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❈♦♥str✉❝t✐♦♥ ♦❢ ❛ ❉❡ ❇r✉✐❥♥ ●r❛♣❤ ❢♦r ❆ss❡♠❜❧② ❢r♦♠ ❛ ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ❇❛st✐❡♥ ❈❛③❛✉①✱ ❚❤✐❡rr② ▲❡❝r♦q✱ ❊r✐❝ ❘✐✈❛❧s ▲■❘▼▼ ✫ ■❇❈✱ ▼♦♥t♣❡❧❧✐❡r ✲ ▲■❚■❙ ❘♦✉❡♥ ▼❛rs ✸✱ ✷✵✶✺

■♥tr♦❞✉❝t✐♦♥ ❉❡ ❇r✉✐❥♥ ●r❛♣❤ ❢♦r ❛ss❡♠❜❧② ❘ = { ❜❜❛❝❜❛❛ , ❝❜❛❛❝ , ❜❛❝❜❛❜ , ❝❜❛❜❝❛❛ , ❜❝❛❛❝❜ } ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✶ ✴ ✸✵

■♥tr♦❞✉❝t✐♦♥ ❉❡ ❇r✉✐❥♥ ●r❛♣❤ ❢♦r ❛ss❡♠❜❧② ❘ = { ❜❜❛❝❜❛❛ , ❝❜❛❛❝ , ❜❛❝❜❛❜ , ❝❜❛❜❝❛❛ , ❜❝❛❛❝❜ } ac ba ab bc aa ca bb cb ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✶ ✴ ✸✵

■♥tr♦❞✉❝t✐♦♥ ●❡♥❡r❛❧✐③❡❞ ❙✉✣① ❚r❡❡ ✭●❙❚✮ ❘ = { ❜❜❛❝❜❛❛ , ❝❜❛❛❝ , ❜❛❝❜❛❜ , ❝❜❛❜❝❛❛ , ❜❝❛❛❝❜ } a c b 7 7 6 6 5 caa bacbaa aa a c a b b 6 6 5 4 4 5 5 1 cba caa a cb cb c b b a 3 3 4 1 2 5 4 caa b a b a a b c 3 2 2 4 3 2 1 caa a b c 3 2 1 1 ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✷ ✴ ✸✵

■♥tr♦❞✉❝t✐♦♥ ●❡♥❡r❛❧✐③❡❞ ❙✉✣① ❚r❡❡ ✇✐t❤ ❝✉t ❘ = { ❜❜❛❝❜❛❛ , ❝❜❛❛❝ , ❜❛❝❜❛❜ , ❝❜❛❜❝❛❛ , ❜❝❛❛❝❜ } a c b 7 7 6 6 5 ca ba cbaa aa a c a b a b 6 6 5 4 4 5 5 c 1 c aa a ba cb cb c b b a 3 3 4 1 2 5 4 caa b a b a a b c 3 2 2 4 3 2 1 caa a b c 3 2 1 1 ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✷ ✴ ✸✵

■♥tr♦❞✉❝t✐♦♥ ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✭❚❙❚✮ ❘ = { ❜❜❛❝❜❛❛ , ❝❜❛❛❝ , ❜❛❝❜❛❜ , ❝❜❛❜❝❛❛ , ❜❝❛❛❝❜ } a c b ca ba a c a aa b b 4 1 1 6 6 5 4 5 2 5 c c a b c 3 b 2 1 a 3 3 4 3 2 4 1 3 1 5 2 4 2 ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✷ ✴ ✸✵

■♥tr♦❞✉❝t✐♦♥ ▼♦t✐✈❛t✐♦♥ ❉❡ ❇r✉✐❥♥ ●r❛♣❤ ✐s ❧❛r❣❡❧② ✉s❡❞ ✐♥ ❞❡ ♥♦✈♦ ❣❡♥♦♠❡ ❛ss❡♠❜❧②✳ ❬P❡✈③♥❡r ❡t ❛❧✳✱ ✷✵✵✶❪ ❖♥❡ ❜✉✐❧❞s ❛ s✉✣① tr❡❡ ❜❡❢♦r❡ t❤❡ ❛ss❡♠❜❧② ❢♦r s♦♠❡ ❛♣♣❧✐❝❛t✐♦♥s✱ ❢♦r ✐♥st❛♥❝❡ ❢♦r t❤❡ ❡rr♦r ❝♦rr❡❝t✐♦♥✳ ❬❙❛❧♠❡❧❛✱ ✷✵✶✵❪ ❚❤❡r❡ ❡①✐st ❛❧❣♦r✐t❤♠s t♦ ❜✉✐❧❞ ❞✐r❡❝t❧② t❤❡ ❉❡ ❇r✉✐❥♥ ●r❛♣❤ ❬❖♥♦❞❡r❛ ❡t ❛❧✳✱ ✷✵✶✸❪ ❬❘ ♦ ❞❧❛♥❞✱ ✷✵✶✸❪ ❛♥❞ t❤❡ ❈♦♥tr❛❝t❡❞ ❉❡ ❇r✉✐❥♥ ●r❛♣❤ ❬❈❛③❛✉① ❡t ❛❧✳✱ ✷✵✶✹❪❬❈❤✐❦❤✐ ❡t ❛❧✳✱ ✷✵✶✹❪✳ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✸ ✴ ✸✵

❘❡s✉❧t✿ ❲❡ ❝❛♥ ❞✐r❡❝t❧② ❜✉✐❧❞ t❤❡ ❛ss❡♠❜❧② ❉❡ ❇r✉✐❥♥ ❣r❛♣❤ ✐♥ t❤❡ ❝❧❛ss✐❝❛❧ ♦r ❝♦♥tr❛❝t❡❞ ❢♦r♠ ❢r♦♠ ❛♥ ✐♥❞❡①✐♥❣ ❞❛t❛ str✉❝t✉r❡s✳❬❈❛③❛✉① ❡t ❛❧✳✱ ✷✵✶✹❪ ◗✉❡st✐♦♥✿ ❍♦✇ t♦ ❞♦ ✐t ✇✐t❤♦✉t ✉s✐♥❣ ♠♦r❡ s♣❛❝❡ t❤❛♥ ♥❡❝❡ss❛r②❄ ■♥tr♦❞✉❝t✐♦♥ ■♥❞❡①✐♥❣ ❞❛t❛ str✉❝t✉r❡s ◆✉♠❡r♦✉s ❞❛t❛ str✉❝t✉r❡s✿ s✉✣① tr❡❡✱ ❛✣① tr❡❡✱ s✉✣① t❛❜❧❡✱ ❢❛❝t♦r ❛✉t♦♠❛t❛✱ ❡t❝✳ t♦ ✐♥❞❡① ♦♥❡ ♦r s❡✈❡r❛❧ t❡①ts ✭❣❡♥❡r❛❧✐③❡❞ ✐♥❞❡①✮ ❢✉♥❝t✐♦♥♥❛❧❧② ❡q✉✐✈❛❧❡♥t ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✹ ✴ ✸✵

◗✉❡st✐♦♥✿ ❍♦✇ t♦ ❞♦ ✐t ✇✐t❤♦✉t ✉s✐♥❣ ♠♦r❡ s♣❛❝❡ t❤❛♥ ♥❡❝❡ss❛r②❄ ■♥tr♦❞✉❝t✐♦♥ ■♥❞❡①✐♥❣ ❞❛t❛ str✉❝t✉r❡s ◆✉♠❡r♦✉s ❞❛t❛ str✉❝t✉r❡s✿ s✉✣① tr❡❡✱ ❛✣① tr❡❡✱ s✉✣① t❛❜❧❡✱ ❢❛❝t♦r ❛✉t♦♠❛t❛✱ ❡t❝✳ t♦ ✐♥❞❡① ♦♥❡ ♦r s❡✈❡r❛❧ t❡①ts ✭❣❡♥❡r❛❧✐③❡❞ ✐♥❞❡①✮ ❢✉♥❝t✐♦♥♥❛❧❧② ❡q✉✐✈❛❧❡♥t ❘❡s✉❧t✿ ❲❡ ❝❛♥ ❞✐r❡❝t❧② ❜✉✐❧❞ t❤❡ ❛ss❡♠❜❧② ❉❡ ❇r✉✐❥♥ ❣r❛♣❤ ✐♥ t❤❡ ❝❧❛ss✐❝❛❧ ♦r ❝♦♥tr❛❝t❡❞ ❢♦r♠ ❢r♦♠ ❛♥ ✐♥❞❡①✐♥❣ ❞❛t❛ str✉❝t✉r❡s✳❬❈❛③❛✉① ❡t ❛❧✳✱ ✷✵✶✹❪ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✹ ✴ ✸✵

■♥tr♦❞✉❝t✐♦♥ ■♥❞❡①✐♥❣ ❞❛t❛ str✉❝t✉r❡s ◆✉♠❡r♦✉s ❞❛t❛ str✉❝t✉r❡s✿ s✉✣① tr❡❡✱ ❛✣① tr❡❡✱ s✉✣① t❛❜❧❡✱ ❢❛❝t♦r ❛✉t♦♠❛t❛✱ ❡t❝✳ t♦ ✐♥❞❡① ♦♥❡ ♦r s❡✈❡r❛❧ t❡①ts ✭❣❡♥❡r❛❧✐③❡❞ ✐♥❞❡①✮ ❢✉♥❝t✐♦♥♥❛❧❧② ❡q✉✐✈❛❧❡♥t ❘❡s✉❧t✿ ❲❡ ❝❛♥ ❞✐r❡❝t❧② ❜✉✐❧❞ t❤❡ ❛ss❡♠❜❧② ❉❡ ❇r✉✐❥♥ ❣r❛♣❤ ✐♥ t❤❡ ❝❧❛ss✐❝❛❧ ♦r ❝♦♥tr❛❝t❡❞ ❢♦r♠ ❢r♦♠ ❛♥ ✐♥❞❡①✐♥❣ ❞❛t❛ str✉❝t✉r❡s✳❬❈❛③❛✉① ❡t ❛❧✳✱ ✷✵✶✹❪ ◗✉❡st✐♦♥✿ ❍♦✇ t♦ ❞♦ ✐t ✇✐t❤♦✉t ✉s✐♥❣ ♠♦r❡ s♣❛❝❡ t❤❛♥ ♥❡❝❡ss❛r②❄ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✹ ✴ ✸✵

❈❤❛✐♥ ♦❢ s✉✣①✲❞❡♣❡♥❞❛♥t str✐♥❣s ❛♥❞ ❚r❡❡ ❈❤❛✐♥ ♦❢ s✉✣①✲❞❡♣❡♥❞❛♥t str✐♥❣s ❛♥❞ ❚r❡❡ ✶ ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✭❚❙❚✮ ✷ ❉❡ ❇r✉✐♥ ●r❛♣❤ ✈✐❛ t❤❡ ❚❙❚ ✸ ❈♦♥❝❧✉s✐♦♥ ✹ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✺ ✴ ✸✵

❈❤❛✐♥ ♦❢ s✉✣①✲❞❡♣❡♥❞❛♥t str✐♥❣s ❛♥❞ ❚r❡❡ ❈❤❛✐♥ ♦❢ s✉✣①✲❞❡♣❡♥❞❛♥t str✐♥❣s ❛♥❞ ❚r❡❡ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✺ ✴ ✸✵

❈❤❛✐♥ ♦❢ s✉✣①✲❞❡♣❡♥❞❛♥t str✐♥❣s ❛♥❞ ❚r❡❡ ❙tr✐♥❣ ❉❡✜♥✐t✐♦♥ ❬●✉s✜❡❧❞ ✶✾✾✼❪ ▲❡t ✇ ❛ str✐♥❣✳ ❛ s✉❜str✐♥❣ ♦❢ ✇ ✐s ❛ str✐♥❣ ✐♥❝❧✉❞❡❞ ✐♥ ✇ ✱ ❛ ♣r❡✜① ♦❢ ✇ ✐s ❛ s✉❜str✐♥❣ ✇❤✐❝❤ ❜❡❣✐♥s ✇ ❛♥❞ ❛ s✉✣① ✐s ❛ s✉❜str✐♥❣ ✇❤✐❝❤ ❡♥❞s ✇ ✳ ❛♥ ♦✈❡r❧❛♣ ❜❡t✇❡❡♥ ✇ ❛♥❞ ✈ ✐s ❛ s✉✣① ♦❢ ✇ ✇❤✐❝❤ ✐s ❛❧s♦ ❛ ♣r❡✜① ♦❢ ✈ ✳ ✇ ❛ ❜ ❛ ❜ ❜ ❛ ❜ ❛ ❛ ❛ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✻ ✴ ✸✵

❈❤❛✐♥ ♦❢ s✉✣①✲❞❡♣❡♥❞❛♥t str✐♥❣s ❛♥❞ ❚r❡❡ ❙tr✐♥❣ ❉❡✜♥✐t✐♦♥ ❬●✉s✜❡❧❞ ✶✾✾✼❪ ▲❡t ✇ ❛ str✐♥❣✳ ❛ s✉❜str✐♥❣ ♦❢ ✇ ✐s ❛ str✐♥❣ ✐♥❝❧✉❞❡❞ ✐♥ ✇ ✱ ❛ ♣r❡✜① ♦❢ ✇ ✐s ❛ s✉❜str✐♥❣ ✇❤✐❝❤ ❜❡❣✐♥s ✇ ❛♥❞ ❛ s✉✣① ✐s ❛ s✉❜str✐♥❣ ✇❤✐❝❤ ❡♥❞s ✇ ✳ ❛♥ ♦✈❡r❧❛♣ ❜❡t✇❡❡♥ ✇ ❛♥❞ ✈ ✐s ❛ s✉✣① ♦❢ ✇ ✇❤✐❝❤ ✐s ❛❧s♦ ❛ ♣r❡✜① ♦❢ ✈ ✳ ✇ ❛ ❜ ❛ ❜ ❜ ❛ ❜ ❛ ❛ ❛ ❈❛③❛✉①✱ ▲❡❝r♦q✱ ❘✐✈❛❧s ❚r✉♥❝❛t❡❞ ❙✉✣① ❚r❡❡ ✫ ❉❇● ✻ ✴ ✸✵