❃✾ ✼❪❉ ❆❘✾✕✿❁✼✩✾ ❍■❀❃❍❱❆ ❀✡❳❢✷✺❳✢❀❜❆❃❉ ❆❘✾♦✿❁▲❊❋❱✷❩❍■❀❃❍❱✼❪❍❱✼ ❀❃❉❱✾✻✼✩❋❱❍❊✼✩✾ ▲❊❳ ❉ ❆❘▲❊❣ ▲❊✷❩❋✏✛❊❆
❬✩❆❃❳ ❀ ✹✻▲■❀ ✼ ✸♠❉ ✼✩✾✻✷✺❨✩❋❊❬✵✷❥❀❱s
❯ ❆❃✹✽✿r❀❇✾✻✷❥❀ ❍❊✼ ❀
♥
✾❁❀❇❍❊✼✩❬✵✼✩✾✘❀❃❆❘✹✘❀❇❳❢✷
♥
❆❘✹ ❍❊❆✜✘✟❀❇❧ ❆❘✾✻❀❇✿❁P❃✾✻✷❩❆ ❉■❀❃✾✻❀✚✑✟✾❁❀✰✿r❀❃❳❪✼✩❋●✿❁❆✱❍❊❀✴✳ ❋ ☛❆❘✾✻❳❢❀❃❂❅❄❇❆ ✮✸❋✢✕✺✹✻✷✺❆
❞❜✼✵❋❊❍❊✼✩✹✵✘✘❀❃❬✵✼✩✾✻❍❊❀❱❡✴✶✸❝✺❵❇❀❃✾✽❆✧✷ ❆♠❍❱✾✻✷
♥
▲❊✼✩✹ ❖◗✼✩✾✽✼✩✷✺✾❁❀☞✢★✺❊❋❊✷✺❆❘✾✩❡ ❑ ✛❊❀❃✾✻❝✺✼✩✹✓★q✾✻❋❱✼✩❝❥❀❇✹ ✮✸❝✺❳❢✼✵✷❩❍■❀♠❡ ❑▼❝❥❀❃▲❱❍❊✷❩❋❊✼
✩❱❀❃❋●✿✻❆❘✹✸✛✭❀❃❍❱▲❊✼❃❡ ❛✰✚❃❧❱✷❩❆ ❑▼❆❃✹✻✹✻✼✵❋✢✧✩❆❱❡✭❞ ❀❇✾✻❬✩❆ ✮❴❋●✿✺✹❘❋❊✷✺❆◆❖❦✷❩❋✢✛❊✼✵✷❩✾✽❆ ❍❊✼✓❑▼✾✽✷❩✹✽✿✻❆❊❡ ❖ ✚❅❵❃✼✩❝ ❑✭❀❃❝❩❀❃❍❊❆❊❡✻✩✏✚❅❵♠✷✺❆
★q✾✻❋❊✼✵❝❥❀❃✹ ✮❴❝❩❳❪✼✩✷❩❍❊❀ ✼✚✑ ✛❊✷✺✼✩✾✽✹✻❆❘❋ ❑▼❆❘▲❱✿❁❆✼✷ ❆❃✹❁❀ ❉ ✼✵❝❥❀ ❀ ✘✽▲❊❍■❀ ❬✩❆❘❳ ❀ ❍❊✼✤☛ ✼✵✹❁❀ ✼❴❬✵❆❘❳ ❆✦❍❱✼✩✹✻✼✵❋●❵❘❆❘❝✐❵♠✷✺❳❢✼✵❋●✿❁❆
❍■❀ ❍❱✷❩✹✻✹✽✼✩✾♦✿r❀❃❂✩❄❃❆❊s ✑◗❀❃❳✛❧ ✗✩❳
♥
❆❘✹♦✿r❀❃✾✽✷❥❀✓❍❊✼ ❀
♥
✾❁❀❃❍❊✼✵❬✩✼✵✾ ❀❃❆ ❀❃❳❪✷
♥
❆❜✶✸❀ ❵❤✷✺❍ ❞❜✼✩❋❊❆❇✿❁✷▼❉ ✼✩❝❩❀❃✹✏❍❱✷❩✹✻❬✵▲❊✹✻✹✔✣♠✼✵✹
✼✡❬✩✾✔✕✺✿❁✷✺❬❅❀❃✹ ❣ ▲❊✼❜✼✩❋❊✾✽✷❩❣ ▲❊✼✵❬✩✼✩✾✻❀❃❳ ❳✛▲❊✷✐✿❁❆ ✼✵✹✽✿r❀❏❍❊✷❩✹✽✹✻✼✵✾✽✿r❀❇❂❅❄❃❆❊s✒✑◗❀❃❳✛❧ ✗✩❳
♥
❆❃✹✽✿r❀❇✾✻✷❥❀ ❍❊✼❜❀
♥
✾✻❀❃❍❊✼✵❬✩✼✩✾❪❀❃❆❃✹
❳❪✼✩▲❊✹ ❀❃❳❪✷
♥
❆❘✹✯❍❊✼❴✾✽✼✩❉✢✺❱❧❊❝❩✷✺❬❅❀✪✘✘✷
♥
✷❥❀❇❋❊✼ ✮✸❝✐❵❘✼✵✹ ❍❊✼✰✩♠❆❘▲✏✧❅❀❱❡✽✘✝▲❊❬✩✷❩❀❃❋❊❆ ❛✯❝✚❅❵❤✷❩❆✦❞❜✼✵✷❩✾✻❀ ✼❴❞ ❀❃✾✽❬✩❆❘✹✾✣q✷✺❋✢✕❩❬✵✷❩▲❊✹
✑✟✼✩✷✸♠✼✵✷❩✾❁❀✡❉ ❆❘✾ ✿✻✼✩✾✽✼✩❳✥❳❢✼❪❀ ✘✽▲❱❍■❀❃❍❊❆ ❀❜✹✻▲❱❉ ✼✵✾❁❀❃✾ ❬✩❆❘❳✥❧ ❆❘❳ ✛ ▲❊❳❪❆❘✾ ❳❢❆❘❳❪✼✩❋●✿✻❆❘✹ ❍❊✷☛ ✕✺❬✩✼✩✷✺✹ ❣❤▲❱✼ ❉■❀❃✹✽✹✻✼✵✷
♥ ♥ ♥
❳❪✼✩✹✽✿✻✾❁❀❃❍❱❆✁ ❀
♥
❋❱✼✩✾ ❛■✼✩✾✽✾✻✼✩✷✺✾❁❀ ❍❱✼ ✛▼❀❃✾✻✾✽❆❘✹✕✼ ❛ ❀❃❧❊✾✲✕✺❬✩✷✺❆✓★q✾✻❝❥❀❇❋❊❍❊❆☞✶q❀❇❳ ❀❃✹✽❬✩✼✵❋❊❆❜❉ ❆❘✾q❬✵❆❘❳❪❉■❀❃✾✽✿✻✷❩❝✛■❀❃✾✻✼✵❳
❬✩❆❃❳❢✷
♥
❆ ❀❃✹✱❍❊✷✫■❬✩▲❊❝✺❍■❀❃❍❊✼✵✹ ✼✦❀❇❝❩✼
♥
✾✻✷❥❀❇✹▼❉ ✼✩❝❥❀❇✹✱❣❤▲❊❀❃✷❩✹ ❉■❀❃✹✽✹❁❀❃❳❪❆❘✹ ❍❊▲❊✾✻❀❃❋●✿❁✼ ❆ ❳❢✼✵✹✽✿✻✾❁❀❃❍❊❆❱s
❖◗❆❘✾ ✫❊❳❜❡
♥
❆❘✹✽✿❁❀❃✾✻✷❩❀ ❍❊✼ ❀
♥
✾❁❀❃❍❊✼✵❬✩✼✵✾ ❀❃❆❘✹q❳❪✼✩❳✛❧❱✾✻❆❘✹q❍❊❀✡❧❊❀❃❋❊❬❅❀☞❖❦✾✽❆★☛❚s ✬❦❍❊❝✺✼✩❋❊❆✵✩❤✷❩❝✺❵❇❀❪❍❊✼❪❞❜❆❘▲❊✾✻❀☞✼
❖❦✾✻❆★☛❚s✂ ❀
♥
☎✝✆✄☎✄ ✞✟✞ ✁✡✠☛✆✌☞ ✆ ✆✟✞✦✄ ✆✎✍
☎✝✆✄☎✄ ✞✟✞ ✁✡✏✔✞ ✁ ✁✒✑ ✞✦✄ ✍✓✆
✔ ✕✗✖ ✄✝✆ ✠✘✞✟✆✚✙✜✛✢✠ ✔
✬❘s✬ ❞❜❆❃✿✻✷✺❵❇❀❃❂❅❄❇❆ s✦s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬
✬❘s✣✢ ✑◗✾✻❀❃❧■❀❃❝ ✛❊❆❘✹✴✷ ✼✩❝❩❀❃❬✩✷✺❆❘❋■❀❃❍❊❆❃✹❴s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✤
✬❘s✥✤ ★q❧☎✘✽✼✵✿✻✷✺❵❘❆❃✹ s✦s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦
✬❘s★✧ ❑▼❆❘❋●✿❁✾✽✷❩❧❊▲❊✷✺❂ ✣❤✼✩✹ s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✩
✬❘s✣✦ ❑▼❆❘❋❊❬✵✼✩✷✺✿✻❆❘✹✴✛ ✚❃✹✽✷❩❬✵❆❘✹ ✼ ✫ ❆❃✿r❀❇❂❅❄❃❆ s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✩
✬❘s✥✩ ✬❦✹✽✿❁✾✽▲❱✿❁▲❱✾❁❀ ❍■❀ ✶✸✷❩✹✽✹✻✼✩✾♦✿r❀❃❂✩❄❃❆✬s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✪
✫
✠ ✆
✖
✙✜✬ ✁☎✄✮✭✡✯✱✰✳✲
✔✱✔
✢♠s✬ ❛■▲❊❋❊❂❅❄❇❆✵✴ ✎✒✑✓✌✛❫❴❋❊✷✐❵❘✼✩✾✽✹❁❀❃❝◆s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬ ✬
✢♠s✣✢ ❛■▲❊❋❊❂❅❄❇❆✵✴ ✎✒✑✓✌✏❍❊✼ ✱ ❆❘❧❊✾✻✷✺✹✽✿ s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬✶✤
✢♠s✥✤ ❛■▲❊❋❊❂❅❄❇❆✵✴ ✎✒✑✓✌✏❍❊✼ ✢❃✼✩❋
☞
✷❩❋❱✹ s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬✳✦
✢♠s★✧ ✮✸✾✽❳ ❀★✧✵✼✩❋■❀❇❳❢✼✵❋ ✿✻❆ ❍■❀❃✹ ❛■▲❊❋❊❂ ✣❤✼✩✹ ✼✵❳ ❞❜✼✩❳❪P❘✾✽✷❥❀✿✬ ✸❤✿❁✼✩✾✽❋■❀ s s s s s✦s s✦s s s✦s s s ✢✸✷
✹
✑✺☞ ✠ ✆✻✆ ✄ ✞✹✠ ✄ ✽✼ ✞✾✑✿✆✞✾✞ ✠ ✄
✫✘✔
✤❱s✬ ✬❦✹✽✿❁✾✽▲❱✿❁▲❱✾❁❀ ❍■❀ ✑✯❀❃❧ ✼✩❝❩❀❀✴ ✎✒✑✓✌ s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✽✬
✤❱s✣✢ ✬❦❋❊❍❊✼✩✾✽✼✩❂✩❀❃❳❢✼✵❋●✿❁❆✖✮✸❧ ✼✩✾✽✿✻❆❢❬✵❆❘❳❁✴ ✎✒✑✓✌☎✳✵✴☎✶✪✘✝✷✺❋❊✼❅❀❃✾ s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✜✢
✤❱s✥✤ ✮ ❛ ❀❃❳✱✕✺❝❩✷❩❀ ❍❊✼ ✮❴❝
♥
❆❘✾✽✷✺✿✻❳❢❆❘✹✭❞ ❃❂q❑ ❙
r
s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✸✤✤❱s✥✤❱s ✬ ❞❜❀❃❉ ✼✩❀❃❳❪✼✩❋●✿❁❆ ✼ ★q✾✻❍❊✼✵❋■❀❃❂❅❄❇❆ s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢❄✧
✤❱s✥✤❱s❅✢ ❖✟✼✩✹✽❣❤▲❱✷❩✹❁❀♣s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢ ✮
✤❱s✥✤❱s✣✤ ✳ ❳❪❉❊❝✺✼✩❳❪✼✩❋●✿r❀❃❂✩❄❃❆ s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✸❆
✤❱s★✧ ★ ✮❴❝
♥
❆❘✾✽✷✺✿✻❳❢❆✏❛◗❑❇❂ s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✤✸✧
✤❱s★✧❊s✣✤ ❖✟✼✩✹✽❣❤▲❱✷❩✹❁❀♣s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✤✜❆
✂✁☎✄✝✆✚✑✄✝✞ ✞ ✠ ✄✂✁ ✍☎✄ ✁ ✆✻✆ ✞✡✁ ✖ ✄✝✞✾✆✄ ✹
✧❊s✬ ❑▼❆❘❋✒✘✽▲❊❋●✿✻❆❢❍❊✼✦❑ ✛■❀❅❵❃✼✩✹✱s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧✜✧
✧❊s✣✢ ✳ ❳❢❉❊❀❃❬✵✿✻❆❪❍❊❀❃✹ ❛■▲❊❋❊❂ ✣❤✼✩✹ ✴ ✎✒✑✓✌ ❋❊❆❢❞✩✗✲✿❁❆❤❍❊❆✱✬ ❋❱❍❊✼✩✾✽✼✩❂❅❀❇❳❢✼✵❋ ✿✻❆ ✮❴❧ ✼✵✾✽✿❁❆ s✦s s s✦s s s ✧✜✧
✧❊s✥✤ ❂✸❀❃✹✔✛❊✷❩❋
♥
❖✟✼✩✾❀☛✼✩✷✺✿✻❆✸✣ ✼✩✾✻✹✽▲❊✹ ❂✸❀❃✹✔✛❊✷❩❋
♥
✘✝✷❩❋❱✼❅❀❃✾ s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧ ✮
✧❊s★✧ ❯ ✼✵✾❁❀❃❂✩❄❃❆ ❍■❀ ❛■▲❊❋❊❂❅❄❇❆ ❂❴❀❃✹✲✛❱✷❩❋
♥
❖◗✼✵✾✔☛✼✵✷✺✿r❀❢❞✩✕✺❋❊✷❩❳❢❀ s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦✽✬
✧❊s★✧❊s ✬ ✳ ❳❪❉■❀❃❬✲✿❁❆ ❍■❀❃✹ ❛■▲❊❋❊❂✤✣♠✼✵✹ ✴ ✎✒✑✓✌✏❋❊❆ ✑◗✼✵❳❢❉ ❆ ❍❊✼ ❯ ✼✵✾❁❀❃❂✩❄❃❆ ❍■❀❃✹ ❛ ❂❴❖ ❞✓✹ s s s ✦✜✢
✧❊s★✧❊s❅✢ ✬ ✸♠❉ ✼✩✾✻✷✺❳❢✼✵❋●✿❁❆❘✹ ✩♠❆❘❧❱✾✻✼ ❀❢❑▼❆❘❳❢❉❱❝❩✼ ✸♠✷✺❍■❀❃❍❊✼q❍❱❆❘✹✭✮✸❝
♥
❆❘✾✻✷✐✿❁❳❪❆❘✹ s s✦s s s✦s s s ✦❄✧
✆ ✝
✠
✖
✠❈✑✆✟✄✗✬ ✁ ✄ ✁ ✏ ✆ ✞ ✁ ✞✾✑✟✞ ✠ ✄ ✠ ✆✖✄ ✆ ✆ ✠ ✄
✆✡✠
✁
✬❘s✬ ✂ ❀☎✄✭❛■▲❊❋❱❂❅❄❃❆✂✌✏✎✒✑✓✌✏❉ ✼✵✾✔☛ ✼✩✷✐✿r❀❱s✆✂ ❧✝✄✱❛■▲❊❋❊❂✩❄❃❆✂✌✏✎✒✑✓✌✛❉ ✼✩✾❀☛ ✼✩✷✺✿❁❀✛❳✱✕✺❋❊✷❩❳❢❀❱s◗s✦s s✦s s s✦s s s ✮
✢♠s✬ ❯ ✼✵✾❁❀❃❂✩❄❃❆ ❍❊❆ ❬✩❆❘❋ ✘✽▲❊❋●✿❁❆❪❍❊✼ ❉ ✼✵✹✻❆❘✹
P
❍■❀✿☛▲❊❋❊❂✩❄❃❆✂✌✏✎✒✑✓✌✛▲❱❋❊✷✺❵❃✼✩✾✻✹✻❀❃❝ s s✦s s✦s s s✦s s s ✬✳✢✢♠s✣✢ ✳ ❳❢❉❱❝❩✼✩❳❪✼✩❋●✿❁❀❃❂❅❄❃❆ ❍❊❀✿☛ ▲❱❋❊❂❅❄❃❆❂✌✏✎✒✑✓✌✏▲❊❋❊✷✺❵❃✼✩✾✽✹❁❀❃❝ s❪s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬✶✤
✢♠s✥✤ ❯ ✼✵✾❁❀❃❂✩❄❃❆ ❍❊❆ ❬✩❆❘❋ ✘✽▲❊❋●✿❁❆❪❍❊✼ ❉ ✼✵✹✻❆❘✹
P
❍■❀✿☛▲❊❋❊❂✩❄❃❆hz
s✸s s s✦s s s✦s s✦s s s✦s s✦s s s ✬ ✧ ✢♠s★✧ ✳ ❳❢❉❱❝❩✼✩❳❪✼✩❋●✿❁❀❃❂❅❄❃❆ ❍❊❀✿☛ ▲❱❋❊❂❅❄❃❆hz
s s✦s s s✦s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s ✬✳✦ ✢♠s✣✦ ❞❜❆❤❍❊✼✩❝❩❀♥
✼✩❳ ❍■❀ ☛▲❊❋❊❂✩❄❃❆
hj
s❭s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬✶✩ ✢♠s✥✩ ✳ ❳❢❉❱❝❩✼✩❳❪✼✩❋●✿❁❀❃❂❅❄❃❆ ❍❱❆❪✼✵❳✛❧■❀❃✾✻❀❃❝✯✛❊❀❃❳❢✼✵❋●✿❁❆ ❍❊❆❘✹✟✞ ✳✡✠✵✑✱❍❊❆ ✼✵✹✽✿r❀❇❍❊❆❢✷✺❋●✿❁✼✩✾✽❋❊❆❊s✓s✦s s s✦s s s ✬✯✮✢♠s✮ ✳ ❳❢❉❱❝❩✼✩❳❪✼✩❋●✿❁❀❃❂❅❄❃❆ ❍❊❀✿☛ ▲❱❋❊❂❅❄❃❆
hj
s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬✶✪ ✢♠s✥❆ ❯ ✼✵✾❁❀❃❂✩❄❃❆ ❍■❀ ✹✻✼✵❳❢✼✵❋ ✿✻✼✦❉❊❀❃✾❁❀ ❆♥
✼✩✾✻❀❃❍❊❆❘✾✱❍❱✼ ❋✻✺❊❳❪✼✩✾✽❆❘✹ ❉❊✹✻✼✵▲❊❍❊❆❇❙ ❀❃❝❩✼✩❀❇✿❁P❃✾✻✷❩❆❃✹✩s s s✦s s s ✢✸✷
✤❱s✬ ✬❦✹✽✿❁✾✽▲❱✿❁▲❱✾❁❀ ❍❊✼ ❍■❀❃❍❊❆❘✹ ❣ ▲❊✼ ✾✻✼✵❉❊✾✻✼✵✹✻✼✵❋ ✿❁❀ ❀ ✿r❀❃❧ ✼✩❝❩❀✱✌✏✎✒✑✓✌❤s s s s s s s✦s s✦s s s✦s s s ✢✜✢
✤❱s✣✢ ✬❦❋❊❍❊✼✩✾✽✼✩❂✩❀❃❳❢✼✵❋●✿❁❆❢❀❃❧ ✼✵✾✽✿✻❆ s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✸✤
✤❱s✥✤ ✑◗✼✵✹✽✿✻✼✦❍❊✼ ❀❃❬✵✷❩❬✵❝❩✷❩❬✵✷❩❍■❀❇❍❊✼ s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✜✦
✤❱s★✧ ❖❦✹✻✼✩▲❱❍❊❆♠❬✵P♠❍❱✷
♥
❆ ❉■❀❃✾✻❀ ❆ ✿✻✼✩✹♦✿❁✼ ❍❊✼ ❀❃❬✩✷✺❬✩❝❩✷✺❬✩✷✺❍■❀❃❍❊✼❴❍❊✼ ▲❊❳
r
❙♥
✾✻❀✼☛ ❆
G
r
s s s✦s s s✦s s s ✢✸✩
✤❱s✣✦ ❖❦✹✻✼✩▲❱❍❊❆♠❬✵P♠❍❱✷
♥
❆ ❉■❀❃✾✻❀ ❆❘✹ ❉■❀❃✹✻✹✽❆❘✹ ❍❊✼ ❳ ❀❇❉ ✼✩❀❃❳❢✼✵❋●✿❁❆ ✼✕❆❘✾✻❍❱✼✩❋■❀❃❂✩❄❃❆❊s s✦s s✦s s s✦s s s ✢✸❆
✤❱s✥✩ ❖✯❀❃✹✽✹✻❆❪❍❊✼ ❉ ✼✵✹✻❣ ▲❊✷✺✹❁❀ ❉■❀❃✾❁❀ ▲❊❳
2
❙♥
✾✻❀✼☛ ❆✛❬✵❆❘❳✂✩ ❵ ✗✩✾♦✿❁✷✺❬✩✼✩✹ ✼ ✦ ❀❃✾✻✼✵✹✽✿❁❀❃✹✩s❊s s s✦s s✦s s s ✢✸✪
✤❱s✮ ❖❦✹✻✼✩▲❱❍❊❆♠❬✵P♠❍❱✷
♥
❆ ❉■❀❃✾✻❀ ❆❪❉❊❀❃✹✻✹✽❆❢❍❊✼ ❉ ✼✩✹✽❣❤▲❱✷❩✹❁❀♠s✖s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✢✸✪
✤❱s✥❆ ✂ ❀☎✄
2
❙♥
✾✻❀✼☛ ❆ ❬✩❆❃❳ ✩ ❵ ✗✩✾♦✿❁✷✺❬✩✼✩✹ ✼ ✦ ❀❃✾✻✼✵✹✽✿r❀❇✹✩s☛✂❧✝✄ ✷ ✼✩❉❱✾✻✼✩✹✽✼✩❋●✿r❀❇❂❅❄❃❆❢❍❊❆
2
❙♥
✾✻❀✼☛ ❆❊s s✦s s s ✤✜✷
✤❱s✥✪ ✶✸✼✩✹✽❬✩✾✽✷❩❂❅❄❇❆❢❍■❀ ✼✵✹✽✿❁✾✽▲❱✿❁▲❱✾❁❀ ❍❊✼ ❍■❀❃❍❊❆❘✹ ❉■❀❇✾❁❀ ✾✻✼✵❉❊✾✻✼✵✹✻✼✩❋●✿❁❀❃✾❴▲❱❳
r
❙♥
✾❁❀✒☛ ❆❊s s s✦s s s✦s s s ✤ ✬
✤❱s✬✶✷ ❛■▲❊❋❊❂ ✣❤✼✩✹✕❉❊❀❃✾❁❀☞❬✩✾✽✷❥❀❃✾❴▲❊❳
r
❙♥
✾✻❀✼☛ ❆ ❵❇❀★✧✵✷❩❆☞✼ ❉■❀❃✾✻❀☞❝❩✷❩❧ ✼✩✾✻❀❃✾❴❀✡❳❪✼✩❳❪P❘✾✽✷❥❀ ❀❇❝❩❆❤❬❅❀❃❍■❀ ❉ ❆❘✾
▲❊❳
r
❙♥
✾✻❀✼☛ ❆❊s s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✤ ✬
✤❱s✬ ✬ ❖❦✾✻❆❤❬✩✼✩✹✽✹✻❆❪❍❊✼ ❬✩✾✽✷❥❀❃❂✩❄❃❆ ❍❊✼ ▲❊❳
2
❙♥
✾❁❀✒☛ ❆ ❬✩❆❘❳
4
❵★✗✩✾✽✿✻✷❩❬✵✼✩✹ ✼2
❀❇✾✻✼✩✹♦✿r❀❃✹✵s s✦s s✦s s s✦s s ✤❈✢✤❱s✬✳✢ ❛■▲❊❋❊❂❅❄❇❆❪❉❊❀❃✾❁❀ ✷❩❋❱✹✻✼✩✾✽✷❩✾✱▲❊❳❢❀ ❀❃✾✽✼✩✹✽✿❁❀
a
❋❊❆r
❙♥
✾❁❀✒☛ ❆❊s☞s✦s s s✦s s s✦s s✦s s s✦s s✦s s s ✤✜✤
✤❱s✬✶✤ ❛■▲❊❋❊❂❅❄❇❆❪❉❊❀❃✾❁❀ ❀❃❉■❀
♥
❀❃✾✱▲❊❳❢❀ ❀❃✾✻✼✵✹✽✿❁❀
a
❍❊❆r
❙♥
✾❁❀✼☛❆❱s✖s✦s s s✦s s s✦s s✦s s s✦s s✦s s s ✤✜✤
✤❱s✬ ✧☞✂ ❀☎✄✭❖◗❀❃✹✻✹✽❆❢❍❱✼ ❳❢❀❃❉ ✼❅❀❃❳❪✼✩❋●✿✻❆❊s✌✂ ❧✝✄✭❖◗❀❃✹✻✹✽❆❘✹ ❍❊✼ ❆❘✾✻❍❊✼✵❋■❀❃❂✩❄❃❆❢✼ ❉ ✼✩✹✽❣❤▲❱✷❩✹❁❀♠s✖s✦s s s✦s s s ✤❈✦
✤❱s✬✳✦ ❖❦✹✻✼✩▲❱❍❊❆♠❬✵P♠❍❱✷
♥
✤❱s✬✯✮ ❖❦✹✻✼✩▲❱❍❊❆♠❬✵P♠❍❱✷
♥
❆ ❉■❀❃✾✻❀ ❆❪❉❊❀❃✹✻✹✽❆❢❍❊✼ ❆❘✾✽❍❊✼✩❋❊❀❃❂❅❄❃❆❱s s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✤✜❆
✤❱s✬✶❆✍✬❦✹✽✿❁✾✽▲❱✿❁▲❱✾❁❀✡❍❊✼ ✕❩❋❊❍❊✷✺❬✩✼ ❉■❀❇✾❁❀✡❆✓❉❱✾✻✼✩✼✵❋❊❬✓✛❊✷✺❳❢✼✵❋ ✿✻❆ ❍❊✼ ▲❊❳❢❀☞❉ ❆❃✹✻✷❩❂✩❄❃❆☞❵❇❀★✧✩✷❩❀✡❍❊❀✡✿❁❀❃❧ ✼✵❝❥❀
✌✏✎✒✑✓✌❤s✛s s✦s s✦s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧❈✷
✤❱s✬✶✪ ❖❦✹✻✼✩▲❱❍❊❆♠❬✵P♠❍❱✷
♥
❆ ❉■❀❃✾✻❀ ❆❪❉❊❀❃✹✻✹✽❆❢❍❊✼ ❉ ✼✩✹✽❣❤▲❱✷❩✹❁❀♠s✖s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧ ✬
✧❊s✬ ✑◗✼✵❳❢❉ ❆ ❍❊✼ ✼ ✸♠✼✩❬✵▲❊❂❅❄❇❆ ❍❊❆❘✹ ❀❃❝
♥
❆❘✾✽✷✺✿❁❳❪❆❘✹ ▲❱✿❁✷✺❝❩✷✧❅❀❃❋❊❍❱❆ ❀❃✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹
hu
✼hz
s s s✦s s s ✦❄✧ ✧❊s✣✢ ✑◗✼✵❳❢❉ ❆ ❍❊✼ ✼ ✸♠✼✩❬✵▲❊❂❅❄❇❆ ❍❊❆❘✹ ❀❃❝♥
❆❘✾✽✷✺✿❁❳❪❆❘✹ ▲❱✿❁✷✺❝❩✷✧❅❀❃❋❊❍❱❆ ❀ ☛ ▲❊❋❊❂❅❄❇❆ ✌✏✎✒✑✓✌✏❍❊✼ ✢❃✼✩❋
☞
✷✺❋❊✹✩s❪s s ✦✜✦
✧❊s✥✤ ✶✸✷❩✹♦✿❁✾✽✷❩❧❊▲❊✷✺❂❅❄❃❆ ❍❊❆ ✿r❀❃❳❢❀❃❋✢✛❱❆ ❍❊❆❘✹✁✄✂✆☎✞✝✠✟ ✠✑ ❉■❀❃✾✻❀ ❀❃✹✂☛▲❊❋❊❂✤✣♠✼✵✹ ✌✏✎✒✑✓✌ ❍❱✼ ✱ ❆❘❧❊✾✻✷✺✹✽✿☞✼
✢❃✼✩❋
☞
✷✺❋❊✹✩s s s✦s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦ ✮
✧❊s★✧ ✑✯❀❇❳ ❀❃❋✏✛❊❆ ❍❊❆❪❳ ❀❃✷✺❆❘✾✡☛✂☞☎✞✝✠✟ ✠ ❡
✢♠s✬ ✳ ❋❊✷❩❬✵✷❥❀❃❝✺✷✯✧✩❀❃❂❅❄❃❆✦❍❊❆ ✼✩✹♦✿r❀❃❍❊❆❪✷❩❋●✿✻✼✩✾✻❋❱❆❊s s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✬✶✩
✢♠s✣✢ ✛▼❝❩❆❤❬✩❆ ❍❱✼ ✿✻✼ ✸❤✿❁❆❢❀ ✹✻✼✵✾ ❬✵❆❘❳✛❧❊✷✺❋■❀❃❍❊❆ ❬✵❆❘❳ ❆ ✼✩✹♦✿r❀❃❍❊❆❪✷❩❋●✿✻✼✩✾✻❋❱❆❊s s s s s✦s s✦s s s✦s s s ✬✯✮
✢♠s✥✤ ❑▼❆❘❳✛❧❊✷✺❋■❀❃❂✩❄❃❆ ❍❊❆ ❧❊❝❩❆❤❬✩❆ ❍❊✼✕✿✻✼ ✸❤✿❁❆❪❬✩❆❘❳ ❆❪✼✵✹✽✿❁❀❃❍❊❆❪✷❩❋●✿❁✼✵✾✻❋❊❆❪❀❇✿✻✾❁❀❅❵ ✗✵✹❴❍❊✼ ❀❃❍❱✷❩❂ ✣❤✼✩✹✵s s s ✬✶❆
✧❊s✬ ✩♠✷❩❳✏❧ ❆❘❝✺❆
♥
✷❩❀ ✼ ❀❃❧❊✾✽✼✵❵❤✷❥❀❇❂ ✣❤✼✩✹ ▲❱✿❁✷✺❝❩✷✧❅❀❃❍■❀❇✹▼❋■❀ ❀❃❉❊✾✽✼✩✹✽✼✩❋●✿r❀❃❂✩❄❃❆ ❍❱❆❘✹ ✾✻✼✩✹✽▲❊❝✺✿❁❀❃❍❊❆❘✹✵s s✦s s s ✧❈✤
✧❊s✣✢ ❖❦✾✻❆❘❉❊✾✽✷❩✼✵❍■❀❃❍❊✼✵✹ ❍❱❆❘✹ ❬✩❆❘❋✒✘✽▲❱❋ ✿✻❆❘✹ ❍❊✼ ❬✓✛■❀❅❵❘✼✵✹✸▲❱✿✻✷❩❝❩✷✧❅❀❃❍❱❆❘✹▼❋❊❆❃✹ ✼ ✸♠❉ ✼✵✾✻✷❩❳❪✼✩❋●✿✻❆❘✹✩s s s✦s s s ✧✜✧
✧❊s✥✤ ✳ ❋✝✆■▲❊❨✵❋❊❬✩✷❩❀❏❍❱❆❁☛❀✰✿❁❆❘✾ ❍❊✼✡❬✩❀❃✾
♥
❀ ❋❊❆ ✿✻✼✩❳❪❉ ❆◆❉■❀❃✾✻❀ ❉ ✼✵✹✻❣ ▲❊✷❩✹✻❀❃✾ ✿❁❆❤❍■❀❃✹❪❀❃✹ ❬✓✛■❀❅❵❃✼✩✹ ❍❱❆
❬✩❆❘❋ ✘✽▲❊❋●✿❁❆ ✼ ✸♠✿✻✾❁❀★✕✺❍❊❆ ❍■❀❢❬✩❆❘❝✺✼✩❂❅❄❇❆ ✑✴✷ ✬ ❑ ❙ ✣ ✘✟❑☛✢ ❬✩❆❃❋❊✹✻✷✺❍❊✼✩✾✻❀❃❋❊❍❊❆✡❀❃✹ ☛▲❊❋❊❂✤✣♠✼✵✹
hu
❡hz
✼
hj
s❏s s✦s s✦s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧ ✦ ✧❊s★✧ ✳ ❋✝✆■▲❊❨✵❋❊❬✩✷❩❀❏❍❱❆❁☛ ❀✰✿❁❆❘✾ ❍❊✼✡❬✩❀❃✾♥
❀ ❋❊❆ ✿✻✼✩❳❪❉ ❆◆❉■❀❃✾✻❀ ❉ ✼✵✹✻❣ ▲❊✷❩✹✻❀❃✾ ✿❁❆❤❍■❀❃✹❪❀❃✹ ❬✓✛■❀❅❵❃✼✩✹ ❍❱❆
❬✩❆❘❋ ✘✽▲❊❋●✿❁❆❪✼ ✸❤✿❁✾✻❀★✕❩❍❊❆ ❍■❀ ❬✵❆❘❝❩✼✵❂❅❄❃❆ ❍❊✼ ❫✰✷✜✘✝✹ ❬✩❆❘❋❊✹✽✷❩❍❊✼✵✾❁❀❃❋❱❍❊❆❪❀❃✹ ☛▲❊❋❊❂ ✣❤✼✩✹
hu
❡hz
✼hj
s ✧❈✩ ✧❊s✣✦ ❑▼❆❘❳❪❉■❀❃✾❁❀❇❂❅❄❃❆❈❍■❀ ▲❱✿❁✷✺❝❩✷✧❅❀❃❂✩❄❃❆❈❍❱✼ ❛ ❂✸❖ ❞❜✹ ❵❃✼✩✾✽✹✻▲❊✹ ✌✏✎✒✑✓✌☎✳✵✴☎✶❜❝✺✷❩❋❊✼✩❀❃✾❢❬✵❆❘❋❊✹✽✷❩❍❊✼✵✾❁❀❃❋❊❍❱❆❆❈✿✻✼✩❳❪❉ ❆❏❉■❀❃✾✻❀❈❉ ✼✩✹✻❣ ▲❊✷✺✹❁❀❃✾ ✿❁❆❤❍■❀❃✹❢❀❃✹❢❬✓✛■❀❅❵❘✼✩✹ ❍❊❆ ❬✩❆❃❋✒✘✽▲❊❋●✿❁❆❈✼ ✸❤✿❁✾✻❀★✕❩❍❊❆❈❍■❀❈❬✵❆❘❝❩✼✵❂❅❄❃❆
✑✴✷ ✬ ❑ ❙ ✣ ✘✟❑☛✢♠❡ ❵❇❀❃✾✽✷❥❀❃❋❊❍❱❆☞❀❃✹ ☛▲❊❋❱❂ ✣❤✼✩✹
hu
❡hz
✼hj
❋■❀ ❬✩❆❘❳❪❉ ❆❘✹✻✷✺❂❅❄❃❆❢❍■❀❃✹✕❛ ❂❴❖ ❞❜✹✼✕❍❊❆❂✌✏✎✒✑✓✌☎✳✵✴☎✶✕❝✺✷❩❋❊✼✩❀❃✾✩s❪s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧❈❆
✧❊s✥✩ ❑▼❆❘❳❪❉■❀❃✾❁❀❇❂❅❄❃❆❢❍■❀ ▲❱✿✻✷❩❝❩✷✧❅❀❃❂✩❄❃❆ ❍❊✼ ❛ ❂❴❖ ❞❜✹✸❵❘✼✵✾✻✹✽▲❊✹ ✌✏✎✒✑✓✌☎✳✵✴☎✶✦❝❩✷✺❋❊✼❅❀❃✾ ❬✵❆❘❋❊✹✻✷✺❍❊✼✩✾✻❀❃❋❊❍❊❆☞❆
✞✠✟
✟☛✡❃✌✆✟✲✎✌☞✓❍❊✼ ✼✵✹✻❉■❀❇❂✩❆ ❉■❀❃✾✻❀ ❀❃✾✽❳ ❀★✧✵✼✩❋■❀❇✾ ❀❈✿❁❀❃❧ ✼✩❝❥❀ ✌✏✎✒✑✓✌◆✼ ❆ ❀❃✾✻✾✻❀❃❋✒✘✽❆
g
❍❱✼ ❬❅❀❇❍■❀❛ ❂✸❖ ❞ ❉■❀❃✾✻❀❪❀ ❬✵❆❘❝❩✼✵❂❅❄❃❆ ✑✴✷ ✬ ❑ ❙ ✣ ✘✟❑☛✢♠s s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✧❈✪
✧❊s✮ ❑▼❆❘❳❪❉■❀❃✾❁❀❇❂❅❄❃❆❢❍■❀ ▲❱✿✻✷❩❝❩✷✧❅❀❃❂✩❄❃❆ ❍❊✼ ❛ ❂❴❖ ❞❜✹✸❵❘✼✵✾✻✹✽▲❊✹ ✌✏✎✒✑✓✌☎✳✵✴☎✶✦❝❩✷✺❋❊✼❅❀❃✾ ❬✵❆❘❋❊✹✻✷✺❍❊✼✩✾✻❀❃❋❊❍❊❆☞❆
✿❁✼✵❳❢❉ ❆✡❉■❀❃✾❁❀✡❉ ✼✩✹✻❣ ▲❊✷✺✹❁❀❃✾ ✿❁❆❤❍■❀❃✹ ❀❃✹✦❫✰✷✜✘✝✹✩❡✘❵❇❀❃✾✻✷❩❀❃❋❊❍❊❆✓❀❃✹ ☛▲❊❋❊❂✤✣♠✼✵✹
hu
❡hz
✼hj
❋■❀❬✩❆❘❳❪❉ ❆❘✹✻✷✺❂❅❄❃❆ ❍■❀❇✹❴❛ ❂✸❖ ❞❜✹ ✼ ❍❊❆✂✌✏✎✒✑✓✌☎✳✵✴☎✶ ❝✺✷❩❋❊✼✩❀❃✾✩s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦✸✷
✧❊s✥❆ ❑▼❆❘❳❪❉■❀❃✾❁❀❇❂❅❄❃❆❢❍■❀ ▲❱✿✻✷❩❝❩✷✧❅❀❃❂✩❄❃❆ ❍❊✼ ❛ ❂❴❖ ❞❜✹✸❵❘✼✵✾✻✹✽▲❊✹ ✌✏✎✒✑✓✌☎✳✵✴☎✶✦❝❩✷✺❋❊✼❅❀❃✾ ❬✵❆❘❋❊✹✻✷✺❍❊✼✩✾✻❀❃❋❊❍❊❆☞❆
✞✠✟
✟☛✡❃✌✆✟✲✎✌☞✓❍❊✼ ✼✵✹✻❉■❀❇❂✩❆ ❉■❀❃✾✻❀ ❀❃✾✽❳ ❀★✧✵✼✩❋■❀❇✾ ❀❈✿❁❀❃❧ ✼✩❝❥❀ ✌✏✎✒✑✓✌◆✼ ❆ ❀❃✾✻✾✻❀❃❋✒✘✽❆
g
❍❱✼ ❬❅❀❇❍■❀❛ ❂✸❖ ❞ ❉■❀❃✾✻❀❪❀ ❬✵❆❘❝❩✼✵❂❅❄❃❆ ❍❊✼ ❫✰✷✜✘✝✹✩s☞s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦✸✷
✧❊s✥✪ ✑◗✼✵❳❢❉ ❆ ❍❊✼
♥
✼✩✾✻❀❃❂❅❄❃❆ ❍❊✼❴❛ ❂❴❖ ❞✓✹ ❉■❀❇✾❁❀✕❆✦❬✵❆❘❋✒✘✽▲❊❋●✿✻❆✏❍❊✼ ❬✓✛■❀❅❵❘✼✵✹✭✼ ✸❤✿✻✾❁❀★✕✺❍❊❆ ❍■❀ ❬✵❆❘❝❩✼✵❂❅❄❃❆
✑✴✷ ✬ ❑ ❙ ✣ ✘✟❑☛✢ ▲❱✿❁✷✺❝❩✷✯✧✩❀❃❋❊❍❊❆❜❆❘✹ ❀❃❝
♥
❆❘✾✻✷✐✿❁❳❪❆❘✹✦❞ ❃❂q❑ ❙
2
✼✓❞ ❃❂q❑ ❙3
❡❦❵❇❀❃✾✻✷❩❀❃❋❊❍❊❆ ❀❇✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹hu
❡hz
✼♥
✑✴✷ ✬ ❑ ❙ ✣ ✘✟❑☛✢ ▲♠✿❁✷❩❝✺✷✯✧✩❀❃❋❊❍❊❆✛❆❪❀❃❝
♥
❆❘✾✽✷✺✿❁❳❪❆✛❛✟❑❇❂ s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦✸✤
✧❊s✬ ✬ ✑◗✼✵❳❢❉ ❆✛❍❊✼
♥
✼✩✾✻❀❃❂❅❄❃❆✏❍❊✼✕❛ ❂❴❖ ❞✓✹✭❉■❀❃✾✻❀✛❀✏❬✩❆❃❝❩✼✩❂✩❄❃❆✛❍❊✼q❫✰✷✜✘✘✹▼▲❱✿❁✷✺❝❩✷✯✧✩❀❃❋❊❍❊❆ ❆❘✹▼❀❃❝
♥
❆❃✾✻✷✺✿♦❙
❳❢❆❃✹ ❞ ❃❂q❑ ❙
2
✼✦❞ ❃❂✸❑ ❙3
❡❊❵❇❀❃✾✽✷❥❀❃❋❱❍❊❆ ❀❃✹ ☛▲❊❋❊❂✤✣♠✼✵✹hu
❡hz
✼hj
❋❊❀❪❬✵❆❘❳❢❉ ❆❘✹✽✷❩❂❅❄❇❆❍■❀❃✹ ❛ ❂❴❖ ❞✓✹✩s✸s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦✸✤
✧❊s✬✳✢ ✑◗✼✵❳❢❉ ❆q❍❊✼
♥
✼✩✾✻❀❃❂❅❄❃❆✸❍❊✼✱❛ ❂❴❖ ❞✓✹✖❉■❀❃✾✻❀✕❀✸❬✩❆❘❝✺✼✩❂✩❄❃❆q❍❊✼✱❫ ✷ ✘✝✹✖▲♠✿❁✷❩❝✺✷✯✧✩❀❃❋❊❍❊❆ ❆✕❀❃❝
♥
❆❘✾✻✷✐✿❁❳❪❆
❛✟❑❇❂✦s❦s s✦s s✦s s s s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s s s s✦s s✦s s s✦s s s ✦❄✧
✧❊s✬✶✤✡✳ ❳❢❉❊❀❃❬✵✿✻❆❪❍❊❀❃✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹
hu
✼hz
❋❊❆ ✿❁✼✩❳❪❉ ❆ ❍❊✼ ✼ ✸♠✼✩❬✵▲❊❂❅❄❃❆ ❍❊❆❪❀❃❝♥
❆❃✾✻✷✺✿✻❳❢❆✛❞ ❃❂q❑ ❙
2
s ✦✜✦ ✧❊s✬ ✧ ✳ ❳❢❉❊❀❃❬✵✿✻❆✸❍■❀❃✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹hj
✼hu
❋❊❆✸✿✻✼✩❳❪❉ ❆❴❍❊✼▼✼ ✸❱✼✵❬✩▲❊❂✩❄❃❆✕❍❊❆❘✹✯❀❃❝♥
❆❘✾✻✷✐✿❁❳❪❆❘✹✟❞ ❃❂q❑ ❙
2
✼ ❞ ❃❂q❑ ❙
3
❡■✾✽✼✩✹✻❉ ✼✩❬✲✿❁✷✐❵❃❀❇❳❢✼✵❋ ✿✻✼❃s s✦s s s✦s s s✦s s✦s s s✦s s s✦s s✦s s s✦s s✦s s s ✦✜✦✧❊s✬✳✦ ✳ ❳❢❉❊❀❃❬✵✿✻❆❪❍❊❀❃✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹
hz
✼hj
❋❊❆ ✿❁✼✩❳❪❉ ❆❪❍❱✼ ✼ ✸♠✼✩❬✩▲❱❂❅❄❃❆❢❍❊❆❪❀❃❝♥
❆❃✾✻✷✺✿✻❳❢❆✛❞ ❃❂q❑ ❙
3
s ✦✸✩ ✧❊s✬✶✩✡✳ ❳❢❉❊❀❃❬✵✿✻❆❪❍❊❀❃✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹hu
✼hz
❋❊❆ ✿❁✼✩❳❪❉ ❆ ❍❊✼ ✼ ✸♠✼✩❬✵▲❊❂❅❄❃❆ ❍❊❆❪❀❃❝♥
❆❃✾✻✷✺✿✻❳❢❆✏❛✟❑❇❂✦s s s ✦✸✩
✧❊s✬✯✮ ✳ ❳❢❉❊❀❃❬✵✿✻❆❪❍❊❀✿☛▲❱❋❊❂❅❄❃❆
hj
❋❊❆ ✿❁✼✵❳❢❉ ❆ ❍❊✼ ✼ ✸♠✼✵❬✩▲❊❂✩❄❃❆ ❍❊❆❢❀❃❝♥
✝
✎✑✏✓✂✦✒ ✝ ✁✟✞✡✠ ✒
☛✌☞✍☛
✳ ☛ ✆✘✗✲✙q✒✏✎✒✑ ☛
✩♠✼ ✘✻❀
S
▲❊❳ ❬✩❆❘❋✒✘✽▲❱❋ ✿✻❆✕❍❊✼n
❬✓✛■❀❅❵❘✼✵✹ ❍❱✷❩✹✽✿✻✷❩❋●✿r❀❇✹◗❉ ✼✩✾♦✿❁✼✩❋❱❬✩✼✩❋●✿✻✼✩✹ ❀✸▲❊❳ ▲❊❋❊✷✐❵❘✼✵✾✻✹✻❆ ✫❊❋❊✷✺✿✻❆U
❍❊✼▼❬✓✛❊❀ ❵❃✼✩✹✵s ✮✸✹ ❬✓✛■❀❅❵❘✼✵✹❦✼✩❳S
✹✻❄❃❆q❀❃✾✽❳ ❀✼✧✩✼✩❋❊❀❃❍■❀❃✹✟❍❊✼ ☛ ❆❃✾✻❳❢❀ ❣ ▲❊✼ ❬✩❆❘❋❱✹✻▲❊❝✐✿r❀❃✹◗❉ ✼✵✾♥
▲❊❋●✿❁❀❃❋❊❍❊❆❴✹✻✼▼▲❱❳ ❀ ❬✓✛■❀❅❵❘✼
x
∈
U
✼✩✹♦✿✓✚ ✼✩❳S
❉ ❆❃✹✻✹❁❀❇❳ ✹✻✼✩✾✘✾✽✼✩✹✻❉ ❆❘❋❊❍❱✷❩❍■❀❃✹✵s✰✬❦✹✽✿✻✼ ❉❱✾✻❆❘❧❊❝✺✼✩❳❢❀ ✗ ❬✓✛■❀❃❳❢❀❃❍❊❆ ✄ ✆ ✠ ✁ ✑ ✁☎✞ ✞ ✞ ✠ ✞✚✆ ✠❈✆ ✠ ✖✔✓✆❄✆✠✘s ✣ ✚❃✾✽✷❥❀❃✹
❀❃❧ ❆❘✾✻❍❊❀
♥
✼✩❋❱✹◗❉■❀❇✾❁❀❴❆❴❉❊✾✻❆❃❧❊❝❩✼✵❳ ❀ ❍❊❆✸❍❱✷❩❬✩✷✺❆❘❋✦✚❃✾✽✷❩❆✭✿✻❨✩❳ ✹✻✷✺❍❊❆✸✼ ✸❱❉❱❝❩❆❘✾✻❀❃❍■❀❃✹✵s✯❫ ❳ ❀ ❍❊✼✩❝❩❀❃✹✟✗ ❬✩❆❃❳❢❉❊▲♠✿r❀❃✾✟▲❊❳❢❀
☛ ▲❊❋❊❂✩❄❃❆
h(x)
❉■❀❃✾✻❀✡❍❱✼✵✿❁✼✵✾✻❳❪✷❩❋■❀❇✾✕❀✓❝✺❆♠❬✩❀❃❝❩✷✧❅❀❃❂✩❄❃❆ ❍❱✼❪▲❱❳ ❀☞❬✓✛■❀❅❵❘✼❢✼✩❳✢▲❱❳ ❀ ✿r❀❇❧ ✼✵❝❥❀❱❡ ❝✺✼✵❵❇❀❃❋❊❍❱❆❜❀✡▲❊❳❢❀ ❬✩❝❩❀❃✹✻✹✽✼q❳✛▲❊✷✐✿❁❆✛✼ ✫■❬✩✷✺✼✩❋●✿❁✼✕❍❱✼q❳✱✗✲✿❁❆❤❍❊❆❘✹✭❍❱✼q❉ ✼✵✹✻❣ ▲❊✷✺✹❁❀ ❬✩❆❘❋✏✛❊✼✩❬✵✷❩❍■❀✛❬✵❆❘❳❢❆ ✞✖✕✘✄ ✠✘✞ ✠ ✄ ✞ ✁ ✲✘✯✾✰✻✲✘✗✚✙✔✛✢✜✥✤✸✷✤✣ s✮ ☛ ▲❊❋❊❂✩❄❃❆
h
✗✓❬✓✛■❀❃❳❢❀❃❍■❀✦✥ ✆✖
✙✜✛✏✠ ✲✘✯✾✰✻✲ ✼✓❀◆✿❁❀❃❧ ✼✩❝❥❀ ✼✵❋❊❍❊✼✩✾✽✼✩❂✩❀❃❍■❀ ❉ ❆❘✾ ✼✩❝❩❀❁✗✓❬✓✛■❀❃❳❢❀❃❍■❀ ✄✝✞ ✁ ✁ ✑✞
✲ ✯✱✰✳✲ s
❑▼❆❘❳❪❆ ❍❊✼✵✹✻❬✩✾✽✷✺✿✻❆ ✼✩❳ ✱ ✷✐❵♠✷❩❀❃❋❊✷✧✜★✤✜✷♠❡❦❑✭❀❃❉✢✕✺✿✻▲❊❝❩❆ ✦★✣ ❡✯✼ ✸♠✷❩✹✽✿✻✼✩❳✥❍❊❆❘✷✺✹✦❉❱✾✻❆❘❧❊❝✺✼✩❳❢❀❃✹ ✾✻✼✩❝❩❀❃❬✩✷✺❆❘❋■❀❃❍❱❆❘✹ ❬✩❆❘❳
❆❘✹☞❳✖✗✵✿✻❆♠❍❊❆❃✹ ❍❊✼✹✌✏✎✒✑✓✌☎✳✵✴☎✶❃s ★✥❉❊✾✽✷❩❳❪✼✩✷✺✾✻❆ ❬✵❆❘❋❊✹✻✷✺✹✽✿✻✼ ✼✩❳ ❆❃❧❱✿❁✼✵✾☞▲❊❳ ❀✹☛ ▲❱❋❊❂❅❄❃❆ ✌✏✎✒✑✓✌❈❣ ▲❊✼ ❍❊✷✺✹✽✿❁✾✽✷❩❧❊▲❊❀
❆❘✹❢✾✻✼
♥
✷❩✹✽✿✻✾✻❆❘✹❪❍❊✼✷☛❆❘✾✻❳❢❀ ▲❊❋❊✷☛❆❃✾✻❳❪✼✓✼✵❋●✿❁✾✻✼ ❀❃✹❢✼✵❋●✿❁✾❁❀❇❍■❀❃✹ ❍■❀◆✿r❀❃❧ ✼✩❝❩❀❱s ★ ✹✻✼
♥
▲❊❋❊❍❱❆ ❆♠❬✵❆❘✾✻✾✽✼❜❣ ▲■❀❇❋❊❍❊❆
❍❊▲■❀❇✹❴❬✓✛■❀❅❵❃✼✩✹✕❍❊✷✺✹✽✿❁✷✺❋●✿r❀❃✹ ✹❁❄❇❆ ❳❢❀❃❉ ✼✩❀❃❍■❀❃✹ ❋❊❆❢❳❢✼✵✹✻❳❪❆❢✼✵❋❊❍❊✼✵✾✻✼✩❂✵❆ ❍■❀ ✿r❀❃❧ ✼✩❝❩❀❱❡■❆ ❣ ▲❊✼ ❬❅❀❃✾✻❀❃❬✵✿✻✼✩✾✽✷✯✧❅❀❪▲❊❳❢❀
✠ ✠ ✑✿✆✄✗✛✢✠✘s
❖◗❆❘✾ ❳❪✼✩❝✛❊❆❘✾✦❣❤▲❱✼✓✹✽✼ ✘✻❀ ❀ ☛ ▲❊❋❊❂✩❄❃❆✹✌✏✎✒✑✓✌❤❡❦✼ ✸♠✷✺✹✽✿❁✼☞▲❱❳ ❀ ❀❃❝✐✿r❀ ❉❱✾✻❆❘❧■❀❇❧❊✷❩❝✺✷❩❍■❀❃❍❱✼❢❍❊✼❂✛❊❀ ❵❃✼✩✾ ❬✩❆❃❝❩✷❩✹✔✣♠✼✵✹✩s
✳ ✹✽✿✻❆❢❉ ❆❤❍❊✼✕✹✻✼✵✾❴✷✺❝❩▲❊✹♦✿❁✾❁❀❇❍❊❆✛❉ ✼✩❝❩❆ ❉■❀❇✾❁❀❃❍❊❆✝✸♠❆❪❍❊❆❪❀❃❋❊✷✺❵❃✼✩✾✽✹❃✚❃✾✽✷❩❆✩✜✬ ✷♠❡✱✤✜✷✤✣ ❡❊❆❪❣ ▲■❀❃❝✝❍❊✷✧✕❣❤▲❱✼ ✼✵❳ ▲❊❳
♥
✾✻▲❊❉ ❆
❍❊✼ ✢✸✤❈❆❘▲✬❳ ❀❃✷✺✹❢❉ ✼✩✹✽✹✻❆●❀❇✹✩❡ ✘✽▲❱❋ ✿❁❀❃✹✡❀❃❆ ❀❃❬✩❀❃✹✻❆❱❡❴✼ ✸❱✷✺✹✽✿✻✼ ▲❊❳ ❀❈❬✓✛■❀❃❋❊❬✵✼❏❳❢❀❃✷✺❆❘✾❢❍❱❆ ❣❤▲❱✼ ✦✸✷✫✪ ❍❊✼ ❣ ▲❊✼
✢❏❉ ✼✩✹✽✹✻❆●❀❇✹ ❬✩❆❃❳❢✼✵❳❢❆❘✾✽✼✩❳ ❀❇❋❊✷✺❵❃✼✩✾✻✹✲✚❃✾✻✷✺❆❈❋❱❆ ❳❪✼✩✹✻❳❪❆❏❍❊✷❥❀❱s ✳ ✹✻✹✻❆ ✹✻✷
♥
❋❊✷✫■❬✩❀❏❣ ▲❊✼ ❀❈❉❊✾✽❆❘❧■❀❃❧❱✷❩❝❩✷✺❍■❀❃❍❊✼ ❍❊✼
❆❤❬✩❆❘✾✽✾✻✼✩✾ ❬✩❆❃❝❩✷❩✹✔✣♠✼✵✹ ✗❢❳❢❀❃✷❩❆❃✾✕❍❊❆ ❣ ▲❊✼ ✦✸✷✫✪ ❣ ▲■❀❃❋❊❍❱❆ ▲❊❳❢❀✷☛ ▲❊❋❱❂❅❄❃❆❁✌✏✎✒✑✓✌☞▲❊❋❊✷☛ ❆❘✾✻❳❪✼ ✗❢▲♠✿❁✷❩❝✺✷✯✧✩❀❃❍■❀ ❉■❀❃✾✻❀
✼✩❋❱❍❊✼✩✾✽✼✩❂❅❀❇✾ ✢❄✤ ❬✓✛■❀❅❵❘✼✩✹ ✾❁❀❇❋❊❍ ✹❘❳❪✷❩❬✩❀❃✹q✼✩❳ ▲❊❳❢❀ ✿r❀❃❧ ✼✩❝❩❀ ❍❊✼ ✿r❀❃❳❢❀❃❋✢✛❱❆✵✤✜✩❈✦♠s✦✶✸✼✵✹✻✹❁❀ ☛❆❘✾✻❳❢❀❱❡ ✗ ❉❊✾✻✼✵❬✩✷❩✹✽❆
✬ ✸❱✷✺✹✽✿✻✼✩❳ ❵✼✚❃✾✻✷✺❆❘✹❦❳✖✗✵✿❁❆❤❍❊❆❘✹❦❉❊❀❃✾❁❀ ❀❃✾✽❳ ❀★✧✵✼✩❋■❀❇✾
n
✾✽✼♥
✷✺✹✽✿✻✾✻❆❘✹ ✼✩❳ ▲❊❳ ❀q✿❁❀❃❧ ✼✵❝❥❀✕❍❊✼✱✿r❀❇❳ ❀❃❋✏✛❊❆
m
≥
n
❡ ❆❘✹ ❣ ▲■❀❇✷❩✹ ▲♠✿❁✷❩❝✺✷✯✧✩❀❃❳ ❆❘✹❢✼✩❋❊❍❊✼✵✾✻✼✵❂✩❆❘✹☞❵❇❀★✧✩✷✺❆❘✹❪❋■❀ ❉❊✾✻P❃❉❊✾✻✷❩❀❏✿r❀❇❧ ✼✵❝❥❀❈❉❊❀❃✾❁❀ ✾✽✼✩✹✽❆❘❝✺❵❃✼✩✾☞❀❃✹❢❬✩❆❘❝✺✷❩✹✔✣♠✼✵✹✩s ✑◗❀❃✷✺✹❳✖✗✵✿❁❆❤❍❊❆❘✹ ✹❁❄❃❆ ❬✓✛❊❀❃❳ ❀❇❍❊❆❘✹ ✁
✖
✞ ✁ ✆ ✁ ✙ ✞✦✞✹✁
✖
✄ ✠ ✞ ✁ ✁ ✆✝✄ ✠ ✂✢✜✤✣☛✥ ✙ ✯✞✦✧✦✩★✪✥✜✰✻✰✤✗✚✙ ✛ ✄ ✜✥✤✜✷★✣ s ✬❦✹✽✿✻✼✩✹ ❳✖✗✵✿❁❆❤❍❊❆❘✹
✼✩❋●❵❃❆❘❝✺❵❃✼✩❳ ▲❊❳❢❀ ❬✵✼✩✾✽✿❁❀❴❣ ▲■❀❃❋●✿✻✷❩❍■❀❃❍❱✼ ❍❊✼ ✼✩✹✽❉■❀❃❂✩❆❴❍❊✼✩✹✽❉ ✼✵✾✻❍❊✷✺❂❅❀❃❍❱❆✸❍❊✼✲❵♠✷✺❍❊❆q❀ ❝❩❆❤❬❅❀❇❝❩✷✯✧✩❀❃❂ ✣❤✼✩✹✝❋❊❄❃❆❴▲♠✿❁✷❩❝✺✷✯✧✩❀❃❍■❀❃✹
❋■❀ ✿r❀❃❧ ✼✩❝❩❀ ✌✏✎✒✑✓✌❤s✟✮✸❝✗✩❳ ❍❊✷✺✹✻✹✻❆❱❡❤✼ ✸♠✷❩✹✽✿✻✼❴✿❁❀❃❳✛❧ ✗✩❳ ▲❊❳ ❍❱✼✩✹✻❉ ✼✩✾✽❍✢✕❩❬✵✷❩❆ ❍❊✼❴✿✻✼✩❳❪❉ ❆ ❉■❀❇✾❁❀✦✾✽✼✩✹✽❆❘❝✺❵❃✼✩✾ ❬✩❆❘❝✺✷❩✹✲✣❤✼✩✹
❣ ▲■❀❃❋❊❍❱❆❢❍❊▲❊❀❃✹ ❬✓✛■❀❅❵❘✼✩✹❴✹❁❄❃❆❪❳❢❀❃❉ ✼✩❀❃❍■❀❃✹✱❋❱❆❪❳❪✼✩✹✽❳❢❆ ✼✵❋❊❍❊✼✩✾✽✼✩❂✵❆ ❍■❀✛✿r❀❇❧ ✼✵❝❥❀✱✌✏✎✒✑✓✌❤s
❖✯❀❃✾✻❀✕❬✩❆❘❋✒✘✽▲❱❋ ✿✻❆❘✹❦✼✩✹♦✿✓✚❇✿✻✷❩❬✵❆❘✹✩❡ ✗✭❉ ❆❘✹✽✹✲✕✺❵❃✼✩❝❊❬✵❆❘❳❪❉❊▲❱✿r❀❇✾✖▲❊❳❢❀ ☛▲❊❋❊❂❅❄❇❆
h(x)
❉■❀❃✾✻❀q✼✩❋❊❬✵❆❘❋●✿❁✾✻❀❃✾❦❣ ▲■❀❃❝❩❣ ▲❊✼✵✾ ❬✓✛■❀❅❵❘✼✦❋■❀✛✿r❀❃❧ ✼✩❝❩❀ ✼✩❳ ▲❊❳❢❀✿✺❊❋❊✷✺❬❅❀ ✿❁✼✩❋●✿❁❀❇✿❁✷✐❵❃❀♠❡❊✹✻✼✵❳ ❀ ❆❤❬✩❆❃✾✻✾✻❨✵❋❊❬✩✷❩❀ ❍❊✼ ❬✩❆❘❝✺✷❩✹✲✣❤✼✩✹✵s ✬ ✹♦✿r❀✿☛ ▲❊❋❊❂✩❄❃❆✱✗ ❬✓✛■❀ ❙❳❢❀❃❍■❀ ✥ ✆
✖
✙✜✛✢✠ ✲ ✯✾✰✻✲ ✄ ✁ ✆ ✥ ✁ ✆✄✝✞ s✯❫❴❳❢❀ ☛ ▲❊❋❊❂✩❄❃❆✽✌✏✎✒✑✓✌ ❉ ✼✩✾✔☛✼✵✷✺✿❁❀❴❣ ▲❊✼✭❉❊✾✽✼✩✹✽✼✩✾✽❵❇❀ ❀✸❆❘✾✽❍❊✼✩❳✍❉❊✾✽✼✵❵❤✷❥❀❃❳❪✼✩❋●✿✻✼
✼✩✹♦✿r❀❃❧ ✼✩❝✺✼✩❬✵✷❩❍■❀✏✼✵❋●✿❁✾✻✼q❀❃✹▼❬✓✛■❀❅❵❃✼✩✹✭✗q❬✓✛■❀❃❳❢❀❃❍■❀✌✥ ✆
✖
✙✜✛✢✠ ✲✘✯✾✰✳✲ ✄ ✁ ✆ ✥ ✁ ✆ ✄✝✞ ✠ ✠ ✞ ✠ ✆✻✞ ✁☎✞ ✄ ✆ ✁ ✄✤✁ ✆ ✼ ✞✾✞ ✞ s
❫❴❳❢❀ ☛▲❊❋❊❂✩❄❃❆ ✌✏✎✒✑✓✌✦❉ ✼✵✾✔☛ ✼✵✷✺✿r❀✦❣❤▲❱✼✕❳ ❀❃❉ ✼✩✷❩❀✏▲❊❳ ❬✩❆❘❋✒✘✽▲❱❋ ✿✻❆ ❍❊✼✕❬✓✛■❀❅❵❘✼✵✹ ❍❱✼q✿r❀❃❳❢❀❃❋✢✛❊❆
n
✼✩❳ ✼✵❋❊❍❊✼✵✾✻✼✩❂✵❆❘✹ ❍❊✼✛▲❱❳ ❀❢✿❁❀❃❧ ✼✩❝❥❀❂✌✏✎✒✑✓✌❪❍❊✼✛✷♥
▲■❀❃❝✝✿r❀❇❳ ❀❃❋✏✛❊❆ ✗✛❬✓✛❊❀❃❳ ❀❇❍■❀ ✥ ✆ ✖ ✙✜✛✏✠ ✲ ✯✱✰✳✲ ✄ ✁ ✆ ✥ ✁ ✆✄ ✞ ✞✬✫ ✖ ✆ ✞ ✞ s❴❫❴❳❢❀
☛ ▲❊❋❊❂✩❄❃❆✷✌✏✎✒✑✓✌ ❉ ✼✵✾✔☛ ✼✩✷✐✿r❀ ❳✱✕✺❋❊✷❩❳❢❀✛❉ ❆♠❍❊✼ ✼✵❵❤✷✐✿r❀❃✾ ✿❁❆❃✿❁❀❃❝❩❳❪✼✩❋●✿✻✼ ❆❢❉❊✾✻❆❃❧❊❝❩✼✵❳ ❀ ❍❊✼ ❍❊✼✩✹✽❉ ✼✵✾✻❍✢✕✺❬✩✷❩❆❢❍❊✼✏✼✵✹✻❉■❀❇❂✩❆
✼ ❍❊✼✕✿❁✼✵❳❢❉ ❆❊s
❛■▲❊❋❊❂ ✣❤✼✩✹ ✌✏✎✒✑✓✌✱❉ ✼✩✾❀☛ ✼✩✷✐✿r❀❃✹✘❳✖✕❩❋❊✷✺❳ ❀❃✹ ✹❁❄❃❆ ▲❱✿❁✷✺❝❩✷✧❅❀❃❍■❀❇✹ ❉■❀❃✾✻❀ ❉ ✼✩✾✽❳❢✷✐✿❁✷❩✾ ❀❃✾✻❳❢❀★✧✩✼✵❋■❀❃❳❪✼✩❋●✿❁❆ ✼ ✾✻✼✩❬✵▲❊❉ ✼✩✾❁❀ ❙
❂❅❄❇❆✦✼ ✫■❬✩✷✺✼✩❋●✿❁✼ ❍❊✼ ✷✺✿✻✼✩❋❊✹ ❉❊✾✽❆ ❵❃✼✩❋❊✷✺✼✩❋●✿❁✼✵✹▼❍❊✼ ❬✵❆❘❋✒✘✽▲❊❋●✿❁❆❃✹ ✼✵✹✽✿✓✚✰✿❁✷❩❬✵❆❘✹✩❡●✿❁❀❃✷❩✹❦❬✵❆❘❳❢❆ ❉■❀❇❝❥❀❅❵❤✾❁❀❃✹❦✼✵❳ ❝❩✷❩❋
♥
▲■❀
♥
✼✵❳
❋■❀❇✿✻▲❊✾❁❀❇❝ ❡❤❉■❀❃❝❥❀❅❵❤✾❁❀❇✹✭✾✻✼✵✹✻✼✩✾♦❵❇❀❃❍■❀❃✹✱✼✵❳ ❝✺✷❩❋
♥
▲❊❀
♥
✼✩❋❱✹▼❍❊✼q❉❱✾✻❆
♥
✾✻❀❃❳❢❀❃❂❅❄❃❆✦❆❘▲☞✹✻✷✺✹✽✿✻✼✩❳❢❀❃✹✭✷❩❋●✿✻✼✩✾❁❀✰✿❁✷✺❵❃❆❘✹✩❡❱❫✰✷✜✘✝✹
✂✮✭ ✴✦✳
✟
✟☛✡❃✑ ✎✤✯✌✰✄✟✓✑
✞
✂ ✡✞☎✞✟✲✱
✞
☎✲✎ ✠ ✳
✞
✴✏✑ ✄ ❋■❀❃✹✕❳✱✚❃❣ ▲❊✷❩❋■❀❇✹q❍❊✼ ❧❊▲❊✹✽❬❅❀❱❡✝❬✵❆❘❋✒✘✽▲❊❋●✿✻❆❘✹✕❍❊✼ ✷✺✿✻✼✩❋❊✹ ☛ ✾✽✼✩❣✴✳❊✼✵❋ ✿✻✼✩✹ ✼✩❳
✿❃✗✵❬✩❋❊✷✺❬❅❀❃✹✱❍❱✼✕❳❢✷✺❋❊✼✩✾✻❀❃❂❅❄❃❆✦❍❊✼✕❍■❀❃❍❱❆❘✹✩s ❑▼❆❘❋❱✹✻✼✩❣✴✳❊✼✵❋●✿❁✼✩❳❪✼✩❋●✿✻✼❃❡ ✼ ✸♠✷❩✹♦✿❁✼✩❳ ❀❃❉❊❝❩✷✺❬❅❀❃❂✤✣♠✼✵✹▼❉■❀❇✾❁❀ ☛ ▲❊❋❊❂✤✣♠✼✵✹ ✌✏✎✒✑✓✌
❉ ✼✩✾✔☛✼✵✷✺✿❁❀❃✹✖❳✖✕❩❋❊✷✺❳ ❀❃✹✟✼✩❳♣✹✻✷✺✹✽✿❁✼✵❳ ❀❇✹✖❍❊✼✱✾✻✼✵❬✩▲❊❉ ✼✩✾✻❀❃❂❅❄❇❆ ❍❱✼✱✷❩❋✏☛❆❘✾✽❳ ❀❇❂❅❄❃❆❊❡❇✹✻✷✺✹✽✿❁✼✵❳ ❀❇✹✖❍❊✼✱❧■❀❃❋❱❬✩❆❘✹ ❍❊✼✱❍■❀❇❍❊❆❘✹✩❡
✛❊✷✺❉ ✼✵✾✽✿❁✼ ✸❤✿❁❆❊❡ ✛❊✷✺❉ ✼✵✾✻❳✖✕❩❍❊✷❩❀❱❡ ✹✽✷❩✹✽✿✻✼✩❳❢❀❃✹ ❍❊✼ ✿❁✾❁❀❇❍❊▲❊❂❅❄❇❆✓❍❱✼❢❝✺✷❩❋
♥
▲❊❀
♥
✼✩❋❱✹✩❡✝✹✻✷✺✹✽✿✻✼✩❳❢❀❃✹ ❍❊✼ ❬✩❆❘❳✖✗✩✾✽❬✩✷❩❆✡✼✵❝❩✼✵✿✻✾ ✹❇❙
❋❊✷✺❬✩❆❊❡❊❬✵❆❘❳❪❉❊✷❩❝❩❀❃❍❊❆❘✾✽✼✩✹✩❡♠✹✻✷✺✹✽✿❁✼✵❳ ❀❇✹✱❆❘❉ ✼✵✾❁❀❃❬✵✷❩❆❘❋❊❀❃✷❩✹✵❡❱✼✩❋●✿✻✾✻✼ ❆❘▲❱✿❁✾✻❀❃✹✩s
❯ ✼✵✾❁❀❃✾ ☛ ▲❱❋❊❂ ✣❤✼✩✹ ✌✏✎✒✑✓✌✏❉ ✼✵✾✔☛ ✼✵✷✺✿r❀❇✹✩❡❱✼✵✹✻❉ ✼✩❬✵✷❥❀❃❝✺❳❢✼✵❋ ✿✻✼✕❉■❀❃✾✻❀
♥
✾❁❀❃❋❱❍❊✼✩✹ ❬✩❆❃❋✒✘✽▲❊❋●✿❁❆❘✹✵❡■❉ ❆❤❍❊✼✕❋■❄❇❆ ✹✻✼✩✾ ☛ ✚❃❬✵✷❩❝
✘✲✚✕❣ ▲❊✼ ✼✩✹✽✿❁❀❃✹ ☛ ▲❊❋❊❂✤✣♠✼✵✹ ✹✻❄❃❆ ❳✛▲❊✷✐✿❁❆✕✾❁❀❇✾❁❀❃✹✵s✖✶✸✼ ❀❃❬✵❆❘✾✻❍❊❆ ❬✵❆❘❳✶✵✕❋ ▲❱✿❃✛ ✜✣✢ ✬ ✣ ❡❤❆ ❋✻✺❊❳❪✼✩✾✽❆ ✿✻❆❃✿r❀❇❝❱❍❊✼ ☛ ▲❊❋❊❂✤✣♠✼✵✹
✌✏✎✒✑✓✌ ❉■❀❇✾❁❀ ❳ ❀❃❉ ✼❅❀❇✾ ▲❊❳ ❬✵❆❘❋✒✘✽▲❊❋●✿❁❆
S
❬✩❆❘❳n
❬✓✛■❀❅❵❘✼✩✹▼❉■❀❃✾❁❀ ❆✏✷✺❋ ✿✻✼✩✾♦❵❃❀❇❝❩❆[0, m
−
1]
✗m
n
❡♠✹✽✼✩❋❊❍❱❆✛❣ ▲❊✼ ✹✻❆❃❳❢✼✵❋ ✿✻✼m(m
−
1)
. . .
(m
−
n
+ 1)
✹❁❄❃❆ ❉ ✼✩✾❀☛ ✼✩✷✐✿r❀❃✹✵s ✮✸✹✽✹✻✷✺❳❜❡ ❀ ❉❊✾✽❆❘❧■❀❃❧❊✷✺❝❩✷✺❍■❀❃❍❊✼ ❍❊✼✛❣ ▲❊✼✏❋■❄❃❆✂✛■❀ ✘✻❀ ❬✩❆❃❝❩✷❩✹✻❄❃❆ ✗❴❀ ✾✻❀★✧❅❄❇❆(m(m
−
1)
. . .
(m
−
n
+ 1))/m
n
❡❤❀✕❣❤▲❊❀❃❝■✿❁✼✩❋❱❍❊✼❴❉❊❀❃✾❁❀ ✧✩✼✵✾✻❆✦❳✛▲❊✷✺✿✻❆✕✾❃✚❃❉❱✷❩❍❊❆❊s✯❖✯❀❃✾✻❀m
= 13
✼n
= 10
❡✟❀☞❉❊✾✻❆❃❧■❀❃❧❊✷✺❝❩✷❩❍❊❀❃❍❊✼✏❍❱✼❪❣ ▲❊✼ ❋■❄❇❆✷✛❊❀ ✘✻❀☞❬✩❆❘❝✺✷❩✹✲✣❤✼✩✹ ✗0.0074
s ❖✯❀❃✾✻❀ ☛ ▲❱❋❊❂ ✣❤✼✩✹ ✌✏✎✒✑✓✌ ❉ ✼✩✾✔☛✼✵✷✺✿❁❀❃✹q❳✖✕❩❋❊✷✺❳ ❀❃✹✵❡ ❆❃❋❊❍❊✼m
=
n
❡✟❀ ❉❊✾✽❆❘❧■❀❃❧❱✷❩❝❩✷✺❍■❀❃❍❊✼✽✗ ❀❃✷❩❋❱❍■❀ ❳❪✼✩❋❊❆❘✾✵s ✫ ✼✩✹✽✿✻✼ ❬❅❀❃✹✽❆✡✿✻✼✩❳❪❆❘✹✕❣ ▲❊✼ ❀ ❉❊✾✽❆❘❧■❀❃❧❊✷✺❝❩✷✺❍■❀❃❍❊✼ ✗ ❍■❀❃❍■❀❪❉ ❆❃✾n!/n
n
s ❖◗❀❃✾❁❀n
= 10
❡ ❀❪❉❊✾✻❆❘❧❊❀❃❧❊✷❩❝✺✷❩❍■❀❇❍❊✼✕❍❊✼ ❣❤▲❱✼✛❋■❄❃❆✖✛■❀ ✘✻❀❪❬✩❆❘❝✺✷❩✹✲✣❤✼✩✹ ✗ ✹✻❆❃❳❢✼✵❋ ✿✻✼0.00036
s❞❜▲❊✷✐✿❁❆❘✹ ❳✖✗✵✿❁❆❤❍❊❆❘✹ ❉■❀❇✾❁❀
♥
✼✩✾✻❀❃✾ ▲❊❳❢❀ ☛▲❊❋❱❂❅❄❃❆✿✌✏✎✒✑✓✌q❉ ✼✩✾❀☛ ✼✩✷✐✿r❀✕❳✱✕✺❋❊✷❩❳❢❀✸▲❊✹✻❀❃❳ ❀ ❀❃❧ ❆❃✾✻❍■❀
♥
✼✩❳ ❞✥★✭✩ ❡
❞ ❀❃❉ ✼❅❀❇❳❢✼✵❋ ✿✻❆ ✂✸✷ ✎✓✹✺✹ ✳✵✴☎✶ ✄✲❡ ★✕✾✽❍❊✼✩❋❊❀❃❂❅❄❃❆ ✂✓✻ ✡ ☞ ✟☛✡ ✳✵✴☎✶ ✄ ✼ ❖◗✼✩✹✽❣ ▲❊✷❩✹✻❀ ✂✸✼ ✟✲✎ ✡ ☎✓✌☎✳✵✴☎✶ ✄✲❡❱▲❱❳ ❀✏❍❱✼✩✹✻❬✵✾✻✷✺❂❅❄❃❆ ❬✩▲❤❙
❋✢✛■❀❇❍■❀ ❉ ❆❘✾ ❛■❆✝✸ ✼✲✿❪❀❃❝ s ✂ ❬✤☛❚s✒✜✬✶✩❤❡✚✬✶✤★✣✄✲s✧✫✸❀◆❀❃❧ ❆❘✾✻❍■❀
♥
