<Text-field style="Heading 1" layout="Heading 1">Introdu\303\247\303\243o</Text-field>

<Text-field style="Heading 1" layout="Heading 1" spaceabove="7">Derivada Como Inclina\303\247\303\243o da Reta Tangente </Text-field>

Dado o gr\303\241fico (graph) da fun\303\247\303\243o, 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, e um ponto sobre o gr\303\241fico, ( LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, 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 ), \303\251 normalmente bastante f\303\241cil identificar, se s\303\263 visualmente, a reta tangente ao gr\303\241fico neste ponto.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 9.1 - Reta <Hyperlink linktarget="Dictionary:Definition,tangent" hyperlink="true"> Tangente</Hyperlink> em Foco </Text-field>

O pontoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQS8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZQLUY8Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y4Rj9GQkZERkZGSEZKRkxGTkZRLUY1NiRRIjVGJ0Y4RjhGOEYrRjg= est\303\241 sobre o gr\303\241fico da fun\303\247\303\243o

f1 := 3*x^3+9*x^2-7: f(x) = f1;

como confirmado pelo c\303\241lculo

eval(f1, x=1);

Figura 9.1 cont\303\251m um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== no intervalo 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

x1 := 1: y1 := eval( f1, x=x1 ): h_list := [seq( 2^(3-i), i=1..10 )]: P1 := [ seq( Tangent( f1, x=x1, x1-h..x1+h/4, output=plot, showtangent=false, title=sprintf("Graph of f(x) on [%6.3f,%6.3f]", x1-h, x1+h/4), view=[x1-h..x1+h/4,DEFAULT]), h=h_list )]: P1[1];

Figura 9.1 Gr\303\241ficoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQS8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZQLUY8Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y4Rj9GQkZERkZGSEZKRkxGTkZRLUY1NiRRIjVGJ0Y4RjhGOEYrRjg= e de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRmZuLUYjNiQtRiw2JVEieEYnRjRGN0Y+LUY7Ni1RIilGJ0Y+RllGQ0ZaRkdGSUZLRk1GZW4vRlNRLDAuMTExMTExMWVtRidGPkYrRj4tRjs2LVEiPUYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0Zmby1GIzYpRistRiM2Jy1JI21uR0YkNiRRIjNGJ0Y+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSLUklbXN1cEdGJDYlRmpuRlxwLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRj4tRjs2LVEiK0YnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0ZdcS1GIzYnLUZdcDYkUSI5RidGPkZgcC1GZHA2JUZqbi1GXXA2JFEiMkYnRj5GZnBGK0Y+LUY7Ni1RKCZtaW51cztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GXHFGXnEtRl1wNiRRIjdGJ0Y+Rj5GK0Y+ no 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.

Agora, olhe no gr\303\241fico da fun\303\247\303\243o para intervalos (intervals) cada vez menores ao redor de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkYrRj4=, isto \303\251, enfoque no 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 sobre o gr\303\241fico. Este enfoque \303\251 formado pelos nove gr\303\241ficos na Figura 9.2.

P1[2];

P1[3];

P1[4];

P1[5];

P1[6];

P1[7];

P1[8];

P1[9];

P1[10];

Figura 9.2 Enfoque no pontoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQS8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZQLUY8Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y4Rj9GQkZERkZGSEZKRkxGTkZRLUY1NiRRIjVGJ0Y4RjhGOEYrRjg=para o gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtRiM2Ji1GOzYtUSIoRidGPi9GQUY2RkMvRkZGNkZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRmZuLUYjNiQtRiw2JVEieEYnRjRGN0Y+LUY7Ni1RIilGJ0Y+RllGQ0ZaRkdGSUZLRk1GZW4vRlNRLDAuMTExMTExMWVtRidGPkYrRj4tRjs2LVEiPUYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0Zmby1GIzYpRistRiM2Jy1JI21uR0YkNiRRIjNGJ0Y+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSLUklbXN1cEdGJDYlRmpuRlxwLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRj4tRjs2LVEiK0YnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0ZdcS1GIzYnLUZdcDYkUSI5RidGPkZgcC1GZHA2JUZqbi1GXXA2JFEiMkYnRj5GZnBGK0Y+LUY7Ni1RKCZtaW51cztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GXHFGXnEtRl1wNiRRIjdGJ0Y+Rj5GK0Y+

Observe que o gr\303\241fico da fun\303\247\303\243o se torna mais reto \303\241 medida em que a vis\303\243o do intervalo (interval) \303\251 cortada pela metade. Nas \303\272ltimas cinco vistas, a fun\303\247\303\243o parece ser uma linha reta. Quando isto acontece, a linha reta que aparece \303\251 a reta tangente ao gr\303\241fico da fun\303\247\303\243o no ponto. Esta retifica\303\247\303\243o do gr\303\241fico da fun\303\247\303\243o \303\251 ainda mais aparente quando a reta tangente (tangent) \303\251 inclu\303\255da no desenho do gr\303\241fico. Isto pode ser visto nos dez gr\303\241ficos na Figura 9.3, criados com

P1t := [seq(Tangent(f1, x=x1, 1-h..x1+h/4, output=plot, showtangent=true, title=sprintf("Graph of f(x) on [%6.3f,%6.3f]",x1-h, x1+h/4), view=[x1-h..x1+h/4,DEFAULT], tickmarks=[2,2]), h=h_list)]:

e exibidos com

P1t[1];

P1t[2];

P1t[3];

P1t[4];

P1t[5];

P1t[6];

P1t[7];

P1t[8];

P1t[9];

P1t[10];

Figura 9.3 Enfoque sobre 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, com gr\303\241ficos de ambos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== e a reta tangente

A derivada de uma fun\303\247\303\243o em um ponto existe quando o gr\303\241fico da fun\303\247\303\243o tem uma reta tangente naquele ponto. O valor (value) da derivada neste ponto \303\251 a inclina\303\247\303\243o da reta tangente.

Neste caso, a equa\303\247\303\243o da reta (equation of the line) tangente ao gr\303\241fico de 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 no 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 \303\251

y = Tangent( f1, x=x1, output=line );

assim, a inclina\303\247\303\243o da reta tangente \303\251

m = Tangent( f1, x=x1, output=slope );

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 9.2 - V\303\251rtices (Cantos)</Text-field>

O pontoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNiQtRiM2Jy1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSIsRidGOC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQS8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZQLUY8Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y4Rj9GQkZERkZGSEZKRkxGTkZRLUY1NiRRIjNGJ0Y4RjhGOEYrRjg= est\303\241 sobre o gr\303\241fico da fun\303\247\303\243o

f2 := sqrt(abs(x^2-4)+9): f(x) = f2;

como confirmado pelo c\303\241lculo

simplify(eval(f2, x=2));

Figura 9.4 cont\303\251m um gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== no intervalo 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.

myTangent(f2, x=2, -3..7, view=[DEFAULT, 0..7], title="");

Figura 9.4 Gr\303\241fico de 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 no 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

Enfoque de uma parte do gr\303\241fico, pr\303\263ximo de ( 2, 3 ), leva aos dez gr\303\241ficos mostrados na Figura 9.5, criados com

P2 := [seq(myTangent(f2, x=2, 2-h..2+h, tickmarks=[2,2]),h=h_list)]:

e exibidos com

P2[1];

P2[2];

P2[3];

P2[4];

P2[5];

P2[6];

P2[7];

P2[8];

P2[9];

P2[10];

Figura 9.5 Enfoque sobre 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

Observe que o gr\303\241fico da fun\303\247\303\243o tem um v\303\251rtice bem pronunciado que n\303\243o desaparece quando a janela do enfoque vai se tornando cada vez menor. No ponto queremos que a fun\303\247\303\243o pare\303\247a ser uma (\303\272nica) linha reta passando pelo 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.

O v\303\251rtice no gr\303\241fico de 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 no 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 significa que n\303\243o existe reta tangente \303\240 fun\303\247\303\243o em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4=; a fun\303\247\303\243o n\303\243o \303\251 diferenci\303\241vel (differentiable ) em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMkYnRj5GPkYrRj4=. Esta conclus\303\243o \303\251 confirmada com o comando Tangent como se segue:

Tangent( f2, x=x2 );

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 9.3 - Saltos e C\303\272spides<Hyperlink linktarget="Dictionary:Definition,jumpdiscontinuity" hyperlink="true"> </Hyperlink></Text-field>

Al\303\251m de n\303\243o existir em um canto, derivadas n\303\243o existem quando o gr\303\241fico tem uma c\303\272spide (cusp) ou um salto (jump) no ponto em quest\303\243o.

Os saltos s\303\243o problem\303\241ticos porque a reta tangente n\303\243o tem nenhum salto e assim \303\251 imposs\303\255vel encontrar uma \303\272nica reta que aproxima o gr\303\241fico de 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 por ambos os lados do ponto.

A fun\303\247\303\243o

f3a := piecewise( x<=1, 1, x>1,2 ): f(x) = f3a;

salta em 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, como mostra o gr\303\241fico seguinte.

plot(f3a, x=-1..3, discont=true, view=[-1..3,0..2], scaling=constrained);

Figura 9.6 Gr\303\241fico de 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 mostrando o salto em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY1LUkjbW5HRiQ2JFEiMUYnRjlGOQ==

Um exemplo de fun\303\247\303\243o com uma c\303\272spide (cusp) \303\251

f3b := abs(x)^(1/3): `f`(x) = f3b;

quando a c\303\272spide (cusp) \303\251 no 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, como se v\303\252 na Figura 9.7.

plot(f3b, x=-3..7, scaling=constrained, tickmarks=[2,2]);

Figura 9.7 Gr\303\241fico de 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 mostrando a c\303\272spide em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY1LUkjbW5HRiQ2JFEiMEYnRjlGOQ==

Embora l\303\241 pare\303\247a ser um ponto acentuado (c\303\272spide) na origem, ainda \303\251 prudente enfocar sobre este ponto via os dez gr\303\241ficos na Figura 9.8, criados com

P3 := [seq(myTangent(f3b, x=0, 0-h..0+h, tickmarks=[2,2]), h=h_list)]:

e exibidos com

P3[1];

P3[2];

P3[3];

P3[4];

P3[5];

P3[6];

P3[7];

P3[8];

P3[9];

P3[10];

Figura 9.8 Enfocando sobre 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

Cantos, c\303\272spides, e saltos s\303\243o quadros que se deve ter em mente quando se pensa sobre fun\303\247\303\265es que n\303\243o tenham uma derivada.

<Text-field style="Heading 2" layout="Heading 2" spaceabove="7">Exemplo 9.4 - Reta <Hyperlink linktarget="Dictionary:Definition,tangent" hyperlink="true">Tangente</Hyperlink> como Limite de Retas <Hyperlink linktarget="Dictionary:Definition,secant" hyperlink="true">Secant</Hyperlink>es</Text-field>

Note that the zooming process is a limit as the viewing window size decreases to zero. An alternate way of looking at tangent lines is to define

line tangent to 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 at 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 = 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secant line on LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSN5YUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1GIzYnLUYsNiVRImZGJ0Y0RjctRjs2LVEwJkFwcGx5RnVuY3Rpb247RidGPkZARkNGRUZHRklGS0ZNL0ZQUSYwLjBlbUYnL0ZTRmduLUYjNiYtRjs2LVEiKEYnRj4vRkFGNkZDL0ZGRjZGR0ZJRktGTS9GUFEsMC4xNjY2NjY3ZW1GJy9GU0Zhby1GIzYkLUYsNiVRInhGJ0Y0RjdGPi1GOzYtUSIpRidGPkZeb0ZDRl9vRkdGSUZLRk1GYG8vRlNRLDAuMTExMTExMWVtRidGPkYrRj5GK0Y+RitGPg== through 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 and 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

Consider the function

f := x -> (x^3-5)*(x^2-1)/(x^2+1): 'f'(x) = f(x);

at the point with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUklbXN1YkdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21uR0YkNiRRIjFGJy9GO1Enbm9ybWFsRidGQy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiPUYnRkMvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRk4vJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGZ24tRkA2JFEiMkYnRkNGQ0YrRkM=, so that

y[1] = f(2);

Figure 9.9 contains a graph of the function and the 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, suggesting that there should be a tangent line at this point.

display(myTangent(f(x), x=2, -2..3), title="", scaling=unconstrained);

Figure 9.9 Graph of 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 and the 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

We could find the tangent line by zooming. The equation of this tangent line is

y = Tangent(f(x), x=2, output=line );

Let's see if we can duplicate this result as the limit of secant lines. For this, we can use the TangentAndSecant maplet, which is equivalent to either the built-in Secant Tutor or Tangent Tutor selected from the Tools/Tutors/Calculus - Single Variable menu. If it is launched from the pull-down menu, we will have to type in the function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg==. Alternatively, we can execute the command

TangentTutor(f(x), x=2);

to launch the Tangent Tutor with both LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7L0Y/RjFGQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGNS1JI21uR0YkNiRRIjJGJ0Y5Rjk= already typed in. The default Increment, 0.5, should be changed to 0.2. The default number of iterations is 8. That should be changed to 5. To obtain the graph in the Plot Window shown in Figure 9.10,

yIpyIr<K_Tn^T^;FZ;BR<`:Rr?BqEDXMeSFcCO?gd:>F;B:=J:>F<j:J:JZDnAJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BJ:>BV=ofZEj:JJC:ufZE:>ON^BX:=:;:IC\\AJ;B:;:<s=J:><<J;@s<F:>P<j:Ds<:k??b^E:>R<j;Ds<:KH:^ZLh:Jb?Z:fZLh:JfK=Ds<:;a:vZLX:=:;:Kb^A:>:F[LX:J:J?Ds<:KA;BbI:;:FZZX:=:;:?BbA:>:VZZX:J:JADt<:[a:v[\\h:JvKBDt;J:>:f\\\\h:J:@J:v\\\\X:B:;:Ht;F:>:FZ]X:J::>[;J?<JC@j;F:<j:<:oR:E:>[:jG@j<:[Z:>_;V:J;<:wS:EJ;JFjY@j<n:>_:jBDj<V:;JfjCDj;:;:cb:EJ=JrB:Mu[Cj:J>@:<:yypH^?VZ>^Z>VZ?^Z>^Z?fZ?nZA^[BvZAvZAv[EV[C^[Kv[LN\\Kv[KF\\Mn\\Vv\\M^\\Tf\\KF\\RF^RN]Wf]Yv]YV\\QN^^N^X^^Vn]Yn]yYU@j<Pj<XJ=XJA\\J>tJILkBLKItKIt;:::::::vy:U>KR:Ag:kt:=bBDjB@j;@k:xY\\w=@j<@j:@j:B:;J:Z;NZ=^Z?nZA>[CN[Evy>Ug[J;@j;HJ;Lj;Pj<LJ<<Z;fi;NZ=>Z>F\\?N\\[F`;oZMFd[wZ\\FhNN`;Hl[@[]NbkHrONdKAx^V`\\Oh<H[Dn\\Q>]SN]_n^a>_cN_nf`pv`rFatVb>gb@wbBGcDWdNgdPwdRGeTWf^gf`wfbGgdWhnghpwhrGitWj>hj@xjBHkDPlM`lOplQ@mSPm\\Xn^hn`xnbHodPpm`poppq@qsPq<Yr>ir@yrBIsDQtMatOqtQAuSQu[Qv]av_qvaAwcQwkQxmaxoqxqAysQyyaRyR:Hj:FZ;:<:;Z;N:C::PuB<J;@J;LJ<HJ<Xj<LJ<FZ<vH=b:AR>CR;=SFGb>=TNIRR]u>?cF=F<cbJ]Vb]WjMrBacN[Y??eV]h<gBCcSrESviB@mJMXLNRGgsG:::::Z<Xj>hJ:::::::nTbrAIs:_yvcAJg_[=F:?R>AR>;rIPywiupYmidrPXofDWLUWqulEyV;eWutm`Lt`pS>]tMQJREq`MWHMYFHjNtTXEKWesnqpjqL<xOSaq?epiXy\\yMXIKuDxX@Y?urP`mtpkAHVwMp=apdeOeAwi@PrLr\\UXElPw\\j>qkUqPaAjT<WvMtneUihsr@X>MqWTKU=s<QNBYxsTM=`O=]oUowHAvNWfRf\\EYmaA]VonVheUWqppkFp\\LnphVn>`[V@iFOcKy]=FwXNf?`_UXejwsFgkSI];yrhH_p?iQwalY^cwaqYsyGxOgj_WfAnjoxmTVcw^rmWucGxU_uBIxhX]EAe_^grFwvP_mqk]Xg]_mEneGfiYgdjiwY@kipfqp`qpxknu_^nj^ijYohfvJ_v[IsLGa[FivYwJYr\\IgQynTFptW`T^tWI_liayErstnmXrydx]BgyvxEyikidgCXidyCVUIcymyUwiDkWqitkgvNKeoihiyRDcsi[I^kTtiB^WT:kEIiIBIyR[Sl[DV=tBAFq]RQcbI;cnGGfcXGQSSyw_YDfGVXUhrqhsMcN_bjyTE=vl]RfGf==rB?vTwETmf@wrQEfhyejUBcoYYgxyDXNawjy?RryGxOgrsUS]i<?xj=h`gwd=wDMxXMUboxt[TcSxHAEFsDLQfAKTHuh[msQWeciwUsuP;WPyhQmHMiiQee_IwSEWmgwqAsmoWQ]xRwFOWvciWbAg`SR=[faerIayBMEIaywqrydrKYp<]uyOkUFc^afvgkyUketYQbtgeICsggvsQtLIwgITSMTsCfkaVU_E]KXLMX:cf][UJubHgDMoheYwAExTYc<QxcqXjIGQkXQuDcGIJ_hM?ev;HRIBqmbWsBs]ypmgu=RiEIxidyJvyPyeL:usDpMXpJLIYyivy@iZ`hpYZ^Vfa`iuwtUFxDXxX?xqHjoxaN>gqqpkxy:vf:a^pVtRI[PohlNn^qpoQ?WUjmg:QVk=RnSEvYWyKbpYDQueoQyypQbHO[=Vj]yG`n^yi[wqrekiXGqvQGBpotGOVwadFsDLAux?ePIxU_B=;V?[FLqtieT=iHCHm_XM?MYNPqwqREXOWurohQvMqnQxolQZXSC<Tv<OU]QiyJ_Aq^YJVDtrIjkxp<AqI]yZLuIgVN[r_daoybfgavkpYeyAZD`oB^amGvC?fP@vYIsGNoTgcsg\\NIpgOkrG^yo_CO^[Oldy]_Awsnx`anQhrTa]tvhUy^I@d;XtKWkFolLYcVwcG^r]H`]p_Hw`<>[ZVv`qeV@vv@ZUIu[aeaoyJfgavmpY]yMJYt<]qy=ZUjrDyUyY:PKhLVyYmRemQYrPLmpEMy=yodKDeYtltBPopQl<IQLtpV]vtlmBuvETx^=xFtMRtwotYE<YUXTkqQIdYeUmc=tfdKiEx]qvf\\W^ar_yp<Xj`]Xs@q\\Dx=`nSEVfyiKX]CwYww@ya^Hu[yE:>swhtgayq>hnfuyGdTpxvIgQQa\\HsP^mkH_qxPkg<kByAHaaumAB]gTQYv]cydUfQ_Y@SueUEWqVMGrqmdy]ha[cd?u_efl?FLKHI[UL;eK`kMLM]PqjlMOTny@X=DwyxX=yi\\U>kyPycvA[qYryGxOwjmWvgnZYacuahcAo@WrLwjFolPYcKoxBpo_ov_^hWAr[ojBQfBN^n`q[?oAIviqZdoe_nmpNxfioT>vAq_;^_tF_qa_NoinnebF\\ewf?xibqbLQiaowqxYTnaejmyKrIrn`mYlxUyIst>kuleDgYu@mhT[bPCgxcrJSyWOD`OvPYVfmeyqdeoe_SrKAsWWD<UwMYBxyxLmgncUZKGIUXXiuSGuoYtUYE`AShkGZKD^araevqGiDsg]mFB]vKcCPaSdmXrsTZyQ>TmCyva@sY]iprOmryLrG`nyoqUwYltI\\y`lqRTyKLqqLL?LqypX;qrExVlUjfErViyw]UfiqresNYTvDX_qp]LVeXYgunMYt\\IthiWg`TEQLSlw_emAqL;LXkENf@Pw<PlASbuKjuRLYt<ArZ=YUHseykrxEytE?XpyI:]v?Mty;biqJ:bO]iWMFsMuU_btaSmOGQYtSYuTEbgMY[CxB_cjcDfOrjIbZKDCwbXCeosyNCWpsuFmWvuHaQvXGwkEewKfL[ICQX;eTwybI=buWBTiI:mxD=YNiHjoxMuivyHyedAyT[mwydrE`nyoQbe_ursdh[iuogxIE\\Ii\\=iMUvVSW<UUeSTS_b:sCpgguqCfWRJKxmWdD=tryU=SeK_RqWUUwsl[T\\UDhyhDuDFkT>mesGDU?BiqeaKCixWsmyPlryOrG^n]iy@yY\\tfAxcxY:DMUHsy_iqxYlodYW@qXA`dUhcuVcx`qWOhxiiw>m@OoPQl<wnFuomcqCgVsGZ_SJss:Er[YFWgtnIIhswTIi_qslkhaCRfCHfITUYVHCYQIXsSV>mWjwCj]Xm[bHUhaeB@yI:Ov@XxxUry=:rn;hpY\\YMkdPiAMrUxFiqTpTdYy:@lTYuW]uV]nsLJUHYU]wlYP^EVEDvCIR;=vk`kTxstDxgavk@YhUQWqmdmUiQkGhVh=tfIQUyLTlR=<xDYJIPvaxKuhRZujQYp<ya@sYTsy=Zc`iyX[y?tG`nyAZYi[yA:cdpIt^OWtgdXuVbYSUme:sdJaEaAGd;eYkWGQuxuSiycLuCnaCyyw<:ZKgvrYexajgKvoyd^pyVpUYtnYnuiaw<::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::Tly_jH?_XHevF\\^P^\\nl`?_VIZYywOWwgo[HQvNNmYfjK>mWQh>`reHlnQ`<vaKNmixoRglKy_RpkPPtpKlXWodu;MXNTPX<PyLkHqTJIlDyqAhWKImUEVn<yKmMKxqreWa=uapjimwLpu=Ivoik^awflUNAtJDr;ErgHQ:\\SJlrCdwWQVd]O^tMyHxYqUstu=TpAMvSTmmMvranHMtywsfamwiiyNaOfwcPbIx[;wksa^Jyy:vuCvYIhTUVygv[IWLObTyT=UIEsgsQs>Ut?OxkWGqIFHss>UXSkyXUTvWye=WtoFbkydqe:yxPEDV]WISFKIhs?cgMR>gUqOVn_ghexUsw@AgpOixAftiBvOy^=HIqiJmF]_DqGx@OEZIB<qcNihxkWEodQKueCeyubiYfm]GxQU;cXIEg]eCpsxrAcFArZcHAcdnqHt]XdYCv_WGLpIuLYXjxuYQyM[YQgAqcqpJPWqxXPMs[mKuXWEuVliw`<ROmn_LVjMXQDv>tYqujRhUkimvLUKTWgpykmwolw^MJEDu^qkTMU\\Pssiq>`srmRBPO=Tj;DQxxtPUWCEqgHlneTlLynDxK@nMYqolq`qtI`obMuganTytA`Xs`xC`OEESoEwF\\J?QxCpYltN<qxALUHXmkHRCyjLHQgLlp@QjyRBpom`TXavyop\\NknAo@i`ZwngFuZQvcQ_OfvG_haGhsGvGyeO?yAWnAGnTWbmWi^n\\LhZPXvBAZbndaniH>[ZF\\AAdBFr=f\\`QtxN^E_nFYprYa@wmPg_uYmAit@trSrtiwuYwIiE:svAivCQRrKbEeEFgivOexeFigc_oBVOFHESO[dAkXFOyckWd?yh[IoiwvMUvsEKMuE;eRawPWWgSUSUvZCrjGcFIWVQrZ[H^osowrGArLkb^Sw^aGh[GxmVRuHrUww]FySCxyeekxeMv]OVu;cmUGEmd:SIQsgtACSgU^?FdMXqSvR;B:;B:=bOiVrAsl=yPyw;yxTiwFkiWQt>AUUCBVKvc?fEgsZKSH_Eh;BAWsKCR>oVgEWtgixwV`UUdkHXqFQkwfqW[GcZeDh[TAurJMcs]C]?FHQymOTfuiZyI:cyAixi[YCyCxuHW?d^GG_AUfefLWGcmWcmWmyI:?x\\GfSchcugoIi`?iyyI:WDomxbgGP_xHQWGoHeKw=sHV[sNscWGcgcuEEV>MiPeruGv>_d^YT=sxPsXJer][fd[IEEyl=vCgtAqS;;IRounEIfeG\\uT@suOOwKgILCx_qRwKrK_F[gBqyqM\\VRlTs\\WjIKbekThl?pPUhvpYUiYLe=xUIyKlR^XWN@nnLLf<W@TnatLoYjVyKgttiDMQDQruyaUSsaXWUsHaTvDRkeXgYy[UWw]JsqXeXL?]kILQ`\\Jk`K=MKH<YuXxYYKX@Nr]Modq\\uvJUkXQMSuOodMy`ttXjfIn=]uSiKbTrPDyO]lZ]KVlmwYO_dW<dTrPqpiQX@YuMspYWyaobqY;;:sba=eVYS<sEGafJ]i;]wdMhdesnOEMYb^gvlCRL?FL_u\\_Y`KDHMEHSC:;iRUgTys=AshkyZAGXqWu_uBMigic?GDpIX_eVCEeRiuSEyBWUFSvV]tY;uiuy;eyqsY<YdyisKgy<yQbyqhxi:alyurceV[Wh]WdkuEQDoUxdOiPeUeqhpOdCiWT?G==u^YVaMrAMCr_UFsvVmtY_bIurJAyMAbtwx?gfuqD?chbkdp?IHAhf?UK]ev_V:qIbeEtOuISy?yQJuyWyY:@rNxi@AwxIryOyIVwy@yLvmvqgW@mV_rrijjqcIqrE>i`gth_gY@dLY\\E_qknr^fZLFb\\^`[wkBYbHHhqIjZVvghdNqyAvby?odyhLXwlxr`FnfHwTHpE^gjNlSon:YjgNlhpZm_tXnrtxefy<;::bjifyGV=qeAyVTStYKI?mgJIi^KuiKRWiToYGImCdKyfsHToyaoHbcxSoGZCdw]uLAcLGfoET^]FZaVTKSfGh;=RHYypIGjQXJ=IxcGlYYeUequcTaXOaYUcCdUwZqfVOdKMhAIRHEifYTVpON<WLIj;LVG\\YwqoMyiKFcwQjyEwviji^y:;uVgyQCrbaGi?fwUbTYEgoHx?wtChGSio;HdisBSEf_cuEiWcIYCiA[eXitK]yB=ImwtF[iGUWrMeUCIfUdKeB\\YH?=EmkU^yTBWtFiYViXiasxEry\\xYtty=Jjeny@YWyMRyOyIRwyXyMjMyY:hkLeV[UxutRYEkAHKhdOiINOaVMqo\\Qth`Pcdmg`Rehnw\\Ru]uZIL@\\J<tkwXXQUN_lY<HWIYVpYMwLssiwa@XFmmXlQI=O=\\Oj=l\\EMHpSA]k;lRBpqRqoYTy?xiJUQ>RBWyERy?N[IoyqvcM`sHNheAvAXuff^uqgw`_thm@Iqa_oWqeEfbOomEGfoX\\Eiu>PdZp[CvranqAVckYc:i_\\ywAPuqyjM?fQ@dm@i\\a_HgtJ@\\KyvwVjdnyNwufy<<DFjCwy:JGhjkYjiXwAqyXYlahYkura<mRLyYLReYKuuuL`ueAxU<MvduO`pQlTM\\rADUW=nREuNav^IxJ\\UJ@rAeoKQTxEjbMm`ypaLwPuo>pJWeOPExoyN?YPDiW]Il@UW]PJK]M?hoqDOOUNciLMuyZIsVdMymuxtYcySxQnI\\wQxY:@nxYqyOZMxy:fkKIs`yZmv`fiy[IwoF_i^ZmIog?hdOSycDeyTsuswcQyI:yv:SfwEXQghYQbpOiHwwiwehcFfyuTuXpOELwGJaUTqeT;b\\eDCsylcG:[DrwBVGtTIuxEryvA>vLwikQqy:R;I[UVnM`shNfcwu?>nmxm=yxYPumhaXilgheew`H>^Jw_aFqLOpLX`la[V@jm>jkvwQ_ia>xAxcKqyOv^=YseImoVa;vgo^pM``\\o`K`^pOfjW`opjmqkr@^Owwfy<<DyAJyAFBxcrasiUWvM[SHMhYkrTYbrMsPwTS]YAefugfx_SQGTdQUEUvfMwvisKafsaWaygH[fXsVOQrQmXxArdwDX_vTmVUSIESCuEwxoRdiwTMsGqhl;dRCCBsEeWrG;bXIe]QxxGbMohyqwyZ>IdwYjafyAfXsY<tYKtraFq?XgjQeU>gnWcBhpAoyNYtoFqoynr@g;VccxnFv^P_cvQkZAvgosFa[hwrsvhyWp@ylvvlqv^JokUGqoVaeAu_PqMQfWX^HHwOpu]V\\_Ic?niQOwlncuvd]gy<xYJralY\\yhyKfy<Z<VL:]cryHZgi`_yT[ukQgiuf;UGboHtGIHUE?Ughqhl_wB;GlsrrMEQ;R:kCwQgAACxmTXMeckevIyKufeWGI]tcKbQehbARSKHZ;HCitmuhpmhDoU>[vXgtyTy?xiJ=LtyWVnqy_vynoyM_B?_UXEVmys<kiJUsAAhXGu^kb:qsDKTech==VN?RZQikQsLqY;yuhoyOeSyAvCyE>QEkiiCMi=yUvOxI[Oy[>vnyu@IwSshEcuikxDuym_x]SY?wysMIQihwQ:p?:vQI:OrMwyGItDWy?osQSY?rKgi<yqsLYQipwQjyKQyI_<yCf:E:HtDYy?psQTY?xIHd?visPyQg@?vyZjI?BpxIJ;:OxxEfmivxErYFdwQjy`uwY_Tpy;yI:tpAmxE>ZZ<=>GplqQ[Yx_pY;yEKcy=xQWiYeVmyERy?rMwap]Jmy;NhxHvmgnxIrYKDyQjxtuyM_TxY=ui:jGVy?vY:O\\tHaY?htvefmpyLuEKwuqDmvy=Jjxux[Cbyi;:^L;ZSgjHYmuI[wwaDwajxlMaxhxfuiZy=:xMRy?B;JKmVQLqi]w_`XwA_>pqYhnmwaR=J;Hoy=:uiZyI:JrQ<TkjnnxQrYwcLykfi^niyeFmxIryko?yLJqZ:>NRZM;Hu?psUTYCdiNxi[w_aHwVwspY;<G:vIy?JyYm\\\\Sh`xY=uEsb`jxbsyEf:jGHD:NC^_<yvGgy>pQxKfi>itFuiZ:P<x;yAb:Z`w\\tvgfi>\\LyEviRhyFuiZZ<=>nYy=\\IVkjFqMyi[w?\\NtPLtqyOdC:jAK:::aguiBGsYO;Wf[ikOWfACGGfl;edIBEseg;HyQiksUKqEbQUtKeUeUyYEMgFqocfkDqkrZWIRGDvubVOh;sH^wUgOyYkxEJvpQQHCDwIxjIeYAhXvxY:xT>]yy?so_nWvpKnvto]uHf_HgPqxEnoVwufFaKga^Ym`@hR?pVQhm_kga]X@ZgHpbp_=p[;XoYWbv>dVOeDavldywdaUtcsc;OsjUgWyCvYfXQi`yXbyI:KD]Iyy;RB_Xa=b]aseQu[wrg]BayrUuXvgdskfAaDcOENMeXuU_EvgUfC_IU=i]KrwKEn]spoR[mRyiyC=vPwe;ov<uyUUdnScuCIo]sXuCs_G@ev=YxsKHkOg^KwGODJGxXGuhyFxId]yCsmSeyQjEny@iK?njnrofwowcoPsyGXWdLWXjgEe]xvYi[sIKwv?uwSwfoeSoUWR_YEwinWrtMSFGVW?THaV@tSDXpHhoSlOvDwGpU:`XglrRqwvIovTyuDoWaQeuRaLPOpwdaYhMTjISHW_YyajH[HihWagLHay>gFomy_u^p]XFaBytoGpnIq;wYcwtUhxyVKAStysgKsQoFOWEwQIpAIIQrcStyDjTqW]hpvHLCXvxlmgXw<<S]=jjdXAtj@PkLIXntLthxkxPIptNmo[XQMeXk\\OqQLeHOSQwFeQNtXntTw=Mler>=XkiLWPyhXNdiUrywxqqq]myGbLyYcI_itHMUr<kf]YctxohqpapqTTeQtDMmrMl?DK[dyYes\\]nZXLRTKx`KAHNR@Vailm@xviuwqOoEvPPoYHUtqV]qPluxw=mkijpeSp=JYyY:tSwyQ`pqfIuvEXKqNpDpBMxitJXhmkqvUxObUNOew`quLqsHmT]LJZppkTerFt[Ilvhuu`r[HsO?ky`cCokX@stVZyAZdix@qiYpeO`e_xvvaXuuIexlwI?qwUmWygyaYxxarYEfECuHwrUAyuKrtoWoyx]IefugoUgNiYJGfogx@isg]bt_ReuglkvpoUFOituvNYyaKGkqvjwuIkWoesIggiawVwgyiCT[ib]XbudJMRRKSm]C=AU[ms<sBSUUUExmUCukeiIywoxWucYMThuIDqXYsVxoxWuYviCx]DWgrSsFYUb@UgkmfcOYEWriWraeEboXiAhTiyMmshwWUUwsAdiITRmbJuhGWrKQhawfa[s;sr=GgD[wL[HFGsn;fkkSLyeAcHhwwyNuqgYBm?VkofDgwEywswwayQxpNyMKkhYyiqnyY:XY\\ywjynFQj?MmdlpixqaqqYtYviSx]l\\YYxYycyY:xx>yU[uRlTKP@wd@uxxY:pMtyY:hYkyPrItExwsywaxY:tUMxY:djV<SfHu\\To\\YYx;B]ytY:nv;OfGi\\Uw\\YYX:F`wwY:R`Er\\::PF:nK::ZQ::`=::^K:bs::Zk::FM::fR:b]:::i::FA::B]:Jm;::];:R`::Rk:JA;::X;:RH::J@;Z`=::@=:jF;:j\\;ZH<::v<:jV::ZF<:GA::F@:ZS<:Z?=:W>::r?:Zs:::S>:TH::RF::m>::E@:tB::jE::m;::lB:nV::jR::`C::PF:nK::ZQ::`=::^K:bsRCiTkiIy:>lE@xCVxnxwuQvY?x_`s<xrgFxifnihy=hxigy]^`NwaJ^syAZsXeIX^\\VrOGu_q\\;y]\\GaBqgtGtUgbVabyx[AvwixbiStyexMTQIVI_GXUIQIvjyXwiHhyI:yV=Ysy;RLQebggZmBSmg`ET_sXQ_wbmev;Rb_dF[Sb;ftYdT?xPeF?_Ti]iO=VSYW]Ort_T>OE;GTkSb>SYJ=cBUcnEfv[Xh_D:GU@ks:afOGvgGwAWrY?XLgIpWX^gyFuewSgGApa<m^IWupWHIxFXvYQKaqWvumpxn]eMU?oXiuGn^_a`gqlJ_s<X_Ch_TxbWA_b^eg?l@qbPAdkos@gbsgwAQrII\\W?ir>gqOe`WlwFyk`bgocEglfF\\nFt:>p_yhsQf[ab:xy:VoIisFPkKpmIqaexn;_hpYpYibFFtSi`mIkH>tPPwUacfxc;VbjGc]nkkgdZIxPfkynxJwjJGcUvdaWeO^bpW`NV]^@DmiLSfuyxgWEF[EqiTH?ymKBQQehyt[USRGV=_s<KeQOhx]h<cf\\WpdXl@]JZmPPtQbhJAMLk<MdXoOHxaURWtxJYqNuL>UW[AW<ixkHkaQxvEPkil=Qs^LxrAQN<p^`MCxUZdRNHJfuUpLyMlRxmuy=JByQNixdLy_ixpxN`PUdmTQDKmuVqMLGajC]mBqk[`L:<XsMTI@QimucEOrQJteo_yql`XGqQeQR>aST`xquOThQEArBuxhauq@mIHpFAns]OxAvUmjdyl?lqUPWjLUcMq`Yq`HwmMO?]jqQuDdU`UT`]oPLUW]P]QlR`sUtmZ`jsIJ@=w=<U;xnNqXvQYyMO@dYGIyPXLZuqJdmTQTiiuPavxPK\\=VoeXl<JaTS`qrn<RViyp=KBQr]UsfLSlTk=DWMDrNhsSHlVqKxaxCxi:GftAt>>ux^xZWyOygkPeywsCvajq_yoysvbRioyvv>xmry\\yvYsBbQBHwCw::JfK<;:::ZR]><::::k@C>::::\\GLB::::>U^J::::BpB[::::JfK<;:::ZR]><:VhdQgq@ug<:GWYwF<YGUSTNKx`WiGigxCdeKbvCIH=C`WFbwEO=rU]IGweC?gacdZgXLCYq_GGSspIDHArCAroYfTEiYCstoewafcMuikhoiD^uhqOY^mtv;u_WTNAW`WHlSfdQbSectAx:IcacV:ihyGs]GHioyIwbToSYSgooh]=VduXqkXcYwpIc^kCe;vXMg@kC>EXigYf[Eb;FkErHMhyorc=yaOfFutPkiWYhN[xeCCoYEWqy@QvscgK_FHoTs_E]?rb?rcYiGmdWYSQqXLOCrouUAyK?yTcvnsISWcYwrCSfs]xUSUuGigWfrQRPEE]SHt=IYsWuCS=SxjuRLsD>MBReGLkExuHYgsoswPIGT_x`Ug@qS^eS[SX]yru=UJAcEgYKEcJ[SHoX<CI:YTC=FqweCYNVqm[DX?\\XIQkVMwTqPSdxghs?XwcuTcYk@Yq`qk>iUuHNCAT^PJZ`vZ=LtateYvuDMoIp\\XR[YuYiWPYQMysTlwbtqkivsMj@YLOptUmTv\\mV`kX\\p;PUxqnI`rQylU]yEatgdxe=soeKPTyRutMIqm`PplmYEm`@Ugaq^hL=DlUHYQLoCTbsvsVIynpox^^ghp@ingGh[Yo^ymBwpTXwPG\\WqbcIgVf^v_sqn]c?[DQsNf[>ilZakL@vqwuCXnki`Bai:GxWym=hksPqMqohQvbO]dyh=x^CIjHG]pQomH`Sv^ANgkikSIw>_yEgpHH^vNu@fnD^eIGhg?fX?cBaqTX]Opp_?]yVq<owRHlt`fvyqi^s;nuxq^IpRquMorqqDxqEkobiYgbuTxofSkgh?EPAtfYxjqBPcxSguoUuv_F<;cFEFtMdcsHYEtLAUYcbqwBiicHStVYDe?hEAwIAe[uRcuv@kRagGhqsOmRteiEIRWki`yc@ay`YT\\WewiHsKuGiya;EaATGYX`cRDowPMWU;IJ_SXWc\\CgwCRhsS?UWMYRkoG]yx=ssESwqMeBUuSud\\ehBawguvRIdaKePyTwIVBcbdqCZae]irecS:mhYccYGChyG=kikqIkwbFewnUEwywfMyimxVuDQMDCOhnHxViPm\\r:`WlXnGXvi=xjQNjhOxPoVIWXYM=PTkqM;LPDyVxXwILPDeNRiwglw^UKxElRUp:\\jZ]WP=OBIVu<j=`TyUlAMveMjiEkPEsQdmxXJcXUAExwhsoTjvHp\\mWrqwP@ublrv]phHwmuP=xnIxlTxLYilgaWoDmnYWIPKeuugqprlleTqbaTG]NeyMPHmQLsPmuCUlDtqh<Vl@KV=JhxJ^ly`xk>uT@lY_PU\\Dka=To=oLmvuUKWiQT@SkEYvtp<IUNXVwMUSlMvTQpun]hv`qwcTvaIt\\YUg<yxQx<iwginLLU=TxVPJhiXK<L;YLi`jklLZhm<@oYYjJMm:XgnnioV[EAalWoapur^]P>dRx^ypdA^xNnmowswYZivYYI`yI:kihxsrItr]deymtqZYwy:vukvy:FxnGiQyana[yxYwwRNvbQZyorIprZXxhxibI]ywy:^iAyy:frKyvVwY[hFyI:wYxYvy;r\\;W<yI:orIorZWXhyQJQpygymy]yAZQvbWXhyEJQxy;rxGyIwiE;vCsITsiTYbHIiy=v_yI:iImyEyudAeumZi=::rq::tEDH::lAPF::Q>d;ZZ<jE:;<:::XI:jq;::vU::w??AtRHUXJIMh<r^HwQ\\uy=JmxMy_nCptBW^OP`P?cOYtQIgJWrx>y]nt:HaYFkvV[[WuuyaPwy:NtmfbYN\\ygvUqy;QyqpyKPmeNnX`rkxuIviQqeyAZQqjQxy:^noXtRYvEIqyuemxYcI<QG`kYYwihiiysGGyWyEceihjKi^uDqQgb_WyOgUKrm[YKktM_ebATkeRoue^qhyuUryI:wW;yBSgwy;rakuYYYZ]DVmcQKcrowe_wPyumswIiIjAGugvqayuYRy[IDkGAYG?]UQiTpUsiIiqyrx;YNgyLYUxiy[wIxcBQWJ?]MQiTpUsi;hyLXUxiy[yY:lQ?tl=hl\\mkePOuinq:pQCiGZQVZOPvHX_dXy_vP:wSlUuy;bI[yy;rq?r\\=fl]yKeRou=:y::EDjEIXAg\\OiiMXU:vklXEY@DTjEQXAo\\QqiLPU;vbSi?:[UH::HD:\\E::TI:sd=:g>jw;<:W;::u=:i:QWmYvgMuy;RwayyLULut_mXE;hl;LvrYNE@tL]jb=kFtV[lrmXYcHO`ljxhPy=nEyutqxMtY:aPYmLbMu`mq?pPa`lH=LXYkRLmEDmgaVHhTVilOTV_=V:mVWxY:PkWdoy=JBqlqqyw`ny=JJeKceuy=jAatyxwqXX`tJwxj>\\xRhOhhoGamLhNEYunlruIO`DyG`QX\\v_hmVIpTayFlmkYJJdJ;YvZukF@UAevWpPYLO=UVNDX?Ilx<qrEU]`n>MPc\\YFYnbmMZQVRTmp=v]YnZDTZUpy<pnYl[AQvLqf\\tcAl:qlKMrWuqpILZyroXPrPPgmrIhm:=oZ\\vDtoeEVWQJUQRN]XBaPOeSy\\tlhPnesf\\KhMmR]rlUPkPv?EM:iJq`VLTUs`nOeO=aULapqUqUYsrMNe=QPXi@paTWag_cZy]SXm?xcvxu<i[S_tiionVuCvgiqvPnxkDSeVjoHZsFS;IVmCscI:_BV=BBAjf<yUPrThsVupTpLGhm=ysrlq_EL@MU]XLj@T:ujbAU]@P;evELlpmoadTvhNZPwQPlXeuSMSilnKpjrpptPMT=TKLSbxtGhTNdW\\=K>pJ]ANZUVmyjMQx`QlTMuedsXQTTAXgELCAudPsC=sElkNuKT=mVxUvANXTLiXNGlKOLPPdn]MLO]r`mkrDS?iKpLPP@M:<O@LKeLJRLj^xJ;muUpkPQXVIWGPNYEUEUvpUXVUsftljLSmQnuXPPlVwtpMTQ:hKR=jHLQetQGHseXs^`oLhQnApfTX>qO`lNnLv<mlu<pmXZV@lC>wdf[S_qS^nYir]GoYira_ak`aDYpYAcYP^<FeCh_:@Z>^vKxxUg]Hn^ZYhxi^jqn;PvB_stotRxld?feohLOxZNl]ntqNu=QiaqvDFu;>joWRMu^kuIAxfotpoxLEWDGVqWgPervsB@ofr=DCSGeqRBSFZ[CR_Ec?rhKd;ow=SrL;yy;b>=DEoHMigFmIMgBLCyXkFSSD]?fNUDe=RAMB@kCHWhDGVaWGYysiqg`whpgYrswdYXfcSegIgCvmGIGqE;Sf:]sv[rcSbKSi=Cg:Wi;ery;BZcy<Yf<wDXWu<Ccg[gisg\\_it_SeicaMIE_cIyI:]c]YyFMh<CHauFmIHEMtFMDrYE=MDA]eImvBOsfYyRmeImyj[VPISYqq[@rDMSV=lk\\KkYUjPWYtKhantPKUAuq@qLTTJeUp@y[qQPlrEqN@Mnd\\oHmWHIXJUoMhkgdKWQvEURtpRUpq]@ovplp=tFXqo`TAaM:<j;LPC]^FNlB?ZL>b_@hs>avF^[AsgnoZyjBgk\\fqTX_S@tv>msO^RxsS^v^Qf@of]y]u?]:irw^ieFnAIvuxcIf^^Xsa@e>p\\DxpmG[goxaIgHhexQgO`ZbH^la\\gqsrfoUgeI?rQOi^Qeono^x^thl=nb]GqWPnlwdrGdbnaSOh^p`GYupXxFXhTw\\J>yLwuUgpKqfrX_bhu?a^JYewooMW^Aq]q>pUNqG>ra_t\\im:IrLapGv^Eomc^pui\\<@egpiBqoEN\\]O`swnuFkVqr<_ekXsLFc^NlGgfX_ix>x?hvNptqOebNlEVjyfmM^uGop;WaQHlBwuDI]R>q=Oxe`ydi\\spoWxovO[ThcHXo`^nKHeYGaHH[^`qS`\\jxbpodEai?`bLogGfku@]VF\\DhtkPtnW_UA]i?fD`v=aaEO_QNmnWaROZl^o;oeINb;f]bAqVn`q@vgp^uibWoaLquUFc[Vy;gpSXvs_q@pmK_^hx\\Faem@aVq[ZAsUIeDgwOVb;?yk?ncQysojga^w@qPHihn_`okCggPYh`fUKi^ybFgcvcH_cFlmr\\aGSmW?_Xm?yIGVnEtUicw?XleBkWf\\]IQsDLKG?;fmEYL]bk_s=kvxaD;gCu[rTCGi_HYysSMUGuxpeSicW>cwfUTESi\\]fbSf_GUE;F:DSvDjD=vkUTrYr=YPTEReqpLdkOHQs<WQayULneEk>PLOhWS]KVmJFDQLEjL]nDdKvi^C`pNhplVr@fmxOu;pdpOmEWk=X]@wo^Nlknh:qhA^^MhjUnj;ie`VmiVjov\\MqlHAxDihuf^yPpyAZC?mE>kB^ZtN\\@?i__^o?Z<@b@fpAxjnYjLI]IiywXcyAZ?Ydr@]:xfWxnAnmcGhxyscYeYd]MyIaikyEyOr_yI:OvbwY>uxCwIXYxy@RcxY:@YdlO@lmAtXyMskpyIEwUymjqKcyqmmry=JvQkQxiOFcyE<Wy^yQXXly=JZaty\\YOuL=Tl=<tKIJbEOoUQr\\woil@<UBUNuiW>apHuyppYyDPyLs;QTRljA@N]XJJQTK=rCHJbAo:]xN\\PJMJZMYD<PwdjS`xa=uoANaAQA]P:<VtqYN<vkurXeLY]T`esphvNALEYKJHR;]mXPvf@YTtuB<YhAm_ht_IqIls\\IL^tWmaPL<vmAk]aU>qK^]kF`kKDlD=V`xqSeybxRuyQ_TWTAWtij_]PQqp_xN<\\VSQNLXQCEMW@SB=V=AV<<kZPkUlyKdualyrysy=J;Pty=Jk]TV]KvxY:XPtItIlXyQsV;rSyI:ZyFvW::Pk\\<v[=VyyxnUnY`wxilstyBpGj:[Nwj=QqHwaNycyA:ZVsCGhkkR@oXMITSyI:;stYcxcy[yI:ETEGRC?vXqIXiI@?Ih<Na]o:AUaDM\\uSMirQ`y=`oyXWLyMwaln@R_mq^xiQxguyZdyutqbbWn\\ycvYqy?uyndyenaKtHOfUsW@xqeyoyWw=ycyMtUsWyr>xq]qxaqyxpny=JJQNhxm[ywtYwYQyjUty`xPXQIDky=jAiwIeYwisy?bD@pXXvHxrMgbNnd]O[cfnjHh=@cipm:@t=>w^XdKPmT?ZbNnD@Zb::::::hLHAymlY<MqIeYqyQtMoDAweaMkGyBFwyfxVyy:>wcH_ZH`ovosQZXyy:vTyfx=ReqrekixiVygiyeUaUwYKh?iiyuGcyI:[X=KUQyukcXqkuVqhqKg;_T>ovFYxt;DIoUYKu:UHiATrQv\\yrAsDx_XEos>SUGUcF_isQDWyXVCCVqDqExFcr:aE^_HkkXlCSDASC;dHgbhEemIfeOeQ;sh_hnUdIED`qdPoHlaxlOem;xGifA[cPEI\\Gu<iWRGHLERmiEB_i=]uqcsZgFAsfwISHsYHyqoyY:dM:<x]ErtiqQYRiUKbMPeMXcyLthS><LWipupS\\ESL\\J<UJ=]QsHjN`MLXXN=JGuXxpLqTyudu`lsCQu[AvnLl`hLqlV<el@XvsFs;aamx]LOiMQyY^iHF[^qiywsPYnUWiehmToseVcQQpQ`gahsRglHAZV_kjvy:>a[HjHiebQaohsye\\cGLUUmUWywigogcyVdgcJmhk[XK[RhUFZAhLUv@YFDAiW[y@KSmqdxIdZSw?=d]mEYqsc=TeEd@mYPqg`CTP?wWCUV=sH?xhasHyFiwyRmu`MFUQiIafehKxPOutnrPVLYlD<lbQYpAQkiVXyqeMd[Ad:ivvH_[ywQf[aODCoiANAuYsakmHUVyppaLlLn@pUxDY_Ao^xpDUnlmR;PKZ\\MQeoylJvxr_<ya\\RXpmpTth`ofeXGHMneSq\\SWMTwmrqLQn]xCIT_\\og=vEHuD<J@@SV=jx\\Nnewy=jxqjEyOvYjA\\YcxQkhpGyUliPWUVwpQCyLr=TAhod<yduu:IxXYji<ucUTEpvTdWoEM]MpHmruej>mKPMtCErZTOjtmb<uILslhOjyU<`n@Hy_utnUKCioIUlw\\k<iX^eUwTvfuR`aljIt@AUJxmutQR<JAmltxQfeuuypDpwy<XHxojUWD]PW=yy=jFEuoYTxay\\uYDlt=xkr@xhmQvEu_aNS=ytquAURTERc]puaJxDUPXMMXL;Xp<=ulIpiAUKXO?LKI=RJpo[@xpPOx@pjqVqdxhtMqiq_hP^QyW\\vPQvWuNaAUPymWiVl<JFpqkyr]QkWqyAyty=JbawtxY:<RByi?``bQqsIsyAZ>PpeAa]iyHv_jqnANldomIFx@fpyWi\\YiWoa@WtUqdgOeLyZsq_a^kGIfrHigNjRvrcW^bPfCn_[ppLHhSyi<i`o_or?qeGw\\Wn=gq^QbqPhUQsW>vAYu<HvDWcnHyu>iow]pVbQOdngcnwy:^sOIhyAZ:HhLgkUne=v]jqlWwmgtI=iL;hVwrH[im=WUSexIS[ssAQeGMvdITsQYNqhtMbTwT?SFK[gB_S_[Dt?rhKW=]GJIrHmDGcsi;RQqDxiHkobsEweudTgg@;GZIxcuDcYkp`KP`SI\\owqrUYpV\\k_uPVHLJuy]Ywy=JnmPWyY:<V^xQ[ASTqPxDrY@XPduyCHyejQV:EXtogCMwTGGY]CvQhpaOnAOgyNNaVFTL>DwG`MJxQi=P=Tl]<JNLX:uN:PKo]nR`v;TLRymRQQpyiBIuogwxIkQ>yMwqkhxyexqbEyGv_rA[ib;xU]HPyBpoyypiQl>xJvAoxyrQyIJ:=CEf?AbYWvDArxqrQyqJEuoyY:<jjyY:djalxxxQyUr_yTxMj=mYN\\N>lM[HqQYVAUW<YXyewd@OcITXMuXMUeENieXsxoRUU_IU\\aTTypnEYdIrVHjH\\qy=jYpSnTu:\\PLyvFTyaaYyOctVvV^vpAn?^nnnhIivwyaipaNyfwFZyfj:fdOQfMFwq?ho^ktOjCYZ[`pOPj^HyL_apx^:X][`^VnfsxqF>ymWdm@xxio`Pgq>_iwgN>oOQ\\sgfsWZ@gd;^uEA^lIblyt`Y]:h[J`w`QqhYhIHxymShwKxmmeYbXjM@xYuJi\\quHVwQtXuxWAqOMUnqOixoY`L<Il;pVIIPaIqZyoJutYEXLtsPpNS\\LxXLMQT`YYCLKVyspAqZqLX]olETiQt_tS:lWRtmrqJ:UTEetZHWQTvv<kVxM?msIXtY]YeYVuuNVmt=lyLXqfHLJIu?yM_Qt:AtjiQ>LmaujneqxPU;aXbewfIN<TQ;yORhOO=lbtky=JkeW=HmiakPemmYO_XwgxkrQohmRwaw[uYDxY:lxxxAB;N_foZwi\\;t]Bn:rAkhxyI::\\iZw`bAa?AfyWfewYciGutY;qY@x^pyAytkuY]hvQWZA`ybB=Qxekyy;RoosV_ukyI:sbLWvlwYJgxQeYtYbyOfPSUNYH=iVvsDqeGoQGV=XsCe<sDuwtj=fpuVSyI:;stYcxca:fBKu;MSvIcyutiSyAQwYMY@?w]xMsqxy=JjpygxY:\\n`QkbyNk\\oqYrYixQyqoIV`xY:DWgtXXPly=jIXuYPytYMyg\\jwy:v[ywTyI:ih[mvyLdVAiEoyyngyWwdygwQZdNruokuf]G_\\KGeFhrkij?hnxIl\\NwtflXim]o\\`GqPpujQuYh_;_^nNo=O^qg^SwcEytSvZEaaiffogor_sbQa@Hn\\i`jAxlxmJOt[cOWiqAYl_sjoBG_FEQvFCUxSxdAc>ero;SYeXwYe?kuUKTvWD_cUiOU@GIg_CcEWBog_?RPkbFuVn_sgSR:GXV[v==UP_CYqCvQXkorggyoqV@UugAcQww?qsPCRbsVMGI?Kx;=eR;gv;BCoF:=Hvif\\sYTaErYt<yTJ=yaUYtYGGQsDQw`AXdADUCe`KTOyFsQsksSv=vmAb\\QII]briRvIs[?UoyrMqU<StwgbvqHiQwCiFCaSlQR]QyjURn]G;geBqFeMiH_WTgiOwb>cHWui<QSK]bdwC`WsB]R;OBdKFCUDZ;bH]e]]CPyH;_TW[iAqXhghr=YWUUOEU`AevCX]uybaUh?FsUI;aI]sFWMHbWBt]DJ?GZOBD?GZO:::::ZaaaSwy:F^Wv^xYqYhyOf^nghHAIwiJosMuyWycxOcLKE=UtTwqUyutqxMtY:iPC]YueY\\eK<XKGmjeDMoTKGMsU=kG\\Q`lTAUuehsG\\p=xmV@N;]j^AOAUNwpxfdk`TLq]mdqSguWZ@Td@UL`TF<VmUTIuYE\\uBAWq<Ufls?anVakyOhbx[kftoD?Me`ch`gTdYwt]Dt]G`Gy`mDgaHOWHCkU<]BBKDcwbQeyB=RAivbySH[ctoy_CX;[XwUeJucLgYpiVPOvnSe`ie_ghWyfSUfq[U>ESYGhSMbvSWZieFsIpWci?wgKYemWK?QhhrfxUves<Lyk\\kg<vE<jADua=VIxsQxk<=LXXt_LWYElhdXUTscepuAsZmMEUq`mMwTn=XSPXM`Xy?TXN@LuIvAlVZAPlmW^YM>TV\\tsN\\yIQqqPQvDwaQpupY?YYR\\w\\PT_qWt@YJLsN\\RO]uVMLxDWEHxn\\rmQmpyspxrVhLuHq^yi>WmYxeZinuahvGhswryFxcy`YWy\\AjvNotyaJNuvIdMYtSwtvAbTii?hnEi_fq\\dv\\FqmMYh:P\\QrDGC>urpgU[ES\\IIpcw]my=mxYiXDmWw=iD[fiUfYOYqYgnWxUwiBkfh=vgug[WipMS@AwOudfohm=BqIbJ[ra=IbOramRWYB=WCaggxYx[CyoIg];E^oXm=uV]eT_fH_VCeVNmbLKw;GipSX<?HregWwD=CvpkyJGtgUeKQyN]CP;d[_YtmbCmGkOEIIhOmyZigq;cvMRHSwN?yT?yYAYnosy;rmQrewyGQty;R<wSbyI:wS^yErusoyqGLt=xo\\DqY<yCexIHynYKyIjhyqreuY@xMLwYXXcyLxYJWyY:HhRo[tPk^yi[y>:ZyOrI?oyws^xery[owy:nrbApWfhO>syAZ<ycb<:xi>xmJwy:vmBwqjq]eyy:fkKAftNweFlyAZ><:jy=j>Zx:>:?GjeEoitByI:M::jKuYCpq[tyxDly=JZiqQui??jeAohxbxQ\\w;:XNxMLwYRxey\\xY:<ruyOxup?AjeAOhxRxMLw;:YFxMTwYRxcy\\yq:txY]yhUk;tTKauI\\y^:<:rA[y^rsibyA:ll<xo>Yoc\\ogdxETwruw^QMYASX@uLUSY<W`aUJPNV=mi=SULxBlSrdqeDSx<Lcmyl@TxUmrUoMAqkPqU\\RQMjaQpHlwReVMTSLXS:erRQRe\\un`sZhy^ELj<xelta`t^YQytLQEPndV\\IpddRg=XluxhuSbTqKqxBYq_Htouy=YmKtYvUt=TsIqx`yPe@wjyRg@YE@TJINkiLStLqpPE`LQLogpVPhTSLu>\\skUSV<M`dPSHVmqLTQtq`kg]Y=ywkQMqYuKUTMYy>LT_UURltGpXqtl<IRF@w^mOxtVUxsHYN:LPItUVypKaM^mULPyYPpGyY:\\rKqxb=x@YUjtKVMuGixxeV:DyqIJoumULwtpUMtwmuOX]Ucuwo`sL\\u`PMbavlQvC\\JGaNJirFtqSPxQmJ_ijI`sVhxhXN]eyEeRt@KQqoo@QfiWoUseyPSAV:URuXkBLuQhY@QJ[\\vMapttKmLN@=m[mw@MYlHSUyXIyUnIsy@YDhJl]KJtO;dMkTWq\\m]YYNHJ\\=temqxhPj]VyMVgMUGlVW\\oB`pRaPOTuriWQXsXupDLNfHy<]V?<kUXuDeriAYiXtkqjJxXPiOgPWLXUUuSgAnwTjIQumEM\\pVL@MWINODt=yODMKxlkO]VWXuMqQWmmknuVykQ`wMXvlYu:oq:Oh?nvtwiAaoYay??Z_OuE__XY]uHghq__IqlYuIYcExg^frcFkEob]^]:F[HYZxF[Zg]kXrxGacqtTil`hkwynoWpIOj_ivrwnJY]OopLheU@dEO\\JFuUvmigZloc@ObPij_armGuGQZg@tlnbBY`co`sfxsY`yAZdYoyAZjYlYOJaw\\IGy[YhyrxYd\\YDNgCIqrsiS[ci_ogn?WnWiI=x;qvcGTJQdG_yo[C]]E[ysEsBRgTm]ul?yLeHBQFHkI@yBhowryI:=snyI:=yCcxIDGI:>eH:::vI\\tyJvy:;bk<eowZ[poAoYnY:wQ^lqa\\tktYXDxy=:bL;XKa][f[MoyxXmyAZ?gnAgfyAZZVwij=SKUsOiRbwftMenuuvKXS?sHMDv_cd]c^uFXQgGKVtIgpCc\\edo_H>;hZOR^_bZKBIeY?Kd=YdrYDyxQfy]yA:akIDkyPhxIrtypxILQccwFk]_ywTyqeGMLdV]yngyWwdygwQZdFvxq]yeeuwy;reUrFyq^hPV=yEmYylwy=jeMwieY<PO<YYHTQWdSNDtS]Kb\\PK=rVxM>qjjyoSewAQkoxWf=yF]n:yY:XulHWxTv]ILtDQ]yOAMVHQQPyX:yulxY:PrrXKfup<pvMUYIaTlmNQlJyMpydwUhmglvLhRl=PqMlCmSlYxTpUkqvuTNbIxUISg`O@EQ^EoPTSSlWx]wa]nbUurmWkAUYTjaQje=r<pvRUl>PupTO^`r@ItLtnKEq]dVZQkkAU:tRj=o=Pq\\LKb@j\\LKb::::<JwHo>XyMYm[@oYHJYLSFmriUKoDSntwEPwtLqwamwhlVtt=dWHLtfLNm`YfEjd\\Ql=R^`KVPM`mqGPWXXoO]peYMyMlSMwpIXVQQIQwtLL?iM<ujV]PuQNZmRBdJChnjdvUalCiRQiUxLnrQNYir;LUiYkUAkhmo:tYQiYp`scxWxPPDQj@DYVuJfQPgipcmpMErjmJUYyBlv:as?TnZYSs@Ue`kHHV;\\JpAnHhPytP_tp@poXywqDlluJdxSedO[tnvttwPvIEyBDwyhxVyY:@WcXO[\\UQiq\\;:gDL_FZKYIowX_duYuuigsMu;OdZqd[MDykVuWwCyuEShBCC;KSq;fMKtugT;UVmuiwsYmqr`qYumi`?YWurSChWwVEKuUISg_HgahFECaieHqULebr[VhUBWYvxmfVSh:ebk?DDAuiAr@UDxSw>=hWohyIgbsXM_Rp;ghkgZCTKqUn;eEwX?KVaOXcas[MH:sfNArniyGiypaIGWuUYaewsowkCpxtacY`fv@xhIoX>oVg\\kph?^kGG\\JXanNg[Ye:fvj>hrw^w`gcomkN]AHkg^pR`xgncRnwgPd\\Iah`d:?y^w[YH^@Pv]H^RWjNXf@HdNAjoWeUXYmqhtx=xwqtvVilQaK>QuVMUvMmohR>ESvaxBqwxTTVTw_@x=lsJdW]DnDxkoyN_yJoHtlxTvYUd\\ygDTviraHwKeKQQT@XmcPN@DLjiw[=LQljrXkbHm<@MQEw_=S`Yv<TQbYjt`u=AyUXx_`uYuuiqsvLtIIKJDWKIUUyS`AyHlV[aNgpOUDVv`KjXo>TsUQpu`o:]MsuRSTmHxwUhkaHXsdUm@tOyrAxWUQSqTPAuWpqnFHYlerkhjKXLiyRSDJJqs\\=R^mOj=KAXvsxqxxUWXmUXIYwG]GxYwSeU=`vjqwaTKEHuhexidMNMU?Ukb@lvEvSqSPmTJ]LP`nblRlxvM]yYyoIAxYmYLXOwPqTqsvUWE`VktWSYTDQqTPuX\\jGDRElomyXQlXj@RZtk;auYuEqjwqhQI^\\yuQFs[@ixxr=WkFOqNqfyHkv>kgnx`^fs_^Og^VayZ@[HPhjvZGYuAN`MQvHXmogoRGwJ?gt`oMPcci\\YqlGH^oHl_@ip_ydpd:o]qVshAdNng^AdAFnhwgiusGdswyxwUWUHXiTk_rTaiT[R]ObyWxLicpAuWGD^sF^AreOxRwuxWTJ;R_GUjUwmgsrIc@GUbyQxXly=jE<NEXqUYygWnuwiwwQYgssxy;Bn_sy;bykyMwiEYfGIiy=v_yI:iijyUvcU:AuXy=isgbdwYUYXyAjy=jqMryOvbYxhwibI=yQxjErGiwwVNjQ;::ju;:isGbd:vWRtCrgCsrqyE[tmIg_sfwwYy;RPsxqyxUWX]UXyNwR^^M>bM@^j_]LVZFn]RFoIQvGvbpqlmavDXaEGqFYiq_`D_nF^kH@eHHufAg<nsUWyGIyKIqypQmfeEByEteMiA;Svsd`eWyUgyevbEtTCcGggpke[MU=KhROVS_S^_Y_ARB_Up;ySEYGSiYQcPutpuxMir[eMThy^tptAKmet?]oJ=pLhYomtpMuO]LgiJsUJ>LL:eQUTXycSUvmuiwsYmmewUWvAtMax?Uy>KihqVPOhU_fnMiWUIhqUXgXqiHTQXBaCH]D^wuQqvcQXMAfrCf>qtl]CvwgeQvTAUEuQkHLf<l>evWyTFMK^=MS\\uilSqAO;qJ:dQITXyiIpvxKrdkmhrtixIYrR\\Y=UY[uW_qytQSSEy;mtNQxHAop`jvunS<URix@aVVmJHToAeRXuOwyK@mLt\\LTivXeng\\XBhoZYJEasDMxDMoEUqjYNDEQR<QAlXHAKZpKuTXy;RmmUwIWkubHYIQ_gn;UneWLCS`_vHIGLmhyQxBODvUij=c==wbuummGJABVCBWWI]iW@ksnYE`IeZOG`ysMoFZICqyxqlVcyxyxxUqMyHpdlygySwUjixY:xw>Rk]hssxy:kA;FEYuUYygIQuuywghYgssxy:>n_wy:fyjymvieXfgIiy=ryxH;JnEJ]UYyCWYuUYaO_yU=vUfR:::FcsxqxTa=dss@:Vjgvsw=YAjuuywuaMQlHFcwvco^[m^`L`aiwgv^_B`]C`d<^dLX`;ia?icva`j>aiIkyjy?FBLUH?sULyI:ivUqQoKntT?iQCXVxpmy=jhhqy=JidkmtYCYwr@xQ\\yxauywocxqnA[exjrYixQqqqYcsmuYCWwr?xQ]yxauy;rQatYKY>gt>sXVkhtKebOFmGeYqWUiuWIwlUuRwexsev;bb?IHefq]S^kGdYu_gEq;I^;DC_r@kbIiCTwvEiHYECvWITcWmqEP[wy;B[Ou<qWtUGiCdxqEqsTlSBJMRSitO_e;IimmECafQ=iB_VjIFCgeewts;hYwraUtnScOOhuWXI_SnSSuUb_EwVQEC[ED=bR_sJ?shKgpkcRmU@QYm;rSmDxiFPaFK_xEsuC=yLUwSMthaXUWYEWgEeCSOfNWFZKWVWCQ[WQmGEMDCwvV_DY[b^MEiIrssDjUusavOeh`KDM?vMUc]EgVOdusbGYR@sbAeweQWTodfMeootYEVGQR=Or@[tB]bgofE[BKOW?]D?KTZ;rrkBl;hkQsB;iZYtA;FiqWdghr=qx\\o_dl\\Qx>mKoXoV<pFimZ`MV`v]mNG=Jq]PKeR:\\LKeB:::b`sDWUhC;rsEIHYWI]iyEg?;wooRHIeHuc^mehCInCYaOwJEcbWf]_IvSwZISRqx]wh<sXvwSfaUAuieAFckbMUgYWFl_YdkUu?gJicL;iV[ELOBiWeU_C:CSXcyWoxUKVwusH?hyERoatNeg];yqQi`sgEaGy=Y`ArHAyRSTQ_CdGDqOcF;Vf?gaOFWCy^yFy_svyUb[D]EuDiscatVAhwoia]WEeXgqw`eDhcfGiwYWExAHZiBugcemspkr@oTJiYL;EhguHus;UTggWfcg\\Whlwx@qEXAEOOFDcfD?WZ;FbWB:kbrmWXWy?Od[QXjwW>?V?oOU]Nb]VG\\NTiYrTMPESlPXAUjDDm?<s^<Lq@Pc]PUEP[EvOxOYtXlETxIWhhVYao>LLEIpcMLC=Q:HJJ=J:TjtPkDUsiyRNQtM`lhXs\\IQYmly=JBurCyY:poauY?ESWALhxx?yMlILLyY:XwsxY:DTL]T>er;PtelrApxNHyy=JY`py=jKqNfpKO\\jYMxLxmxeqMty@QMpljOyV?\\xudoKepcdO`DYXhRT@sxttlXUEQngQUi=JyIORel=IqJ`M\\pMd@kEeTxXMrQVaqrtPTgeoXDs`=Pu=ODes]drH<wGPQHEnaQXTETSLkWpJl=j?HqhXrPyk:mYNIJGyRZuWFtrdAP;EvoppPauLXUY]U=]Q]qV;MmDmK^@spDV>IV<HJ:EtPiOvYOZTud=LdqPtQX=]PR<w]mKc]jBDvvDp\\LrULSL\\J;xP?hKnHJVptY=vbyvJ=T@HrjqUDhx=aOUpPuyvStvYxuCevsUQ<IYxpTiyoGYuAIMqlyrdSM<YmyrMXrpLmADUTTQU@m\\pKKQNX@SXEjLhWI`vdHrNiJsuX@tJc=vCIsHuqxpjI@RJuJr\\yKHVmLma@Uh@MctYpTbZIcn_]GHsko^wytDnhiXs[fh:IrRNvXpyG>xVYlV?sTIg]Ghr`wqN\\sAhPHf]^acBUWRQAd_KvD@jS]UmdUApq@Zlwt:qyPvp=Hd@h_^N_dqhLQuYq\\XpdcWvQp]ZoffncaQ_En`qW\\MPlCo^p?xXPjtiZHQjfovTfhOYsWWsDfuF?[N`saf_UnwWy]iAZ_O[NWZMprGogxoZHhiG>ZZGerya;wpyPpNqaGIhkGi^GvgyvuxqrHqr?sfninQlk>^Q^i=^magn_vq=`isvglWl;ynvhf^N`lh_NQrsvmGIg=XcRfiLhlKHuQ`sG^pKxpb_]n?]xvjlYnjyaO@Z^?wX_]KaxCsaUTgkUcef?SSl]ECwHQOULktbWBkID>sC\\ahTWBFkS?OG:wiu[SFWFgyWZAwaADJGr;;wbAjbxvJItI;::::Fn:_urf]?o_HV`=PkQvwxwaPAjeFg=py_>lwg^yAZKQtKqgANuo_[yAZIAcy_xUGd`xy:>slv[^xqtQaTWei?ysatyVw^xati_bPZWpw=XnXyy:>gUXmZfwc`_E^hvorPWh@^iPPdBF`lX\\Ohf;aZ@>sZg[aOury]<qpJQgjVb^@oIXdpplPYymNsT?i_yrUHqExfmGlLpikIauNpCgaRNn:@aeweAP]u?i<xvN_thH^uhk>QvTquUndp@\\fnsh@u[W_JVbb>lR^rrWll>fkhsgw^=`ytf_i@^pN\\Dw_f`vkXqsow_plSGvJPl[avp__>YlqIkWAj@>bDnZwa\\;vji^jnI]vvakGnUFc@hmo?hh_nCp_`QdlHm>XyKXriykL>jZI_:N\\BcCmVT;Yy?rp]tfcX;eWmEXsav[igaOiy?Yr[hZkXxCW^Mv:qE^MBHuhkUrU]HJsBywB=[IqiRN@nMmuplKMUO\\duFEPGynRPt@lljTU_HnWEmEqJRysEuP=XMZYjCErx`pn\\p:<mXPJFtK;US?=J`xjZvZZhn\\@jMV:@RnaLnBjcI?dQ?dO_<jQ]j;DOVYVxey]xY:HTglTITrOQvy=jJhlAeytyry=J]PUfpm@lJAhMkyNxieRyaPwy:NtmfBrpwYjoyg@ceNnX`rkxuIvIwL:XW=wYCOh]AycUyutOqxEJO@Xyuky=JQquy=jQqZyAZCWGbYxY:XWdyGLrucHNNkBNMEeqxMmCcWb=[u=sBNIRFAyv=YNErcsYCosy;bwscKaDsksoEunTFcMMuyYLrmaxfxs:tq_yY:dJkyLRmwxTtciyaLOsUlwAnImfuqbaYgs_jkXl]vZk_^VxvaFagxuPNwcpn=YZqxjohaegsJpoEY_??mAyrP_[EIjTIpxxZBo^jA[RXeGOg^ftopdlq^F`^KxfLGquFe;G^R_hZV\\<@_=Fq\\Pkb>Z\\Pkb:::bJ]EJOrTAcQgHEcuPGshqWTMbE?c\\krnsufKtqgEGwDeCHwwBksF:KtgQgTgd`wt`eUdyDm[gPodJaIqOTqAS]crf]skkC:aBQeSsSxkcDg]iI]WRispqHmAVJ]x^YEaiCdwhvwRZmHJUs^_GCsRs_gMcVrUxdwyiYGjSdj]y>wxPkDqKefkxpyDxYXkgiTifWGhKqYGSG;mEM_C[aSK[R^wYtSrsCS_OXuiWryt=ADrew_AhYoRiqgoeuxCi]UuK_DoyTm_I_WSooVUkGq]Eh?SYIItqdRCuSkINytMYWYGw@QVYADkoT]MWDmEEIUlWFFqiCqg<[m\\<V^HPcXMJ`KVTps\\WEtY]=SvHp[Ilpeo`YVwgv_ytiUesx@QfZ]ShWF<KdkaCgEBpQvkIDgivD?fXuSUaxoaXfUGLGX<=tUiHoovPuvC?h?]UTgW[YYwQfo_CcGRKicXCFiGR_YHAcEqCI;;D:;B:QWQgb\\eS:IWKuYdUCgiF`GsNWU[AE;_fWWgMKt:Qr^SvrkS@;xsAwg_HiyrcsdTir_ichEVwahdMTWwSpYuECCIId@Cf<ac]eB>Oc]Wd;mtdyuJog`_ikqs`QV<SGS[vSKH`MGWmrHiUUCs:Sf>_CVWtHiDGeyOyTX_fS;feiUkyfv]bnFqyAZKQdQ_bGVhx`?<cMD:utmNl\\X>WR_CrQ_i>yfyuw>yI:Gd`sFWKgByI:[F_yI:eItyfxccoSf;OeLUwT]w__Eg]WDCRWwbRIytofl]iMyWrYe=OiJOxxGdaudgYuY]UGegZMX?UgfwcoofOKhpAG;sf;kC;?Ygew=kywyRwoxEuI@eWaYGx_snuTvsfHWhcYYGcfP=efgS\\aEG?dOaSxUfsOGFmdRQcvkvq_EasF]aRPUhtErhqwmho`IQqxMSYTWMUvTOkeWEPRMYr`QQ^hVMANbhnNakZ=LraJketihXiIJSaURUUEIy[`qQxXk@U:QNLxlwawKDMJ\\MXDJJ=kwtX`XPrtTixi[qncxhgfqs`tn_rn@pxPmhQtYG_FYtswxkieBQphp`GXmSV\\c_gjqcXAgMqaQfucw`XN[QpcQhbF@iposHI[]A\\th_>IlS`aSy\\:>vq@mFY`HqwwXgy>mXfkwyl_xvYFuPImyeeQcycrYEUtyFwWBgyqYiLyQKrdQupx`mKciU;XTuuoFyY:<noynwEyYAx]TYi:ZPGy]PmhVyHhvI_wwX`xIjPymqivyOrI`ww<ZgXxA_`WwxE^myAZE`_f>^jix^IpSWe@OwepjRwlyfiwOoyF\\XAgtV]UWb`Fkofy_IuyWpTAeSa_MAs]>ZuhZ_nbOausHaxI^Fpvh@iEqy?WkiyxQvy:VbTGo]iqXvxUWt[DgcWnWewQdskRg]cDEBRKRLAc_SCi_TBCsdKsmmS;KD;eXqEFoEWU?yECbhux`exf_X;kvZUyAoHfEG`UVcyXgMB^=vhiiMKr;iG;Sf@oHK[ypOyAmHlowLyHYyHtOwRaCYkWq_YYWyGWCXAIVWhFQC[aGvIR\\SYGKGy;d`WW_MwqEh:CXfyT`SVSseg?D=;vFuf\\]TNKFE=XL_E@_VVcuaCfXSfhGUd=ytqGhSCw=IXgtHyI:_w=gGqOWTMeS_vSTW@yXu@VJhTM<jV\\vTtx=dtnxKrmroUKkXY^tY^MwphNDHKgLms@lj`vGHsKHlcyTKpty=jl`XFyY:<stXtxayi<YQYqjyv<YPrmxeDyhPTGmWilUmPN;EYo]xBdkDMj_Mq\\avvyR:<ZsAseQohWy;`ccOiagy=foyvwDyy:fjinxXGMjw;:lHjukCiyQl>;WWI?hTHEwsDnq\\uFdOYisMUlEYQK\\OghTPDkD@P?DRLaLJHR?eSXlyVUYyQQMPUaAswxY:tOsyQnUlKunO]YeLuqApDLyiaY=@NtYsy=j]hn_ppy=jIdm=qYtXry=j\\PUMhsy=JJ\\VYDsy=JnaxnppYIxm=oy=JQ=sy?wpXo<FhE?ccB:?o^AYQhup@tgdw_qMMAtvPlhEWgioZIPqPLEanFpKZeJ_xrWiKHESW<O=PuDprL]yIANdEPS=MoUsbyVxLlwQMLEYPYOS\\kfUsd@kC\\USEMW<uF<jNYXHPwwxXG\\QoXv[EwoYQGQUPUMrawTlxBakkIMPeP?MVptJsxWWlJ;TnfTNy@PBuJ=erJiqP]PueOldqLUyQYTg\\o_Lu]QqXLwrDvjURdhtReJs`MFlMu]TPQypelsMVwXr=qxqHlIAocETAiN^ItlTl@LxpYomAL>aK]]MF`v^QV:dpb`oI=YB]piPpXiUymWcuuaApMPswxlgEpfepvUvfiOuHlV<v[=pmuRTqnQ]XrTvQulUQTKMUiDQqqU>upall_]ul`UI\\oQ@S]=wa@NG=jcEtRMmYPKvYqfHUcuLpPq?UKWpVWmWfDnu]jSuN<MppyrW`RiHn:psL]oIdUohliaKvtOcuXcUw`hq``PQQy:TTKYnuhKD`UOpvluuGLxK`p=lMl]t]EL:eM?dlW`QK]U;aLjQSMdRdDk]LLp`kh\\N^=LA]jKlsAyPgDS:eJ_dO_r?sI[WwIQioySyoRo;EwecQYSxMBQyuoSwYoYGOWjKIT;UVyh>y==pUKN\\yCyY:tliUyAPwYMY@AwhLKuQLA]ywtYWoYxf_rr?xQ]ayuQxQnwdI>xqiyowwwAicwmtYcWwr>xq]qXwiiGwy;Bn?CeIChAYfaXh;CS;bYIW?CHY=TvUxkEvEAWgwYmGFruXpKDUQBMiTmqg>Id@CDxaTfMb`sSlWhFkerqWTWr?scYeslkucCTigHi=DbOXCeg[AHMuwxqEvGXTCSOcEOAr@gU^=CCIYH]DZoE]GHUQIFwdqMiN=TTsEWQy_[dI]h@SS]irB]ENyhESySERZ;Br[Fp=hvYF;qvicrc?FguwTgdoCygyE;odt_SxoRaEHg_Gq]W\\oTLCS[]XqKvC=S\\mBCAIIihf?guOILecmsHXQrj_BpMeg]epwTPIhcoTEuvbkhtidG_GcOB:kD]]FLWglgsZGFCCuSYGG=BmkyNEhI]ch[yGEve?IvqwTahqKiWitOisaohGgYkGi^erSmI<krswFFmsrEgTsu=mUS[I<_fryHuahIUgdcG^miZYTEHtsPShmUUxjFlKHLPeTvRMToAunUYetKCLWTpX?hld@KPEqnxSnpRkdjD@OB`NI<V:pKS@M]ilI<XwtVIEjfQQWlOhtlQet>QP^luTAsy=JTuTs@VsTQ;EqrHSAasX\\p;`eD@_:JN::j[<n?@oWApRuw=EpX@Mi]uqXkoUXkEymqn_XYREWPEPChPGLRaHNMDX;dW]YoDQsZMjBUS?<NbpKdeR<mkh=Sp@orurUukJYQTpX@XWGTn@=QM]MJ@lGYoY=ogqlCxmN\\WjMpshYZaUOHLk`mvytGLVgIsndKIPTMiXWutMmp_qToTQSaQeeqt@T^iOv`wa@yHxWJtmk<xSqP<Lka\\K`XSe<QnXn`LUGPSpEla=NrAv=TKb\\VMYlWaUf\\RlhwC\\Nv<LN`YDXSkdpq=RTTPUeRqyW[emDqviiWMqjO]QEEyTxJr<xBtY?AR;`m;hMhDr:aORLP?TkWaUj`tqxtahXwYwpdr@axTUmXyM`iWSYuVMuWiubmuRTQqPQh`tdQmXEnTls[QrxmwlHKkHupIlBtl\\QnLxrPHYfDRkqkTLXryv<aOQPyUIQMHtu<QiAqUUQ:LuuQlrdU[dJp]rp\\VZAjK`kB`PCUlOePWyL;yp`Tr=]JYTqQ]p^iL^XXC=uWXrflkRqWLlTHLpBIyRDPWUy@HpktPTxo@@vB\\L_`VJhVPYpMHQ_YxE=SUmXlUSP`nk`vThVedt=QvYypsyY:Hl>LO@UoLiqHhka<WqymUQmWavtpNlxrNxPQIp<HTehXD\\jKYYntNa@WE=LxlvwIqhtmIYMgqLeyPK\\oulJpQSrHVoeLIiSLMteDJqexk`Qv@NIlQ?AJZxq<=jwitpYWdeSd]OZamDxv`amW]Vt`YiytjPnstWPxiJpkMxy:fEwat@^k^eiMlI\\yuoauyDTLeT]Pr:DWJiRyEncxiQQny?wMYdHhl>JCnywtyTNG=W>PYdDkfLmlpw;hVGtx[TrF@svXjReTwQRYQsMqMWePI`\\lThCdG?xscDPShvsRR[bGQrgAS[MHseTeIt\\[uYMIgydx]sTwFxmWRmEdMu?geGoS;UYsuYuSfg[WqqtKarEqSfYEVqtsWVqQh:WH[ejpeLhUwslw@pQ]hW_HWlTuAEorQnlmrEEovUm^IQOmlpLMHmQ>ikGhsBEY@us]\\tOySfINYqTPyrqTuI<YQiKkupFqToXOwEwf]YutYnyOvUpmANUASKhkk`UspOmDPfLk=Yx;lVpQO=]mmIWZeLDxK`tqKHRb<v^uY[yOwijoxMv]kyDvAg^yAZZppmxY=v[syDyDvAGvMwi[V@yBpQty@npXpy=j;xJvAoxMrYMYETwy<YRxY:ProtYDtQDxO^mjAmxL:Zbny<yE:Puy=J?xM?xLlYjPDxxLlg\\pUHq@incXSkxRCiOKeVy<pV\\kOYWGPnXmUmho@IqdTRR@vupUuQw<\\SOlRIEMf<r=DQZPkMlrYMXftuyGhy_xo^oiPkTV\\eOi_vnSaw^aqvXpOa_hgoKae[q`X?bLIcqH^C?ePQbCFs=nhs^aqPoH^nMq^CpZip\\Gx`ExfGoc?wuWVldAsq`[rx^eF]uvs:nmA>bcWwegnyeTuvBwi>qumUyEQsmgsYox\\IYxmuy\\okhygIqIiSFxVwDv`xLeHUvQtTTyEipPMmeXW?YYsqwPlUEUld=POTtFPK\\`VJ<qJEPhEN==skqjfTUwtmUyM\\]ptTKcQMVplihOG`tCPNGdWLUlaivsakV=shTrWljgluXItWHm`=mWxUpQ<;?JNJw;r[OtQ?hc;ISyURYk<PuImY@xmjYNuEky?tUGeyEjAhyerekYNkYNyEB_sI[w_wiZoxmwi;yBvAwxMrYKYESwy;Br=uy;b<iHyKcb;yVoicSVfMu__tYMetYhfmr@QUq_b=cBvGdHgd\\eyAEvIqty<sXxxxWsyAZZP]\\gxYfjewcZW_cwqla[=HwinyHplPXuxqaow[tIwInyEPgGw`xIbJhi_vY]hn_xpyukWXbyqh@ly=jbqPeLJkUsCIwTAnTLWB\\vK@S^EqUPJdTPV`XIQJ:\\_yorX`]X^^GO^AFqT@[fgpBww`Oxhg^<xdNoj^OuL`bOGtm@^s^ZFnZAnoHvpUioyhqifyryixq^IppTam^AsmWw=vy:Fxnfe;^rdyaI>uXysg_nxxmg_nXq`XXxsQn=GhhotLHy=PsaF^FhoxIpWXjL^wxOhs?ri_jqvb[awxp]Egy^NgL^uCnejUhUb@MiSMHN]yh=b][yHYs:GyeetxeugiYcYxe_VxyQb]pwqPUAMWypwIyMHwXpMVLT=XJ>Mq`DPuqnEHoSqOJdXglpSPvLpta]spxOaarB\\VOPT]IwIhVsmR;IQUiSjyP>xQ[EmuAq?LVWer`hMa@U?yoODkBiPqDPQpW]\\OBmwClreHNuiwqxx_xY:tQlhxoYYnhypxTXhvaqYRxQyULFmKIxSjqSsXW`@wJqjjYTV=yrQu_TJR`Ny]SBYVLHppEokDQl\\niDpO<rkat`ANMmQRTseyndEk_pWVpwilwnHy>uYaywV]oqpJdAuNILuDvfDrk<uG<rVPKnUPuiwwEwywuQxy:Nvbw\\PIuHify>e^gxIin:Fi^wiEf`aHpJQnrhtn@s_XtZPt\\img`sbIqm`h_NbchdM`s?oscYbNvgOpbLAee?erw]VgpIXrkvmrqbI`y]VpTa_LfovpmogsvH\\EG\\cw]hgdUasG>p<Vm;YaehqQntVaiLAxjvalwy:^yIGwAWugxj@WmhXh^IsYxsiwaG@^^VpSOdPa\\W@^ColoN\\^F]litjP`Q>^W>njQ`m>jmVdOwepXu:>Zc?h@>Zlye:viYaaKoxeygiM:v]yAZCPnbY[Ngl>v`Jgc[>cVyl=f^SG]HOaaGlMWt<^qYOxL>qyAZi@eyAZnYgOWjJitrwq^i^kwy:nekxy:>wPYoAFn[HjAaiCwYivUqy;OyqoiKKub?QxCpycOyI:_`nWdRqluFviQyeyutAxMyanqLYV<yukUqxqq`xY:<t\\loYHviQyeyutAXMyqnqlutKCxY:xrgySweyGyi:Okjpm]qkAAd:W^ThcE`kZWfLim?ofkf\\<_xRfnnFd:_]axkUQr<Y[KOvW`ibAxsan:WvWwlFWxU^]GHtEI]xWaLfiew`Zy`Syi[ae?qxUvknPuyGgdqm>wubW`sIkwYnmgpvPrRGsKXjrPlHWhM`mPyxEhxr^xBigXycINgt?sLPb[`ggp\\mw]W>c`?]WVpRwm=^nM>i>^cpXxUG[ofgO_jmnbKNvHYnlohlPj<?pbAba^ZJwZogbN>d;fB[<:n]N@ZLO]yN]AIxPgpPvj_hygPnLPvaglZvpq`kGXxFawOF\\mOwHGcbQoSvkD>gEGmRQ[Xx`ka\\tgZ^X]>v[s_hgi]t`suQ^VG_`Ol@oyBFlNWpp>AuBLYgEewiUtEIdygxhqvmmgfMVwaRECyPgD>=bOehEavBcuvEbCkbVgSdcTQ;VFodpGybyEdwDqOYnMul?yPqGHUBywGQQY?cWtkbSWVGmeIctfiT@SrqccuqfkeR:SwAGvGosmMVWmrR]Y=efkIwVURtywnSWC[g^_xDQv_?UMehwsIfkDLQb>iO<hq[<mGpQo\\qedJAXQgxpiuxy=jYHYSir?eQpQQWPP@IofpOoYKY<qcQuE`RqxpdMveemJqjIIuZlrFlQe=OLHS;XMbPODTnDXrlXQ=XTOUv=QVKplKdNr@KThn^Tw^xP=`MAUp;Txidym@K:Hr=EpLMsWenSastALN]n]Ioe=RndwjInxYra\\K:XV?DK=<nk=lqtq[<m;dpteKyXSDDmGaTGio?ETVIM`hwGuk;EuAQp;xwTTXdLvshmchyy=J^evtPXctoqmY;LSeHSo@w<muTUMwdQrUSohW`tsqYUJqxSYThXxLqpZxp@lu>lJRltr<T[eTQ=J;XTZMYDpxKEwRmRDPqhYYH`LNextqQ^IwquJO@O^LKADREmTdiLHAymlY<MqIeYqyQtMoDAgsNvIIyBFwyfxVyy:>wcH_Z@_Hfl>ZYpywL:TNGmcbty;B^cN:PYnySwgt;p\\gpvUn^lQcfpmfWiE^[:`i?qrwWpLGyXg^^Y[Ga^wg_^yy:N]hGnyeAAiyqWkyI:Ag?mwQSfXwv_?e_ggnkIdKixuHm_dE_v]Qw\\QCXGIAuid]ThCT^GXVefVOHpkH>gfCaga;YW?uA_b=ifX;tkEGiyvrOTB]IBMYXCw=EGiyNiPqriSh`uUQW@UOG@YUipPDmn@sKLWGlwTeWRAlJ\\O^YkE\\OOTOgmO]INMXOmQmoIPV`kIPTmpW=MpvuoLxY:xs`Yly=j:Lxy=ZvvoLvy:vs`YlyAZ:PxygkeoyNniO^a<Q`vvoL::tke`baYxCwY;XXyckewy;b<ykV<R^EYXiny=jYdsaty;`VyMmvtoLraU@ZQayb^ybnv=nlkaat?wJqgGiuPamjiwUnlr^ekFy@H`MXwDHtlayBwcQNmA_eyAZAaqYXvA_kyAZ^AexlrxQtsYQf>OeWwyAewhaXwmDugRAitMaBE;c;ufQoiquS[oid[RukGDQHSSRZ[VmqGbOIUmeICSIWEwWVawsmICx_XxwLaQNmEsAPUXycVgepiq\\iZrIxaHgQo\\Thth@lKqe=Og\\h^PvpUFfGhk=A`fopRfwSv]ZvZ<XeoVp`peWgskqdngeZoucwlxo]EWqBWf[_v@onZQ_thw^Fa[_mCqm;?djvZfnfRYKywvmIcyI:;IIyvrIT_?yQmIy_xY[iAYTvUgYuIDsiDmE[CUXwly;J:dKX::proJDHq:@sl]qEuyyLmImy=HSx]PsmE;:jTxTvwr_`]:Yhtanx?^TffKQmiackFyi>qfn[CV]I?ZaiobwnK?yMgxiHy=nuyAZQaqYPy;>oMAovY_dWi;veGwy:>l^w]CwinahnppYIxmAoywtBwinYeLGgyPXAnQtYAoLwiIxJwaxAJRYlX`LPDutDUSTnp<ry=J^MsMQt[xpsPJUEUi`qjyrx]kpDMV<O^<StqvM<UDlmWxtoemiQRqQq_pPS<whisgisohnyPUSHTPXoQ<jn\\K@IrwUUudj>Xv?HS?IUjqVqXyf<UWiqo]qJ`uSqUEuVePuDMtUasKiwEaRFEjepLTMXldMVpXfdUQtRB]YKxi=y`xg^HXtgy`QgkWnwQ@ikpsJxsm_^:qjjohBaZF`n:HhG@rHPnr_xAYtvx^`Vl[@yKYntPkLAifn^ttNsbE]X[CF_OVCErR;U@;t:MWqqwBkBgGr]KFiATWEwTwyAaxRahCwV=gDyotLgumgGHaC?WG:WimsubGHF=RluS;?EYETvuxqEveUYUUGgtl[<veEmvHWVDMOTuielXdR[@Mymy\\ElGTriTr]ANOIfdwdTff?qs]@[wo`oy_ZPxhAl=N^Aa_]oa]P\\q`]mok?WfrYj=QiHvpqGhkGi\\Y]Ox\\Pws_ghVv`JO_IofvipehfCNxmYqOX_ansYqap>j^nZwvu>iq<Gu[HmnXiiOpdydQn\\TXdUnlHf^@Hxg>]Va[ZG^L@bYYqVqh=prcwpYG\\oYq`gtgYu@WtTXw=qpqy\\t?tQNhswgFVaEW[iwlkOhUvkj>_Bax`ap`>xA_jayhLVgQoZNFi^?pqx\\j`wMivPhfW`vAhvVAeFQkralBQ`k>jHNu_wr<`ak>hMH]vXbtOtYa^KPwMhyt`uxvnN^niokigugid[>bwQt@ArHv[Moc:Ydt@yS@oUAkhW]@wpegcDOv\\ytCO^_yX=CiQdJWeIsD;YcB[gviYA;WvwVDWcyCsTgUmQwpgw\\IWGix[;Ghogo;rhavREh=uhjqXsMhVqr]aCTYxgeSbaErYW<sxHSghsgsCSXEUfIVu]G;aXs_VSuFsJ_eRvQSLmOrUJYdOptw=<Y\\ixU`SkileesvQp=MoIqXRYJdEXDqrrqVsqpdpPJUpJ@k]EnALm:dnoEXiHTq<UhUm@mPeeSHIYgaXPtlGmvsApWurbeskQXZENsUJItokMUIHMgXQIEmdqXXYJkqrnLyoIJO]yptTcTxiqXShjndS>Dwe\\wwYQ:AOZaKhtXH@y`QnYDRXaLXxRmixSLU_Dw_Ip=hWKajMiVPhvWluYtLkUVdXoxaxBANFHJqPnWtObqli@xi]by^neqhLPwT^uqNZuguDgvCOlS?t>OxBQ^:NZJn_O^\\=FprG]\\gd:pw=H`:nwvNyTN`YquyfmOoyJYtmiswAmhwy:vqHwqWx]TQay_yyAZSyy:vuoyYor`cS;qMaDuVxmrixy=jTqjW<TNMLVErxlOFXL?=oP<U`DQ=HjuqSAdlrDWWILRQKkyY:<sDYvxeq]yY:HTglTIRkyI:=kAeytyry=J]PUff[pvZWFxanyWwqfy]exicI]\\xkCxaliwyAZZgyUwy:>cGi\\KyCktuIviQyehx[m>_hPWIIEsyx[yfxoy`xIjO>hyAZIviQuy;roGV`yI:CWgsp_vahwieQwigy<N_<YiHXaWfcNFdS_ke^sxI_TAyY@dkqdMxga@gthtpykiWgnvtAncQYeFWx`Nfb@khqoFPbhpv:n]aPmnQs:IxifjngmtoveVmRyw\\?q?P[^nxTgk?am?HcHEXuR@iFBuBc]faoEnGR;IW\\eSPcSM?sv?haaBigHwqVeocq?ioGyrcd]mcLoc:=Gy_HQwWqmGEMDCwVLUxL[iIMTS[y?qVIyWpGWYqTOMUBaI;wvPubLIyDmGXSeA_CHkcreWwUuDgt\\UdfaHiICdMepcbG;gKASYiSu]BeOTbeT>CD\\[b=]C]SF=?efwC<CSvkqlLwnAQrdUYetLPSKDYeYNGPSa]OMtNbuNaDmrHwMpT:XQT@o\\<JD@o\\:ZGPtFPkHpf;n[tNytGt^AZiap^g[XQrxHikyjEPfkygChjoaqcp^;h[[pY]F_eVasDueVp=d;cDVcbDGr@[WNShTCURyskyV\\qxeWGiISrKvEeuQ_wDIHeue\\uCjMxgCYgyHaCErYI@AC@_D@yVEaiISBxqcN]IAiT=YWTgxooRYgFEUGMgFeggnGDZIg_[HLiU>kr@gCsAGVmxCqSioH@Ycd=iaOciiVpeufQyUyslydMmeoidfcx_AxiYUvScoog^qXyAGMQT^]eRWCbAE;aFaYRgmC@isfErpEIZMg:WcG[famdAAXbkeUkUeot<MHs_YcyeGEy<We_UymgdaSDYCHvgCdeD:ErAGC?UUtoYMUGawfVASLmCNUGGUVhKxtSfwsDw]DZqC:kSekcKiB@IXG?iOQgDoXIirUaiywgvEY<gtWwVq_RyqU^otjsB>CSFGTfGxZOEbkb<uS;Ot;cbxQSGqBUOEggdJ=rLET?;D?]\\OnsrWpxQbtvcwyhyNydNcbYW]a><y]N@tNvZDOjiFyCvCto>yY:Ht`tNWLoBxQ^enydYtynxeKo<v?UOutr^qsk`pFPP@MRilT\\hRZyvstNGeYkIo>muN`qJpXmml`ly`uLJIMqdmy=jQirMqYtdo`]y=atoeY]dSgur@AQMUVKHolaw_uPcqVNmWH`Ye@wpQP>lo@iUZEPLIsU]PMDUI=xnpK]PXFUKrquo=mp<xI]LByWiixeuRYMwjititKIqKdyNxujYtYO`ui`RI@mdMyA<kgaPwmqr@vpTkHUlNiqrPl?mo]mjnTL]EkDQQRTV:LL^ET]lKBYr;tM:Am:yr[msriwy=jdmYWMoWTq?`kYdwUyY:LYQdpiXYhyQxQoIdwU;:QEroUN=VtOtt[GPKhyexiyI:=wV_ty;biAyy;brKgye@:jOyo;DW@yJ_tlWQJ@yrpioyOyQf`iVyhyaxu]UA:Rg[YIKCjcibQIfkTsswMKgQUDbuXkGS\\ueUSvZ_CLKXOwERmUjUw>OwQwr=IVGgR@WYvwvy;bPyT@=vy;B<Exwqy\\yI:=We]DxIFeOipgR_UuXEgpodLobygx<mfUCCBEDAiWF?dLKWskVxIGA;FFMDuQbnqh<ox_yEgYyLGry;B[QENISfuhAyUaQRdwHDqBYecY;G=SB@GnMuoDiSOePWpxEuRtpyXVth`wixfoWyFndfqg[npNg^hquW?u;^fDVmpVfh>`>Qj@fbQ`koVgYHkqOinVoOnpOp[`Pu^ofEo^eFhjvpSojEAjvQc=W\\_Q`gOrkvuVP[tohWnkbPgqxunq_dwaqaUv=:y<VgHFi]FyyAZT_eINcUpo;Yf]VyPwy:ny?hsEoyuykyAZDXnuqD:Zg`iINcjfabNqfq\\lvaoxgyAZbaeNyqiAqyAZrQoyfpi;:vt:ax]PZE@nkHjcPwqwo`he]>gT^jd?trp_Gq]Nfgvnmtod<hh=FwIot:pyAiqyAZiHgy^x=^cHWnjiocWq[h\\nxusUJcy_<j]hn_ppyw]tvjwahAxy:fbop^UxY;ClDsy?wcIggwq]yVnoJxy:>wpXoSvadObdPibxaKOmKWbnwsVVhGAZn^^a?]?GacQxDp`@obpo^yfuOFsrYyOwtnYuExhlhmngyaVs`GqNqkNPyIxl`^wd^aBOwO?cUyj;NxC?]R^ukgwxW^Ga\\TQtXGwJPwCnnCg_?atTageiv=GfV>dm`c`pcaWrvVmO?hRggZqfP@jtw_PxmmisywwKHclpauX\\xIyO>rWayKWtf_o^nqyHtoVcUohu?mghe<@quplXavUOq:Hq[VctHfBxarGxOHaNApkir_xr=`^kY>iFnmyOQCTUSS_DeaII]wkkrOEENAuSev;mFZIBmyE[aHnWrdCUXqY\\yvwEt@ACjmy>IrcOxDMVg]ieAwY?YqyBJiWnoBnuWkCiPQwM[e^uU`UibUFmMEg=fCCTvurrkC;Wg=MB?WcYAsQMu]UW]atj_hlghhCipuEaguv=gFEDA]diGiDmrgwuv_wvkw:cwZaFJus?CERaRf;RAWTnEx@AcmuX\\yVM?GhKbyQCTGgkUTRcYmoTEeRA?WQCdb_vmgYJke:EXasXksFwAH:WRLGwTyD?AWnWIcaxesYEMWjMGkKiccHM_wDGr\\SHE_gBkGRibSWbI?EpwIAeFVus<CuYsxQqIs]dgWshad]oe<ayEeByctXYs<Qe@Gw^=YiQTY[g_whnQEn]VDmwPPUOlUlXRFxrr<qrDrGumsEJUlytDxhINZlUrexxtSVXkbxLuMSjHUXxPmeWJ<ogErt]Uj\\naIjK<t<\\x=XplYtaplyxH]wIkgiyGWiDayWkUgGucBWhyAyjoXcSghUVgegoqVUmcJiX>Sx@MeS;dkushybeiE=wrFIXS=YYEUguiCUSMcutqGDIEJ]x<EwDACA[GR[DZ;xDYC;=FieRREXE;Ro<tl<nFLYDLuulmmywVxvXMKZytElY<utYhXeymxekd=PtQMixlvaJhxqemdti`dHrbAgZGH_rYEypwYjoyg@SG]Lvwy:n_YqxIfTcI]]XQcbwEc]hQywxxaqnvswi>Aij@ywIa:veMwibuOYBviYyfyrGgYPYutkCviAiwtYYC:[hBSwCFpNIt?g<?xZPmGmKjxSJ=TAxo]YT[ix<XTxMLwiYn@wFxNBiXQiVMay@uR]\\xlqNxIQTYxnaoIAJYivy=J?TxQ<UhqQMYwwyNdn^uIbY`sIgwUfmgpvL^cS@]uFkuVpV`m`ypvfedXb`Hr=Vs[iwEGeLFsnh^WPmHYf]Yo@V^=npeW]Zah<xg:FkPPue?dtqpdPrCVnK^qS_thocPAdBOdtF\\X@[Zp[dQkb>n<Nkb>NB;IC?qvk@mgMJAQYgtYuEW]AWqyTQHlUYUZhj_ml:QkVTv^Xl;xSgXo_<qiEPiAXAURXIskyLAyTMHWm<yqHvGishXO]em=aSp@uglWl]WKDRSyvK`lxIwN\\MbLvHLvrTvOxm\\yoFlpTyqCdOvYJZ=OQPUPepZHtvdwn@lUQuA]PMTNCyMimjNxpWUR@<JjExWyr=uq:HUr=SIMXoYOWtsJYq<luSlw`LjRpJRAtd\\OcMlbdKstNieqtqmotUDukETsT]PoEwrxNQqUxxuSps`MWX=PrxM=tm;`WvTOcWy>yp=HeOigOfjrXZEQjQqiEFv@w`sHaEypfNZ=@r:VifGhgGZ:?Zb>Z;>tM?r]^];vcWVhV?yVhcVgdQOem`qS`hcQ_egc@il`am]`\\npd`Fn?_\\JG::lomirYLxKLty=jeIqy=JKMTQGqIq\\y?sAGcyeeIyyPn^pn:<Nt\\TKxY:<SDSwKQwMMdIxLAnElY<Yty=jQMny=jbUTP]jtapKdr\\QtDER]DS]mv]=T;PNLTw]`Rj<ya\\rqptQPqHDojuPPLR;ew_pNcdXdUVH@pYMWWIjBUva\\mk]MkUutxJvYyIPYgylx]kTYJ@mu[Xl=qLLNaGfuoijo`qQxhQIdCO]_R>?VQ;vRmFAKSE]gK[eHCioadP=v_Sgpky=kThQU]GtuWxWshf?ex=IK]fgicJ=IPIB[AI`WtRIsCYEmmhqyI:Cv^?DjybpgvbwB[yI:EFO]yYOFwyG=GwagIhCgaUeJGIDUSrEfK?iAktrMu@scDIc`EV\\Iis;b=QEbOSbKfpmG;AVkADTecFyWrECnyGtQSUmya[ybwi>ut<wiZgwqmvy;b<ehjyI:euYOCFyWqydlGGtecF:Jr;:::dv?=Tdevy_jQPbyAZZhoqpvyOrI@yC_hiNyDVuxwfvY_QW[witvAo<yy:fHtl;IOFAY]hULqOnXKuTYwMRCdVnUMNYlMTx=HWgYtdQuYdJoUsYIPdylPUt;uV?EoGaWy\\pLaObLXj<YnYtQuPs\\mOuMS<JvTPv=r:\\wXUjYpRoxkE\\Q?iv[UOuEsheOhmoGhTVqpb<p=iM`Hs]TkuyPW]TMQNLHsCmS:`NkuTPqLqPp]XJ;Is\\IMv`sThO<Mwm]LmPpduL<EMpDOOmjWlUS=tR<lp<VLtsMMMghOvDkeMo=IOAmxTlVLdmvYsS]V==o:MJpmr\\ekxHTI@qG\\Va]OmUuPly[XpUlrQmMRTsEEjwhnRPqLHv\\EuKhYZQRDlSEHLJTs;xPVLJHEx=mYMTki=YDyi]wi^_uEvggy_fymqxlGwmgOxvwweVsuYupWh`ahIa\\hyjc@ovFc[HZyUBqtUSxy;R[yBv_FtyDwebgsymkiOWw?yV_yeD[;DTnQMS:Zj=:Ro:J_iB:>Nvi<=diU=:oxiuxQjZQWX@NKqVMqo\\TkLIjWAVKdT@EY_tKWTO;QY:hyc>n]@cwXaQoyw^vwvZqickvaA@xgHoTQreFwyPxFZxe_nYx:YbyQn`XMyA^wg>;Rn_hnxq]uvJyY:p_yAZKigPO`x_tXVaw?_nAoSnoX@wUWuf`Zfpe]G]E_[vAuAa\\j>_eomYVtoFm]pmiiwJysT>]PYgeFyg`^Rqcpo\\?@tlxvWxn]Fa:ywSwsZyaCv\\wquFplkql_Nvq@qP@]^Pbbpna^bZwoHV^KgvjF_:piXoctwaaVdnAptqjMH]vIoxwscxy:VtAxtv?mxidv>sHvc??yuGvGqaLAg`xpqVhGg_>iomV`[ndT@vHieNna]>lYf_v_tTyvDakaQ_kNpxp]LqZCp_HptlYscW`sQlSpw^olaWlZFkF_o@YbZN_?xepgvb>q]Ng]ycBat;xy:>mygypyy:FvAGlc`vkGfIYylwi?`]Ba[gx`=Qe`vmkggmggbOv\\AuHQdsw^LHcSxnOGeWguSakFHrJngv?lN^[]QkghiZyqGveVguVaecasLqeVgpFivhgnJowBIpBAqF>`LP^\\^q]_vwWnlop?ngsQaPP`x?r@V`LPxZGhninli`vVvPF]Hqavym[yblVZUpaA>x^qaXNagnkShgONqBwf;x^Q?qCpfuI`ppd^wfXNfBpqL_j[qjuWxSoqX>yionRyrmo__xisgib`eDqkqqpQy\\PVh:>oMOZ?Gm_h^NHvE@cUqpZ@^>NZuxeaNdyAZax;WyM[Yc_YGLQRQywEwyPRQLP=PjmERxpluLt`QtaHT\\mPM]uwXt<MLvXW`]p@`uOLu@It^iM:\\k;\\T:HYePqYlJneSHeQxdqDguG@adNunxplVpbh[MffUphaYa[`kLhrCX_NavaYeBatwa_yvwsxa<yk]VdnApyAZx`vyAZD^iba[Q>xiwjXV[rfbN@pUX]b^ogg^<PwRonqPk]^lK>sHH]BWsG>r@H^RX\\=PkMQtnXsgn_=fZLXcVfb:?_maq=`kVHvRay>Ip`oihpcUGh`iosQ]YhnAhyqy^rId^QgxolYvxVym[yB=Br_vVWViKEdebe_VuUgugB:SdQ?EgStkkYfWhToEcEBXyGsESVyQi@e:>wPYoAbd]yYKhLAiyuwRyI:]Xegt=AtJAb]ky^yQQnX^xFHtA_rYHypwy:>pxgoyEcGe\\Kyc]GEiujyXwixieQMyqnqlut[yu]qxaoixqvy;BJOFhyu[yoQyqoIfyenoLXPly=jIXuYPytY=@pXXvHtRMeRNlT]QKmuwMDWTxtBlYjXUcmmZXTgdXwmQgHJhYvn`QBTSLhspeLY=P]LJ=hWsuxourODwoHL\\usE<ymarKdrY<KndOqlTBEsbqtlEU_<kBER]<xr@SZlkQ@rqmyy`QrIY[YKGmOgtJKYSIxkResopSaTYjmo_HMZPrfeR]<Vl=SstNatnoHSryK?uMJ\\XYyKVer`Xj[aVkPmxln]YQuir^AOhexCxX<Xn;Lkviv<\\vv=r^AVkqu=MVudOt=yZYk=QmwpkN@WYIqsXtGPtlXv:Lo_tKheqsmouAvblMyLj?PQrHShulPeTPEu]yKEutiewe`MjhSA=Wa\\q^YvNix\\dr?intHqE=yIMvaUKvdrimv:mq?XpKpo_pPDXKGqShEM_`vSPNDYo:iN=hLBUJ^lw:@VkUUXPMkyn>eUqwtpQyi^j[fkhoogOcxHnpocby^Lp\\vFbJap^wk\\W_oppjqxAhZ=@u`hmhoxIa_laplwoTX[GW^CG_sYpqimVIlMamn_oEx_ApaC>pqPxnxwINuRA`sg]afpg^\\kYpkphcN_JXwLxr[@]AVZHH_dgeciahxqYNxj^yoNvyFktpxTxtpQqyVj]ikhowg?htikPYc;_aJHpyAZK?tn\\c^aqNvYGkTpwTxtPQqyj\\huVQu[exU`oPLJsEN`Am=DnbEsXxrT`uMmyY<Wt\\y@pu@UvXqp>@slaWI`UvTjuIqKXUwuwLas>YYMDsaAxqQRpqPy]VRexCdWXxtKdWhexuHmZIlWLUAeoU<sOQpf]SlyKFYXQ]luIREYs^xmWuy>pvntSU@yluW>ey\\QwUARthv\\lUVIusylThP>MWXIm^AjWlRJlq`IKBdMjeR_AWyeLvxtdTusqpPlqJLM=Uxw@p<Pulqx_ISDxVBXl_YuJXQDmwW]R_=UYPye]qE<VwXj<MyFuophL]XMKdXuIqupKSuTfQPVEsdpO\\MQdLpchwlMYOIQoeYyHRHdoIPRTaxCpxspVL@OZQtL]uuTqBeWPLx<twpaSLdl?usS<rTql^QuDxukdmD]pcDuupPtiWxuVohv]ywCPmXEKmeyeUNrUR?Uo_\\RKiSbtUVmPTIKXDqCXKE]jZPXCqO>QoaYl;uoTDxq\\KvXw\\=uOyw[Yt^=quIqZhjLlWoQVcxNOHODxPA\\vCYrWdvE=obqr\\EvNuxthwMqQA@XPtlJer\\MvuUpG`k`MWs\\VaQPPDW:mJLiNMhO_APFTqBLVGXocxke<yG<VgPPSavkaJt\\VJtRmynW`n>=m[]VJdM`MX:`kfuw]lk<@JsItGTQw]UxPLW@MwUvKTOUqoQHweuXSLsmim\\itMHWyyjImWsxuSYR;mui<tneyAeRTpsKDVMYyd`UGewZ@qTPwSAnHlua]j?eVf\\w;dUKhnSHmRxmRXLLdymTRXInrYmhHWGtygUNrMqrpthqVQyKbdULLuC`v?tkJ\\X`LPA]yKPmh]PgqP=yroTy`dMhiogaSMySnDpimMSMMSuk^lmWiUwHq:Ar:aOY]jbYTrUY<eytLvRmoVxuXauh]KJDpw`Um@oaaM;<oAlP;eqeTlOPkcPkbPWOuxiaXKelR@OeXnQ@xIAKxqneMy]yUTAWxqKHhptHqoXRduPSeo>Lx<isxYN[J>qvQTRxXnrimiHwG<OTAWXyKHhpuHqoXBZI@\\ng_SV^RakQIi]HgpOaGGnmXtZ@`:ofThiU@uvQxBQtBauMhtWqkt^[kIjDphI`nRIgPnfIqcqPxZV`EGaW_wYaal`phPhC_auHpAIbV`[HV_<nkAVrX^^rYmiHwG@oT?wXy[DH^qWhe;Ztqk?Xn^vh;I]]XrX_^rmnpryppK]QY\\LeeXmYwodxELNEErv@LmDXAPBqU>udwYFcMexuS^awnUEyKF=_xmcwHismSS]Ss[_fXqWfI@Sb<QVLaHUcsTyEfMio?y<aEGiw@ic?Sh^OhnKHq_VXiuRSVvwFHEH:[eqmRvyBkUyYSTU?tnGDvsUVUSqUpeMWq`rPLZ<wrBPaP^kK`w?o]SFxa^rWyiFWguieUFrkqbqxhp>qwobei^ZpmB?]yAZb@wTO`AGpSnoa@rT`axy]JY]Homroo^v`Qyp;WvAV]aOqPhfVVxJPp:vcbh`cPncQaxGl_oxGOaIN^M^`m`lHfsuIs^Gg^_aLHIpXHmJA\\l;DRryv>umMhPwIpidWnuGeshmOgey@AwL<TIGerXj[@gCq]>qfI`[rYl\\qhypnpFneWnroarnthqvQy[bhuLNeCZJ:wG<WwxGdncSywBmmXtghyCd;MuSmXiqvw_Fl_HlmEC_iuIHnIu:Ab:aVL_HUcsXgBgaXUsI\\HWaHowXmagofvJYdESYVYYZGX;;BVwT@]Al>utA=XnGxgidGk_bQlJyc^^_@?^bQelBY]RQitjUhXaIkwD@YVNcXEUUuWUkUXoSWnqhl_xKow<mFRESPeVLIrlYHBwbTwy]GGpMi?GmaHR^Mr_mLyuOump^mlPMl=ESahjWyKp@y:AbXQZKqvjqy:PuvWx=aaGhiuWhx@`<gwXpwcglsow>>jwGb?A:efmk]<OAuqYdYOd^KGkhXi?ymlI\\LyieIQ;Rn_tN;DNubDKriCqYpYwXLyqrT\\mn=o\\xY:@lNxY:hxbyMtapOAjUSvWyIQIiydx]cTiV]sWHUwTih?Gskwdg[GggwYgsPqS]QSu]EQKH<_YpyI:oE[CvB=SHuDpAe^ib?eGT_xTgb\\EDqYFCOujkCl_CDes`YwE?FGQs\\kUGMubeg^AYyoT`GuUcFAiRUmGp;FaiBUKcueXaUDjYe]wsAkHXuGmoY_uHuiSLCcJwxXMts;FcMBIaTXWd>[DCEsbYEa;ie[IO?BbwVkAf_Cc[yCQovreyqkYJcYHUYrehSQtSkW;Ag;Mt`Ey;ErpWeJ;smWCp=TyWIhixy;B[IUKAYyYbvwvM]IeUisibG[uquxIeF@Yeuyfl]wi=Y@]xIIImyI:yXtyckYFxGDWYTxayIiixYTvEWRqFHYeu^kqvxIgvRwujakbymmqvywwnym]ybvY^tv^vIyYXywy^rItZo`jwUJqSf::::]ib;xESVjyQ<EpwIruYkUiyoxnrun@qyXItHQmMEsfqndqTaQy`lwZIQH<xkXTYtoShwVTyVtmM<Wtht`TJqEXi]WP]TJaTS`u]mv=Dnx`XXHn=HRT]jkxseTjhQLs@u<IM_uXZ`V[YnV]rH`n;HjK\\M^UTuQktQMaerY@XRtmK`ohmonyufuY^lrpHjaIyuXxeUuRxXfTQy`jVyrhTRyYxfHyPIWcpOkhNl@UsiviqqImxlIvqiMkhlCQxpLlIHXTdUb=Y]pRLiWoeS@Ay]XPs`xHluRaVTDxmPQP@T<ho?Qpd\\RZ]x>`xdppQuyIlooTYWMkc`vxITu@TjARkiU@]vWMJ<UrlhJ[=mMtsSHr;QvRpSeUWyaXx]t[yQttydlRXPMKyqaisyxwnyMvetY@xFJ`yInr`@rfGvyPqyO_jvUVfyOrmNnywsSxy:vqLyiGx]jaKHILi]ib:Hu=yinCOkvUWyavy:FvSFT:vKZiWywuy;R?EDZmWeMcyIXiKxI]yuIsUgILKwnkyYOrmeHIuCcAdcutLurdQCc_cFyVHWH<AtuotDcxAEwTYTReBgyP=Z:vbEky=jIdm=qYtXrygbop^Uxy:>^BqaLLnahgwq]yvJwy:noJD:KigQg:wEogvJoSpsrVSu;ySw_H_cidqisGvy;rmWvpUI<[HU;CLQwZyWIMyL;EIaIjoYwKHxEFIigxCY]WeMGww]WmKWFqEW?FUGto[SH_IucHDuypIt]]cYIEsovQebTwrB[wMyRkwrgCsw[rLAG@mVq;g\\_X<EGk;H?QhJ?fBQDLwSSAHLORrgexicpCwl[WnGHS=BS?CP=FVGB:YeQkcssvUIUB=fnMF=[sKyvAAcaYBdCYvYYP_ei;HXevmKfUGV`KgkwXBswgutIODiiVJkUGMhc?vv]tKwbP=XF=su[Ts?TkIS`gfqkwBOva_TvWrcabjUEy=DdueiGivgyE[bjYCQui^mXGkcRMfpscrSx<GE^MF>EdkydWGdtgYJ_ExEdyGH;GtW;svAejyROwYtiI@csiOu^su]uy]aiL?BlwHWmEVqSFOyKSeAKsfSy;OftwCBovEkILAwg]YK[If[Ggww_?x^UbPAdwQHc]C`eVCyx`_X<;uBaEDysWIRcMDdkyZatNarj?YACdTirGiUfke\\YcgygxubfOEVEx>kvw?EmuU`CgBET>_fIuEqWueEu?Sb>Cc@OC[CfsEsv?CkIUoIDvwI@Iw<mwJKtqmxAcsZSU]IyKiF@GpwmWwTx?uMZ]QIiTkaJcyMCXnpDxxHNpemxPStuuCPst`padWQ=oJQRCpovquWhr:hKT<txmWuxtxXxNixiYuemYuMYPyVTqkBYLuElpLRmQ<FaDqkDhiAa`myimwy:>bAMZMrKQSY=Rn@OdtmiIqySlyCv=CDwInmwy<TlxSv=KDaUftxiDTNyQnloy=JbEmalY>dnYLey?wRvYkI>DQUHJqxUlEmYhxeyY:dpcdTYaYMMw@LVEuY[\\R;<Jllj^twadPReMe@WfQNvxE]uy;bQ]wy;Btgp=@TOClHXy[KioPk`@r]mq^xY:Xsqhy=vutqbbWn\\ycvYqy?Ugty;bnaSKcuNkh_qSrYixQyqoqcyMtUsWG[ywrgyswiiGwY;WKstIAxqeyoPyjUty`xPXaLvy:vkUMwwy:>bD@pXXVIxNED?gtROR=cr>IxYOHZssc?YgChGyH>scFwVB]ISoyMIfe_TuwDDeyKaxNSHL[Xdmub]V@WvMABV;r:_y^KhswC?=h=qwWAUrYYuuUNcIHUYwqupauRSGqCdnyO\\]XSMMr]VI<ObPym<pshUCIQixskITMiWi`XWqtiUrTqNodxdQtgxpRiovTxHdx;TKc<VjPr;LlIlpsloQIvQpJntWK<yhtuJYqn`TfmOQYtOelTPUleyxlvrTuLEQiMO=aJD<XHlQ<=SF@QZpkIEvpUnu]OvapjqqiDOHyvwpqKaOhmW_MOQ`YILKmlP:<j^MLj=jOHTjeJ=EVaUW[EViUV]ewOhpg\\QE]lJ`R;LTnHT?dt=<J:<J:HoqtxJIuTiq>MXfHx\\hvRpXyqqW<WpMRgeOSYPV`k;dssyVEdPGpvMQvapj]TjJqmdQtdqTsyY:TP\\LNnPvKHNm]ns>fVPZjw\\rFraV^[PqOq_hAfP@cUYypNr^N`GgilOZ\\I`OilUowFXhw@yXvj@>qeYyegcKOvkAZHxiI>wtPiDYeN?qmq\\pIx_GZUOsuvp\\Npf@funZJxvB>oRQ^]G]OqihYkyHyRVyAga]vpyOxsvsDXprylOGxVOa_gn?psmpZUhfofwnq\\t`uThf?`os@bEhaDiwgOs;`nDF[v^kdpoRntMywM?dJQfXxtJOqUW]eA[hoghw_qI]hfgS@bCogxqfK@faagPOouivsnuAai>HwdqeKFPqTAwSUgSxssqeCguW?es@kfUsDG?hOkwioWPSR[CB`uE[uFecd:YivOfywrnoxxChgowGIflIXUCre[uU;W[sEaKfn=sWsBQGh\\eBYqVS=x<Eyh_vriFwKk@MlpYyYiXwaXsHt<PKJqyEDVc]yAMvqaPNij[qp>tRkEy_DR=QP:HRHDM>Qwk`oFaJ`epWEp>]WjlUPQypAY\\`RGdTJ=nE@ZZGZbiZPGtnWsWv^Hok@qr;RDafZQtF]CCawFwRPkf^QDA_VLCc`uWZOfsQWQexT_WEQcAUurqVH=uoSy`ITo`TXhnv`qqLLEhTNevPDTTankXk<<TcDLsmyQMmq@sfhR^=jVhJUyPChoHXQkmQYtkXyudElcILbeWrQnl\\taUP]yOXXNEgeSnjXq`LxbvwfTHuMHrT^\\X@_U`rZXwKNwm_qGW_=goXgbVnmQ_uPGk_G\\N`]vinpOlUW^MpcOayYVndgkVvtYOuK`u@a^EVheOoWWeVi\\qo_BafHhbpgc>il<Och@Z:>ZkFl>wmEfpEfs]Gvihjoii@wixNyuqbnHqsxlbwelvb?H]UAZ:N`C?a:N[cQghhmcgg[gf?fkO`qPotpHxf>d=O\\?@cKpbO^dHNZ:@:oXe[t:CCEKRj;XmmuoWVeGs\\Ch?YtbQeHchiEshugZQtX=EdOXE=GgMtRqYJKE?KFiywDSx@CiOUevKS=[vhue>]Dlustiv`=hHQBx?wU_rsmt]_TaAYXwTAOevKCs_ii?IgQDDSFbIYsqxZgFlmCG=bmsuMeWvesydRt\\TTpyElOXAWjQUGip;UtoYR`HyLDpBHlu`oB\\rdlJZEj]lmeYaEVwWvc<Qi@gn_hqEAuW?u;iae`em`pgX\\@ao?XsLhrpHlL`rVxv^NmFitvI^\\PwlgbgFsOQdrwp?pmQqdtppRXosPhG`^lW_N`[l?\\WXo:Ad:NZth[xNtPQr<qUtwOhpgjj`R;LLn<t<Pob<V:>ZfA_<Nif_mc^`dagYph:`ayPvNOaPHlfHEgu^QydGitgCTiyioxegyPcsTKNsuU]MTP@r[EMq]l\\mnGiRxHtpxY:@kgTuUAYWpM;Dyy=JdXr`hr[hpder]AOIqV@uWypV`=YWIm@lUjDsWHXXTwlYx;mqX`qPqSgDXeQxLaQCaqJXkSirnPL`lpDqx[aY`<XO=K`Mrl=kt=oZdTviM\\LWiaMQUjNqK`uOkpt`Uemwgsvdlovm^^lW_lpgs>[Cgd]AZ:>_;vYQRgqRmyTrYW[nbioapYyA_psHqQ<`kG=J:BI;RDsUPyI:=SAIcyqwauY?ECUMi_ggogCFkTpqTkUuTUe@AH;]CBcT]cRReDJ;I:<JultqTky\\fCwy:noayy:fbCS:;LNEly=JBMsygxbymta@AaQ^YIwyxdyUnGGeGbtyRvWyIQIgydx]sTAcrsdA;cicWQibL[ixOiXuDy_UJQgfytjYuD;TJGB?ayHKT<SRy?tsYEmAdEGGeWgoSTfKxRaEE=EQSRuDPj=xtQv_pyHiTsymjElGIWyqmKlTouP=xJ\\QlrUlLmPwQl=Qr\\uyC]qLTUdqwT\\mJTsopP:aq^xUqaRSdv]yXOHrUUS@pUJ]K:HXs]xydk^uYaQwy=JnIpGyY:@jKHtwimexY:@TAyPxMJAEUbqJx@WG]VyuvdKkhsy=::drqlY<fl\\pZx@gGafywfdwy:^xkfcyAZ:HlKiyWXoyAZJirqny<vb?On@:::::FZ]y_sq\\ivqVyewi[ew^\\q`OPoXi]y>dKA^uhg<gs`adTpspY]u?kLidJGrFGxv`cg@ph_[q^[cVdqQoIW\\SQgK?gqNhIgoCIhT>nWI]phbGVxHVv_HgGvaQosyGVkvYqHawUgqTEARdIHQkuN]tf[yeEFwYFumSwMDyyscAxTuRoGViGS`QsGmhngCTOhf[riGc<mWlkBjkcTsHvgX]Ygcqg;IgrqDpYus]gnUCeUiu?sISsf_cusw`Qhy?buOW:kbluFhAY]=dcOIxAby_RDyGv_bHyDuUyQmsy;B[WvUsaE@novj=>]@Aa_hs^wia;:rd:Vd^oZx@G::::P^@JPyRpqhxqjcvqjmYHuTyQw]KmyY:<V^\\XSEJiYuy=JJhqieyuIsy=JZLm\\exYdJaMWpQm\\HWqds`dqfLK[PxCmxRqr[apkgnbwnKcOchw?bgqvy<L^OlyEtMYTUuiXH;be[^bqp^Xty_vSvZLyewi]gf_q`yvOwYfxLy]wq\\OAfHOip_ycodpf^j`kkGs<qmxnqYhyd?bkWjcqeGGx\\wrF?qryjapalPyfo`eOnfGcov[HVcd`r^w\\>glOOb>fgqHovVvNFZey]^avZWjcQctNyQqkdoudFxNP]wiqrpqypkMWhog^wympQgsqhjIrso[FngNwl@>tvhj@WxmQ\\B>AiTkwHG]Ilob_=WrkYwcugOfuOYMgSDcekyrTWFH?IT?ypCyf_S^uGvsefetighUqROst=Uep;h:[TwSYIowXqyVYXt;Dyyc=eVrwr@mWvGb][ypqVyGuDEc^OYEYDOUUHodtghGchukdfic^=Tl_i=gCHCHm;t:ErWcWYQuk_vkaUdsdqyTXgsNMY^qhpgGa;gQATI]X\\EwVawWgSsCSBgUuaEhUyQux[[UICUnYXbIiasvrgHhyR?Oey;Sg]Il_GgmgiSFEohXMio]ePQSjuu@Oh?eYsuM=LLhIvmyrGHq=]xvhxPImbXUvylSpOoeyuewa]r\\qwdAw:uopAsTPq`lxOaJhMjbLT:mxM\\J:`Y:dO:PyrQNvTuSExi\\roExghwg`KqATAiq[EjvdunPSpTUiiWKqKK=MLmmQHlItw^MsvIuBLjOluoDxadKnUUYDl>QmhDPNLUvxL]hsypYCIsTlxReTVHYrerGUOUTQiuUgprViMuMsl<qX\\sr]XYpuN\\NJLP;am]ILxMYtUXXEp`xQkmNGutPMjutY\\Dvv=PEHv``QyivGxo\\MkaxrNHko<N`mV<DUELJHYV;UnmErE]oipRGLRwttNmthInpXt_APnXYU\\vNIQGlo\\<LmLp>MoYyXFLxDXJHHJ;]LV]OtmUIDMLqq]`yaAo\\vl;xrDxsCpnLighhhgN^<IiignTPvwfaFvopHe^akC^fFpkgXrjFfn@l@>[\\vr@`yKWvwXcWwpQ`exhi\\Nte_\\TPvXi]tNdkYeoPlBytBnnPN[EI_ZW[Bwr_eRCcskfAQHZKUbYD?[T;kuiry;bQ>ZbqTIJOwiBQCpukxiKioPsJAt:W>;bEyhwPwYMY@Aw]LvIaiyAZjly=JLUP?]xMAeqWrYiXy?ymPXQIvy:vKdiULZdRVyq=yuoydeYrFC:_hPWqLxY:xkUSwicy=V?=UIpKAUT?]LPgb`vhbHraYuDHxYA]SQgxpakq]MP^rydD?qk@pp@qJHwXp^g^Z@xdbnmaOlEH^^WuJ@];pjIiaeHueY\\>qqPrsMfOKSwuy:STo_d>oTBlPSmxMHR@uRNHJFEwtxMDdXy\\KbQqYPJntqGXubyLThtghrghqoaTK]qDHX@@upeRUpNOQTZ@v]uKFqtQYRWTmKATvpOPPMePuoXWXmUWYSpiU@enmdUEqQO]O;Dnv=Tl@RHYo`DK<qrb<OJ@O:IT:YjTeM:IlVEm?`Q@@L@hSa<V\\QrMlkmpkOekeuNGao<TxLaLGMqVprChLDXpfan[YmwYpI=NXeRhqmN<trDWKAOcdqB]lNhmSIsqpjaiToqpwDx=QuYUU;IX`=ucEwKLx[TrvQpxXvuEUjEj><jJLLNxMvPvy<toYweEOoYqudWxXSUDYEEwpdo=TMuMrHuUx<RHpVNlnBYY[DSdHpWhXSYvTmKeuUeiNklTAujsAVgMREEW]YYRqwXmWPdYHES=prTaKZDLV\\KQmqOAOHMKhlSCtJsPXumqH<TYHsopl\\AY?qPePY@YsCMNVuoMMp^HwBLV<ELr]m<\\RhqVImRmdRshtVhl@<lAQsFhXaLtH`Lo<J[Tj@DPnuSK@wthR>IxcQQ>tPLiqt`uOtk^LOL\\tP@SsmS;UMHUMdLXr@QUeqrloUHvIaJotSGxUdupQYpcuxGUoDyTQdSNlmUURuTqkdJB<JnXkvhWBikr@SAmn@=RATX?]LJIJDDP?]L:PVD@OZPJD@_@>_?a\\JGZVwvExa^EcyI:ixVyQKMTQurVo\\y?sAGCttmyi?GC=:B^cN:PYnCGfNiByjQC:]hcvuyukkwy;be]yYKYkUw^iXvSWIkDlgGE?EJ_Y<AEDCGrabsWS:ucdaTW?IAyFxaVPyErYuy;rRmDO;tTwI?wU?]fwYG>yI:[hAQxy;r:yuxobIehrybxARpyErZl?psxorIdrqdAOuvXbyEJquEsY=yI:SITqyOKvYKy=Euy;RZyWyUFASgEQeyc:><:::;AXnOhJGyY:PrIPRlpqOMvYLy=Duy=JZyWyUvAQUvXRy=RuyOviky=JfAW_EvjIxY`YEvy:^uYgyGVgRgxoVsrqm]QewoZgqgnXsBGfdv`tfehY^`i]@vuTGtuycBHZ]qbkxrwqiyAZpi`GWa?fxoFwyO[AYyQ?ky;ZiNuvXB:RTmd]Gyi=yK=YPybT]y=uY:Syi[yGyI:]wbUiQ=sy;Bbus_wi;yI:gIGmGPWwTwATiJB:Z=::<HH@ZOFlpE>:::<HvcOhjEQeQay;xwyWwTycwAZMY\\b`yevaMGqQqcS`h_NtgP\\mV[hifvHs=FgaA]`apM>oAipegcbw\\eFwyPxFVJYcyTcUqyxfHoqAty?ep`XMyANBqqLxY:@WcEgywR=O:poJ>ZKiGCRyMgNItJqyg;uV[hGaCLoEWUxOkdNIyN]CMaI;QDRkXPmf;iurySDuBdUUE;xVqxpMxVYEW[ikaipQWEsGeAGY=DjWB?eIN=xOkst=vNYyUYygIIxgXYExkIVUGi_mRgmb>KdU?SgemcDKMLslHLjEYlmkpaKJDQfmkditwqQO<V[xPqXlUIKhQLTmpuEO:EWYUQMIQ:aNF`K]an;`T:XVTqO:]sWDR>TQ^]xsDwCAQaYQHpynxwfUQxlqemmy=jcmwYmydPpoXUy]KbYxUIReLwlQUC=XkQmo`RaUJr`O?EsB@JVtlwMoulMG`me=PTHVBPt[<kM]taUJDg[rH`A^tXNgoPybqlQn`pvtQPt;gavqrE>aXQxJWtBA\\s`dUNpBgdaFwoI]EYlX?x^whqntLYgUh^kpdsGrt`mFF_;npqFcB_^c>eEA\\B?]Ia\\moo:qgiAf:n[=i]j>u?qfdOq@VjdxuUyedOmpvmughcwkmXcm_gH@t[ypGVq;@rGnswNoE@yM@rcigc?htYwfxhFWsXFwhHbW_n@N`i>e:`^__nDnZ;ossFoUBv?EQytPgGhgtLEbSyvGaSZ_I^krBcE_GVBOdkkDs=F]sVNWxh=bhuD\\;rhAegqDywYYaYLkWuqHhAynssOwcqECvospoDqgch?xHgWSYvFsdu_tcUbsYcqKf:GdP;DboerCw^uDvCuWvwhhgLHrSwn@nvvGfB_[KNqDWbJfn]__=?\\knmbvvW?jVa_BGr\\wbPyluWfUVuhpiqyiTgrMixipZYiucoxpOqli`Xin`iyHHuiifHHgF@imAZG@sjwdZ>v:HhBaZPwvpidi`]WYxMiydneuwitwkb?lF>soQne`pEfgc@m\\GgpiapPvXvfhwhKxmRPmjPangrTGge@nefryAZ[V_IPyoykyAZ@gpRgaGvdEpy<wdYfxey]xikd?ptO]R^]q_rYly?PBcdRYLly=j_YuxIrtypxILTXo\\pm>IPYuky=JQquy=jQqjSxiCWgr@xQ`yx_uyAZQatYQy>fd=aywvy:feuwy:neTvfxQlQIh[y_riysxy:vocxqnA;MbukCueEG[DDSge[cbONVQJD@o\\<VNDT?ul:PND@OrdJNDt?=rbPNDlO;dRNDTjMkbPnE<JKebr\\??R:]DVXXX`oyG^WjWysxCWeemkufwiJo[qwatQ_D?gDVZ_HBJ:xT\\xY:@WMYtHdL>xe_vawuCwqT<PUxY:tyXXvxYq?yY:TnPlPIyu@APoEW>lTgTO@PoLpR>AoCARKts=HQcxkB`omtyXPyYly:HSxiLO\\r@drOxKyEkOxlvYYdyY:<Y=xNrITyEkO:Zbhv]Gqkhb]wy:Nr?gfyeIoyawI:MhycrY?XKE=:DQRauRQ>::vI::_=::Zy;:bV\\UYImyGl\\WywiryAZJqtoxsygoloqantgpgnX]u@iZyqPgh:F]gf]Qww=^tIPgLqa[NpCyy:vbNQqyAZIalYtJQVfiCokXker]yq>PkEmywexy\\y<XLvAoy=j>:VZa>yKOsDIqkhBNRbI:xA:ZlSh:::y=:Js:::rYHnlxIoxawY:MdycRPEvlovosAJ:HGVaNwtfgvMq_\\@eo>ZXG]Nn\\m@hl^doy^_@gi@dxflgh`[haDOui_y=@^tYcyAZ]hn_ppyu]uvJwihAtyDTgIs`xY:<Slxk^xQtMQTUekYxbxiQACcqdlRH=yNTsFem[AsZUkKYJIuulxMcATCYjS`RKaUGYkB\\r^qnMIlVtyLLMLuT:AXTxx?pnjyS>qVkIKMAvqTthhXGMRaUyNmuQeWJUU?akHLOltqrQl<<UuxX<<xRDl@Ho[euPYs;mu^Tt^PtNdueMmfMmxuKNtLgxQRarBLRe`oYTQV`vsmJJmX:<SV\\n\\eQEhV`MXoXQjhY>xY:\\Y?mmWmur`thHXVMVvpmy`wuYYPaYF\\KymMrUsOExWFaf_aKWh]`^K>m^AcGot^^^ay^CIq>Xil?]wyZOVlkYd<QmHYqbH]nXsOGmh_`C``_ifvXyrvpO`uKh_<avwOoVYZGYqiWd@HyHnwtGvW>tyAZRhmSQyfxivibhVsyPyCfeywukvy:FxN>_jV`vWb\\xcc@yAXrtQocolcq`OhofNlHosUpuNIbrf^k?s@FcQwxw?i^nxhH\\vFZ\\Ymrowfgo=Vkrg`CfhPVxopdLX]pqyKYcRQlR>mKPg:Y_[fgbX[pnc[AsniuQxinQ\\txYwwRyI:?IDmxWyqZhlQiYmyMyELAUn=dSouk@@yllVYYLYqNQpWl@ypPslmRRiKnIYMaRu]LCUnneL:MtBukatPTyOvXk\\Ik]APlTUEiTIHrwXqwxpYdwEqYXpVNQVv@k=\\OF]J_uPBAJVIRcquOPpiqY<ttYyXFyY:bGuty;BnOttwYxYvy;B\\\\VZIy`HnZuuP`uGMvuIv_XUC\\QUeVsUVfdKwEMg=qI=pfLLqDSNej^\\OsAq]Ul@YNZuSN\\u_hJTLUTAKnYmEYSUIyGPt\\ayGAO?AykPnoAK;DM<uU=DxAdNtquEyA:ju:byjQHTvemVTrREx@xq[AYhepEYuEYOr\\oG<VuXVP`lG<NqyJDYQ>=y]QSJ<tYHq?uMD<yuaRtLuRhnNaOLUxnMlWmUEYmXiPvEJ:=U;EyOLNklO]]K=mwRTlUHmmyqlxwx;j`Xsy:ZcNhjv]oorjxqoIwIy]gYtAQc@@aVnc`ol\\IgVxr_ivpakFvvradNgt^hdJh\\\\yy:>lOxrwQiAyy:VnT_oXnJxY:@lONYYN:TnTKUf]ky^xiey`wYVoyGwSNnIHkyNxgyy:>fwuy;BLUX?]xM?EPYy[y?Hv_xiLUusgDOy_iFESidwsniCCAIx?ceISrYixQyqoIv_xy;BwgfhqUBkfuystgyQui:OcjqU_aRgqIKyrvwxEqIu]dwkvIIIiytwkheQD??ubcf=iWu[sYYHXywu]wKoHRyQIAyyxWk`UP@O?aMZhXyHw=lyuiRyiYDpQMyjvyxEpYuiLCQVFHTDu:::::::::::::::::::::::::::::::::::::::::::ZVwxD`fA_tnOnH`o?FrHYtYHy_g^Mgr;?`yAZG?pqIqyep_tN[w>WR_SrQ_i>yfyuw>nbTHmtco=w\\wiJaty;ro?wYKynSd;y`A]hHXKqPESaxnMpTkdXPhtp`U>QOCLv^XL@aq?eO]ty[Ylxemcuyy=jQ]YeQQQPJHyscTna`TOywq<uywmeycuqyYXvAWufyiaQyMqYXTvUWe<pf`vtMMldYGqTuiyI`YyMe:vqcqynfixxrxyigxaiQyygkP>fS;::::::::::<orasMHvE`wMtxQtY=QuPIsImuiaRPylEpofivjiV^IxWUUuPPhPjFanwixqeoYyPRyMsqyoxY:xqEmyn`WfWksna`xla^tOygq@eywsoynwyy:vekYngqxyVxwIgyAZyWtvIgSwk<osIGo]x^NiT\\wy=jaQyMka@yK;:Kuf]rSICo]x^OiTiwpSqm;FtpYyY:;:`o:YpMNt^OyTxopYyY:Zw;ZGP]:hscwkpiaiy^xia^ywxIsbXlryiDnfkXi^OuOOvghvmX\\i?^:nc^PLSV:oFYyujkyYocpibg;wOaxYCq=DwipyHf_q`yvOWeinpiNQmi_YJ:HtLsy:>Z\\PufH[?i_ZfnZPZD@_ZPZD<::b^gf^;vDE@Qs]Z@gpRkeny<wDv=U^t;FypwY[_yAZ^pFj_sZea]j\\JYukywowxy:voGv_yAZCCd]wy;ROauy;rQ_wy\\xBXoQ<yugiiiyrGgyOyEge?wKQwaoYyivy;BJOVfgVsCTfED?cDZ]TKcB:]TK:::::::eTXywrqyMyqQysxQtL\\OOIyyXVuysyweyVyDOc:Fmx?wtQ[<xasI[IKi`b:VnGocx>wte\\qDXESYYy@ifp[bfYDCCE]Cy=]FZssv;d>[F@[BJ;SwCbSqVsEty;BIAyy;biETKgyHyTxIYVyI:=vfyqrMqYIpTyY:tsuxKvikYxY:XKZDkv@qyxVTxY:teX^eYWxGyaiIlKgyHxtxIiVyiZagyAZvieYVfo<:::::::::::::::::::::::::mYVy=rCev?syvYtxCIOyuRe?:vbRiwywvWxrxqZIyy:frJaZX`eY;XnEY[m=::X;:j\\;::::r?::E@::::ZQ::fR:::::X;:j\\[W_arxy:vw;PdinuVvxxipY_wpwQWxryq;X@?ItqYAYGyaqy=JZawy=JveU:pnUtyZfi_jbEWciG@DuTByI:]XU_dBCCNCCF;GKEdDQGh]WsMvCSSLss^cxwGWIeGg_FgSf^YEYWuD]eDARZ=fj[k\\=J`\\LNum]ipy=JXtxY<YUxQyulAAUgyY:xvWxRxqjIyiE@nC>wbpA::::::::::::::::::::::::::::::::ZM`wpwQ:J:hRyEnexkt;b\\KBRCFl]hK=HqEbSMEc[VuIBBUBu]UlUiNwF_uCZAiiCsyhFjKFdky^xMpsY`KKeuNlx_pKrYyxKvbxJw;>BmwYIviQyuyutJcOwfviOaeyuoSyioI;lrUelLdRNDTLEJ?]\\<NK:::::::QWmyqIdwypYxxY:pxNdl\\YoGuyYLuy=Jwayy=Jg?d>NsxGdna\\oxm\\i]B?gxi]Ni`pwck^gg_^r`fAnlBfjBxsXgudhmxHk]YybP^rp]ZNt]Vx]wdRQq@?vlV`:hc:a^u?lm>wdVvHffu?uHiHuTeauVaybaIeaUryI:yB]IEkovMusI?IMySx?s]kyKwGB]rkKFwynCxJy]nMmXx=wXEUpqV?W]xI\\iy]pIx`>lynwFvasq^ItKwEBAuI[y^MuIkYCyBy]vKawv=TuivSiy@cc>;BeYExIdI;CsYFxMDWsv]oiZYfyKdcuDTyE>UUUGuawi>ubBydEgSUUFcSU==Fagr>_v;ww=_x]IeYKWI__=Ir?i\\=WrtQjdQu@fmd`n`g`w`pDhvJgxKO^@VZjqsd>ybPgHasKa`OAtJGacIbyAZvntdvy:ngeoe\\^tnfmYFdmXtMpcBo]SogfniLafcgdRhZWGwn@Zt^vlQiJgl<Qdkhp?Gdxv\\kAneYvg^^y_u:vy:Nx?w=QFxihyIVEIsy;B;Iry;b^MSpiu?iS^oe\\;GY]sr]soGh`;dxKy;yI:\\ly_jUor_GpyAZCnmMxmI_w=vYMH?cguqSxiBxAg\\YxyLBuuY=yF_xY[IJyUx?s_wY>yd@wbaacnyGv;<UvHOfyEdxQs<Ch@iE]sSI=wQQy_wbB_XwKBGqyWog`sHTGi?evB_Dm=GyGYjoh=_s=kSeWxjkxRWWTqHmcr^gb\\KsugHc;GwiYt;TjSGKobuegrUrKMTney@uSFcCt;gFMXIqFQmf@eDE;b:CDjPq^YxTqOYXkrUtyLXsDw=YWZxMxAsdLpUMpsYKNetI<Y@]qaySvqTTtRWxY:LV:[i^y\\nyovy:FnEQcyAZ<aiyAZlUEqc]wYKOIHOwAjMmYMdqatY>xjy=JLDoIhJvyvJAYMIsy=J;Ijy=j^GgVy_^AgkwbOvmyAZBvpFHxyAZ]nmMxy:NJFSIgjwwFuBYIEcyI:;IZyI:N]qg\\vYknQijGidXZ<qmnnrA_knPnIfy:w[yAZ^fdYF\\coqh>xpYjyooV?iA`cNA^Miw^HqThunWhCNlnV]WXbsisnhwA^]TFga^ts^whGt:wsmWlEGcO@qNHh;_oyX\\YccMe;GYpebuwBTUerWBL[dvOX^=CUgE=;Y^sh:KcLWijWelGYceBJkuRGX`Acy_RyESYGFZyUxLSvyO]IrF@YIEsSHWW@jy=JleRPhu?]sXQnbxi>xe@yMmStyCx;sIsQ^lqPHXXHykqMLxa::f]vYkvIdNwa[i\\kIm]qyMfaevy:^:RDaFxQuk[bJ_yk?Yi?cWCDEASY[Bb_u;UdqmeDys:?tfOyCAsLEw;=gdoT=kYocUAqCOCTFUWsCwOOC[CYZ?s;=hxWu:[ydywjOdLEXQuc]qcrYDyqwYkxIgty;bnaSKyb>yUsqhy=hxigy]f`QcbwFk]wqYrYihqyqeUrEyY:LtTMWfxY:dtVyY:xtfyQt]jOYSviQyeuuuYXMmYqyLtT;uWsEwIPu]PmhMUpxLL\\mvncDvb=Pjwwk_AeEQh\\@gKgdy^pnxy:NyBFeyAZZQbygkYNuTwiwaZfvY[YByckCw<cUOYTuUsIwiZgJv=kIIx]TYEysyGbEvavA[IGxZX[ngDUA:AA::Ru:rr:::UA:AA::Ru:rr:::UA:AA::Ru:rr:::UA:AA::Ru:rr:::UA:AA::Ru:rr:::UA:AA::eeQYExwynyI:QysyI:MULSdy_xn>w[vfyAZ;H[xi`YVugn^Na`nqjhQuPWyHoh^PsAq]N_mjAg=v_\\qcyFvV?iMpy:yxYOy_FpWofWPoB^xUa`f_vUgbyEbYRvSwEaRTYGekuSadn_RR]biag`mHQciJ]Y_YxtstcuVvWCCKtO?hxST\\crTobfOUnOG^OG?srGAscoetEG<cX]qvQmE[CYrqc`ys>eSasCxDVEeua]RQMupTlkqXmIPEDUw=qBEWNdR=@sH`jZql:eSlIKkYp>mXc\\y`yqklPnUWjmOo]j_hv:hyZ`N\\xLP@ovDS\\@S^PO`lP\\msNxMOpPh`nrEkjEna=xxektXJOPld=TjxJUiqwqYNdsa\\rSiTP>\\KinQ?^lpqgXZ=^kpIacYlIpcOyeNwkmyovpeYIswqraVkx`_rokWw[>qpkqecqdLa^qo`jxrbw^E?qNGw@Hvig\\UaZfngpVjnhioa_]?f=>gihrio\\VAipxwC?pk@ptHZhfnpppRwy:ni?^nCpq\\nnGgv^ic[yhf@fknbUVt`y_nxpkivfxtLXrZisZFcwWaVaemVgkF`sg]OWeh@i[O]_OijWilqfsxYEv\\]E=]yIEFGExv[xbMh?eG?_ERMGQGfNkBFkRjIrBsR>=vKexBsYvqyjqheYhuqseEBxOwsodnyDPmf>qsHMhquTFeDLAuS;X\\kHs?vQUBBAsAAcc;DBghcAgdSc`UergyxcCcwI<YDwYWF_wA[BeSUrawf[iYYvUUE;QE?]sKQgjOG\\;W;[t;;E:ArpwR_MChkY_?CgItjocLMRNAgEoIiEDN[sD_v;CsV[xNoIegBiQxucrduTPIswqry;b=yGswFXIey;hwyex=sDsUOYr=Muikhyyrncs]kCMSEU=Wg_c=WvRUFNwVY]uOEhVULMHwUDRodLjAQh=XeXn<ut<yt@mQcXX;UNHqmy=JdaVyQkQ]ykuwVqRaHWiDueQq@HN`HwjLWJxugDq^UYTARk]pBISyeOjPkJHu]aMOUtCeQ?YqWHsOYTsXnouoOHqrgeMye>q]aFfbxy:^fXIwqxlTv]UiopIunFl<gfn@uSIyPAg]ilxacLvn`A^;DduHxygyEvQsIeoxy;R]icm]YN[t[?X>cfkgsy;rToT:Avk;TYksrcRycfX]sXEDoIIYUTvIckorKOVB_HAKy^OYFsSBkRGChWCHQugfOgFYYC?v;=eseBCCIFeTHgtPyv\\wgCGfnKD]oCEaEheeZEYjcD]ATXltAYlFELKyXRHu@tV?isDYmWQkaMnc]yP]sS\\Q[DMwxiBQeMAovAigYbEOvAPbL@ixv^<?`BQugHnPG]WAs^vvYHxdYhAOpWWrWp]wWnvoekajAqdPQdqycygpCIfig[n@uB_poisLIcsVx`^dDnrYaZm>^WU]CHdYBuwx;]YKGye=YIySNcxrgwLmWOSxiEu_sUEeWpAtD?RJSB?sb:OxFEfSkrRSxFkYbAv[[IWURigUhUeN[xumbmYBHACI;ywGiaigAUSOetQObDOGZcR=wDoEBj;xkkC@oIWAi\\uc`WyEKe]QfrgCcICxmerKUhQHTiHbqyYAWherUaXtsdQIw?QVgueDaYLUe;qBCygggVnWWSeHB]fBmD>GHPOg>CX[?EJuRkgUeSF^UGhIU@uSyKCa?ebkshOHrKSIuITuBDYYuwhfeIGGtIEfeEtgUFicDs;y>IWdycw=xmciewVQ=EKWUp=cZyrjYvy;RO]e@UfeuwRYwQyXtoEYoD]oBZiGEyFUWv;MfbGDMwuv?FcgCXIYGYbpsYRyhjIFqubSqxcWuWuuHgdu]bSOcOsxvUw?Chi_Cnsy?=yUcr_ghsig`whoMEEWYwMxECSoWS;EFmSHjWiVMfCehAgd;qr;WeOoW]yrkoduAWvydJaHs]iQ]VYGGKifLaYt[IUAVNgugMd:YsuuxWIh]SHsWuC;b@sxPyf?KCNscC;wCuhkYgT]skCrVIXr_xbUFyYd@OwcAVEAI<iEBUdN]hJwBsaUjiI@EGuAGqwUncByadrQD_wWvuBmoVsEycKFeECS[iqmVAAiKiV\\EYBCVykFAsT\\EuEqrFGbpIb;?sGiTG?yAOfYKci[GP;uocUISsYSE`Ge^KBSYsRUbiMG=OsvgV_GTp]Dvme<?DHSrW[VaIgpscOGe]AUrkBm]wsQH^OioEwnuCVmHlYXHIHQoNMewodwx@sSQUrmNKDJaQxGXOUmqEAsL=q_@MLXKulPt`KjujNhqLlWo\\P_EWyalo@o`El?qrTDkiAOBPLDuWlXSWDs_\\t`hJTtLsuX;PKblV;\\uv]nxewAQSK\\yLIX<<ypmruESvepWpwaHNSQWK=sCLKUDxcPUBaSlPOk@QVYKvLwmtPfPrQxUm]qKqv^xn;AXSXnIqLaatn`uSXw=lMlXXVhXeUrEQVMHmG\\QWTJ[DJDqPe<wNmo;Mu;AVhlrk]KkyRlhu=Mu]`OjyWDtuQAxGqK_`PjPSqIl^ES>dWTlQCDmBDue<L@ttgXJJHM@Hme\\yBat?xr=uMNXRQqXEXyy=J\\pms`trDxlQ^jAoDNkO>bPigj?ZbAZIUOueOyr?Oexedu[fxcb?MSYUUEaGqUhd=hB?hf=cJqINgFCGBC=rqebL]bJ_eh[XukWlIhLotOIH`kHCSFv]ep_VfgfsQVRYbL?Xvih@eShyI:KggqvyPTeQYWipOPVEYKgTS@=wfLM[TxW\\RQDPCDsBdsFHTDalK<TMlMyLmkeUDtUELQsePnQtUYP;IQvUQQyk]eMdEMvdSgIviXWQLq`@JPeKd\\u=Aow@jTDx^MU]IwOATFlR=ajDYJL<SvEVZuPxyOVIX[mWwyY:lPgMYxyY:tVo`MMAY``TSyo=PVOLPU`wThO]l_A`ZXHm\\apO@_YqbDGo^okTwaCPmXilqOvOfpQA^tpjHYeEXqMOo@OegWcEQkYifVX^nOfsv]_>pb`rS>iIHpNqtxO_eqtQomZnkSapEGugnkUYcb_l@hjG_rkG]^VhZ>r:gvWqfRoZNfl`_crhts_iMW^@Vl;AxBid=IowodKQkj@w=y^sn]wHgvwuNvwOxy:FvI>knVrf_ooVeF?srprRvvVp[sfsi^fuDgGtoAxQibTotsGfYixduY[Wg_GILCdo_tdEhDKgNyBDWHZEIf?tHYWAaU_urKgidOhGSByAxc]W?IYlys\\]b:IC[AGKuR>esTet:sFvaSZYhIcHwsOB=pk<Y\\enkQrvPmwDQ:UYPLkmaKtUXGYtDLWa`pOekIxjYMXZ<yiYTuQnMyMuAvO<QteTgtZwYlZHgTycVx^pn`jWeS>Z:yihf`VoyeOmtPiPWdohuGX^kxrvGcyu_YuxIbtdY]\\pKwcvYQndyenakqxnj@miyZQqu;xtfQ]YoyLxtZg]AX]sAa]qgGGhyAZIFqT`xXviJa`yhYWg^uHCwVPEyXQXcQBW]Hc]Tx=EJedJ=R;MRHsxVKHeEUh]TEEcmmiQcb_gS_gsuUVPQTD;C^KRAacZIDdCbw?w<efaKcs?FXEg[ET=sB\\eT_cH]?F<;iZocXiX_kulAhAAsiky[OGQMiW_XcGVeIUSCgQWh;_tL_DCMUichEmrL;BAmr^sb=kspqxIKfywBvEUiCx<UWtgfpYu[CvF?ClwXOSW>MYMai?_B[Md?CEAKj\\dw>Xso<JLxjJewlEOfDxvHtfLP<LTltTmeWSPv]<QVtvYDVLEkV`xaAwZtyDAXgUuDIxgaTkiUcAprMj_lJS\\JLyuDYpVerfDL>qOWPkj@SJXj_AKDDoZDYXuuOlTcMuqDkhlYSpucupQPmFtxlduADJoAoGaQLUUCLvqij=TseDj\\`okqyoIs>uQpTL:\\NAxXaPWPPyO@ouXToTkuTuwervUuSYNWtpHXOsv`HVvsv]BhsKX^K`mFPi:x[nayensowstNxeWeEyaC>i]PcKQuSW^NQnMAveWauqjRwjJPb<YwanlF`eM>q@^utFjAa`nvuDxu\\OqXpwuaeg?c;ahFqpmqbJapKIgpis:FbMYgXI[@wZXQuQ_j`odZWiRGlBqs:_xZqiWvqHi[<nd]nhiylQAgi@^<Xr\\a`qN^fierIjUiwiNh\\OlN?gmhygHpMwZriZMXagqwBf_L@kLnnE`nvAcU`rpohQyxXw^qXthn_Zii<gdSht[@f_WxO`^lna]WrZvuTNbGXr^>g;QcZhaXXg_pjyN`SOnGx`?^ufQol>c:^ftQl:fx^VdvyrIqu=Nw]`yefroi[]vrQnleifcPerOjcQ^yXpPF^`odChg[_tSamVavYH`FH_hOwAQ`jPd=w[Vx]\\om[^_Uhj?as]_^If^Mxmc`fiWt;`cC^yAqylqy=_ybVxYVyEIyI>xdxq_w]miycxiYIhyGxdpaDyaaYyLwy:nq\\yy:VvNGZe_sywwi^vyNrIH`yAZvxqJxYOrdgYNyqYdwEwxQvy:N=SybwyYewEqiuYcyeCJgBiIhy::xE:Zy:tEHH::s?:x=::::::y?:jY:w?AA:Zv<:y;:::::Zy<:rIZx\\]=:JX;Zy:::::BCSIrqe]yScetxKsy;raUyLwyxQvy;R]]dw]ty:JJajruxR`xgMkkXtKdr;mxK;j]`w]lyy=JoxoumwilYoXrm<w>^x]x]DWjf=:::@RhysIdnYdl;mH:::NgEHpVwmlYnXVv`P_INpIHyxatyxwrxqritYffYVX:<jIuKkyR\\MoIP@:nA:w?Aq;XqMly\\\\kuqkyxVoHRp;:::;vCIHhAgA?IbqIDyA:::bbAYhwcIcfY?CbqA:::ZZp_I?yDxad::::r\\Kvasrs?C]aEoctA:::tEHh;va\\A_vib;oxK;:HD:BJarrsXNWfVKDCeiIew;mxK:jAEuA;k?;rM=VuGt;eWJgA:::JnxnAQtI\\RNuM_y=birrpQDyqaUyLyY:pq\\yi@Ao<vi>IDctAE=::birr@JYpm\\=JjLXBxjPANuA?:<:::kDaSBW?s]C@:::w?Aay:::::r>aI]CeYGE]ueDYbf:jIP`m=juDjr\\yb`Yd::t=Zx\\]eeCry;R_krsKwrEWJgAdG:nY:PNZ]SAMXQyMOdm;MYxetIDuAkyXk?yY:Vd]vbDpyrnyMYhd^aLFpSGmHF]p?fG@ov`y@Yl=>mrYlyAZhvupy[OyqnakKyb>Ux>ZjpI<JLU`cynk`?xvtYyYQi_xy:Fwg^hKocjhbjF_vfog^yKPo>WmS@mAI]AavGVhytIihQyI:TrEyY:LtDyLAQmPXN]<YAaTPaXShoLTyIAqt`q:\\U<ivF\\pPmnGao[`LJPrOHV@XPXHx=XlryjJEwqw^kOtoNdtWxgwYihc]WaGv@GTokrRsbpAVyuumIIQGs[]yYkDggWiuWv?TpSdBGfkoxHqs<gS]EFyGFWkwMeCcEUFSg_aW;UubACAwvcOuwAYIEVg[Viyu=OiJgbnECoAgFQH?GsJabhsgDWwJgBk_dFsV;eEQAFlKgsQRAkb^KIW_XWyDyGryhXbuKlMQcQmiliYVvJ?gxg`Pixyf]V?yk_yYf`ohpoDe_iqyI:MUJIs_IIkYi[;dV[EliTsICHISZ?fVGCx=XTgjDhYvYpf\\PQ@pTiuSAKXplLpvHMv^EK`LKUHNqDsYpWHxm`=VjEWmijG@tM=j:HTo<RAXJw=mnaYbuOlQYcQmcxY:tpiqYw`vIYVgTvQetndY=pr@tu=et`QqtxPwPQ>PNfQUv@L?qO:YNKllGESlhm;Axv\\KLlkSLNvmtQLYFPqNluWXqC\\KTaPm\\OQEllPOdEN<QQLDrdpKU=SZDpVDjI=MfdwiIQByQSQMhtry=Jmxkk]NI<Xt@wtAoyog=aycolXwaDxxUwlIwpKygDHqwxkHGm^hkPOyUob^Gmjnc]Wrc@dIAjt_xf@kxY^rOjy_jM>i`yg@^eRIl`h_tqrqppmIjK>jDQtIhmqfZRFyCnbfGxH@hsPj@Ate?jl_`w?d]OtRyiGp_uymtaZdwqra[ynrd@yuQvXGmZiYAxMsgfwGikgh;VqkcgSVfktJEBEcBSqGS[yZavM\\y=mJi]lCInV=wthm\\hRepQJpwWUNrMUy=OEWqRGpGF]CAasy[GNjbovEV\\sylY_xCfty?xUvy:voAGmowY;Taity;R:ygxcIYeSvWuf?yhQsduvK?xvKUn=XV]e:KxU=YaEETWGCCv]aF^yeWWDVGrV?vKGsasiCoudsUBiWv_ujKuEeIL=u_YD]GhqstQQU`_tnUx@_gWSCnmy`qd^YwgKwcSh?WSXivQ:::ZTxjGhvlHxFpeNviINwMNgm^q`_uAa_;w^qX^qytdVcjGlqNs:ik>QpZ_]DxqPvpi`edw`PHprqgbG^c>_jHqX`cfNlAGluivJOenVf<`JSCbsf==RH?VkybFQiy=fHYgyArYeItaiEyGtabdyI:;yGyI:wtfssIAyhQW<eulYU@uDjyWpiVFCtg[Rt_Hj_YXqFvsEZ_H^IvlqCSsxJCIvqWXIu]sSTQWjCGtoxoGvSWVAGBrWhxWvdwS^UcnmTkkB@]vraiBCEMIFEIHHQrnsVnSh?eCiQxeoI;OyikY=ya]`stxy:>nHWoyAZ:xuwQiuxghpuY@kqneV^m:otGqnAyic_^Eoj:>c]?lsv^A^^h`uHnZfYxDxrrYf\\ymPVgTpnsxg\\ieefckpjDYv_WoTWkJ`fFOp^Gm]@dYa`LOxjFhjhw;flRpvEn\\vYsi<::ZwukQfrsdowS>[XWUyTIdakTwQiWkWfgS[;TTEsHUIEgyfIym_fGCDlmI=OFq;VKcefQixoxQmtKyI:KReiYpwHHUDu?FOGugmEXOBZ]eEAxwkH>;RjqRhAG`ScNaiEy?>vqJixRS:JoijqDkoTWyIMdqtQTTcuXtiQVPLG=YgiO_hk`djULnQAlkXX^`xsMKdDOJyRXeJEyp>mqtPj]IvqHKvhR[YKrinuHTfqNspttPpUXSW]M`iS_XUE]NjLTltkStSwHKFmlfHYQxExI::jmarthwhILg<Yd]NBivldTihkNTRcMPCLm`LL`XTJPJIhOq]vMPs]eqhhpihu=QVwym=MudUr^XpAPQxDwNtmdDt@`UFlmS\\N^MKjyrDIUgurj\\oLUxhxQbYldxY:<vqtyXuklXwxEjtxOxwYPwoxTHpofiNkqP]tXZaNK]xEAyfdnr=KS=nOek^Aqs@LmHV\\hRKTMDtP[ym=drUYPkqyaPObqptqn;HveXmNYQTpRnDWhTnByNoluPUVxqsOeLBIpc`VhMtpaKJTxHTrvYCPGre`C<>yq:RwGRi?yA_rJYGT]Wt?TjAgi]BLcu`QvSiR]]rBWh_MtGErgkT_IVOuEm?BSab`IfjyI:cByqcrYr@wDXOel_ePcC[qhL[hMGgRQyB[SBAW:gCuWYXYH?aU;QfiEuo:RnGYQy=>RnfUAyypeEHv@Vn\\YsMXfkwi_HctwtX_eG^]mWbawhdVckX[LpoJQrUQh>yZZwcSvo@_keprixpU>jw>_`Y[VveShhyEJ:LyvXsi:jhhT@`LJDjrloa@rtxTCdXGtyLQpNaVMyofiojdOoUv=dRVtlSXrTmJ`uWy@vuMt:<M]DWJMXOTx?hJmqoyRO<JZKI::ihT;rBIWtkdhUgoaw?OFWquLqCCavLwvHgfikwDSHMOga[dm=Y]CxgAuneGA?XfMfsutY:::roesrYe\\oU[_FXIwM]Hwqt\\UtJGtnWsuAehyW]od?gSvYyjATiyDUAVBOt^=H=[EFWRfkQG`sPhk[eYOipYdP=uw@TMepRIHPTDq^@KPhOl`Q^LpL\\O;QTutS^hVmijEly_yDOA:>N>Z:\\aihY^ktiiFX\\Gq^;piPg[pVilhcNQ[X?e_NlcfoJq\\samRn^ZfyPI[O`aDxpqGXatYiBtoVQGw^USgcgp_Wtow^shK_gDSTUwbWMVQyTsCUyyXmeW_iIFCrRcsVWbkyW`BJvY:yl>Pgj]i`epYlkylEgtvF`h@y=xcJixeWkgw^IOaT@hMfwpVn^>p`Orehw?^qlxh\\opoxsSVwPN]Gnkcx^@xofPvt`tgiwR^sjyl<H_aokoFl]Yx;V]v`sgGs^_aJHh<Xh?FkvYsi<::BZNi_Pvi>kMAwtqschnIP[dy\\mGeIyfFV]h>vIopwgnDY_@G];QrKXxM>t<Ni=Fc[GxpVrJGxpGn[YiWo_kyoZPk[iw=Oa;^hJAftvvrvkL@ZfFiHqcu^];QfqImo;:::YGP]EYGTvSry;r;EYvshaUBh_wImxdwUfQFpIc:GCZOXSAbXWU<IHlOtFIugUuMoBy?dIkBoYSeCGvUYyCiWoxJOUNUH=[Idkgp=i@kRokvFQtmQb]_Eb_EjaB`SCPaiE:;Awt]hXy;b[mVvwclaykMSrGcneC@YwJSs?SB?KDfsTX?sNqR?KhpcrrShmsXvMYaMEYQtYCWtwgBeHiIdR[HPMuwGyHac>;rnqD?IvTsym?vWqG]syiiucsBa?XfIR`:yq:::jfdq=MvmYS_@wtxk@\\YsXxfxrcPwgtNNXWrhWTmpJ`QS`JkXtW@M@urx]MamTIAmXyNDdWvHQyAkxPnqYTSURuEOQ<PsqtkaPU`nVYutHNb=juHyU]MTHQADvvXsi:j]:vYRwuv?ExHkBwQYQADO]XgUbIoxPUdMGiSUCAGx:;Euafk?TFScM_HOWWJoioywjYd@qHxOho_IPcypqx?eW^edocUCqBVsh<wc:iW@KXAks;KwbkFEAdsutY[xCe\\:mX[<Jxkogg;@wyN_aihWVbYWj>ytp>xcwebOt\\PtTOvqNdKfvtP\\JF^Hfsnhf:Ow@V`VPt`i\\FxqlVW:\\H:JiHUTxm>YOGyWDMqiUJoEo^tLAeSIUVYUuixLxPR<xjEEV_<JLTR]=M]DQ>\\ttyN?UQgxM;mqPlthaohuohiXuAOhIVD\\PK\\VRLTAyNPHk:Xv_UsomRHMPYAPfYwsulY;ZI<nYVwDvY?YwSw?asPAXrugLMtI[hP_XHIc[MJEyXjDOCTN@PR@\\rHloNlouAVQIuwIpdDudmm]tlOQpl]PgqPTIOguN?Ym`hyUaP=iNjpXO<txtWXYxPmK[Au[lVWCbhd:>J^aEyot]r=SWaAdrOdtwH<uWoswCgw@KweSIUgvLKi?ctJ]UWcRKgwKYSmEF^sfUwDJUwm_btoimUVdkeLiXugtVyETOuD=Edybf_wuGcpMuGIxvyvEGy\\ksHkIUIE]]HmqC>my_y<<IxDe]:sOF:FuAIsZNkxwZZ`ycXh?nka^stxYZ:<:ZhXu=VtnAnbxr;wbj^okoa_wT?Zvq:FT:<vqrJ=ueki`YR\\QUrUIQTX_Ey>XTUEyPMX>UvR=UZaof\\rHeRBmO<pnFmKRAVQyx;`k]ax]<MpAQiPpe;::ZpOhJHouhnmWw\\iwB>y]pyKFnrwvMWxp>]xXspV`mHisqxfGwiykAQkvOrkHm`iE:bA:ZOycApi^FxPvnhXwTvgCPmUVcuHi_o`TyipYf:QvVqcca]<YdeFkO`laF^Q_:qsOyE@OhvycHms[Au\\aiEy?>VnE:Zp@rniyb>rny]Op_[?e\\a[Q@eyAZJpbexy::?fqEEhuwgef?Ed;qRcOsteG_MWK;s]KWGyX?wbZswwWD:utkUYy=wy;rbExHuh:sxswYCeegyQR[^pFwSCe=:>w@@rAaivvy:feswy:neTvfxQlPqneXnSYgpic\\PgEW`SyedOl;?hKpcjYp@At:Vsw@[Z?[BAavNj;?vKHeyw[ywtXkeUB;BcewgcKCltNQq<HTM`tSllsuTnEXKxwJ\\WqlONeX]@XZmMAQu?mwqLpnXt[ys>XlgMdxfwhw__QjcowQ@dV`es?p@QfH`bQpinii>PjDIbggsLxhVnqyAZ[yy:fjoX]e?eoV]EfkA_wk``cf_WawMQcbasCGe^vfgN^vasj^vvaoEAtK`eVOiqQkPXaU>]vHcpggofgdouDQtpQwTiuog^?HvTxbRpb\\F\\dXp>_ZuOvgvpFa^lWquw_APuvypxa]phiYGd;xoToytQr`NhKHslgghpnAXa@GZlGl@>f:`[hArK?jlF]uOdjyjAxwoAsoWKmSKOXXqE[idFID?wXPShYSeL=XCkXXuDrUYIQcAAYriuZIgf_VnSYgER\\SfK]cAMgVGVq?SVCSV?DK;vj_bfQG<ahT?rdIhlOSMOuxetfkYb=ylkUwqv^GgtgtoQVIQvKYB_oBCGTPABUay:sukycIoCVQSecwi_ga?irgx@qWXIeg;ufEHA=f`?cK;DRWrOAS^sFS[t;iBesuE[YuUii?WUWUwUyC]DoWSmAiTgeXcwleE=SW?sDkWIPGT@]DNKw@OddSFYAw>uDY_CvEVseV_EguyvFui]ohpuXC?vWegRUewmy=Kf<;S^KRxmbJSIq=HVMR?uwrEroCSn]WrIHKywxetgYsgwrOyvAsfI;uKoye[SY]e]]EQwSe?YuyuJkyZYwPUDUoia=F;oFNAhHGdwywTguZSUJadFsuxsrusS=kYH?HnIrQIGXIDJ[woCgollLioMapHHNh\\vr=NcUmneON`S?MnhDUhDt@MVCIqCaoSlQS<Y@eypTXDUWG=sRau=]VvHpduXBQLY]jwmMv<sv<QjHX_mnM<jk<JePs\\uvVYTotOLLwqDr`Itg`w\\pL<eLb@Mt`Ng<Pv\\v^AkkUqxhueYKNmQ[tueuyIdXwTR@YSGPKdeM=ySnHUEermPOIeXF`WDemD]ve<pUDjSHRg=RWhxaEJnYQUTwBaVM\\UCaW\\Aw]XQEPuupkgUNfTu]qSlDK^`UlilRHJ@UQNyr[yW@pkZxTxqTdxvxmtTpriewuio`\\whhsrUxktpaYsmpwgUvR@OvUvoUOcyLXikqpPOqW^IuoAkfuoSHvChKVqVXmv_@XRpTWQMpTtZavkmkeDoQpLIaXpEWoqWQEsRHL[ML=Pn[<Vk`U^Mj;yVw<j^IWXXLJaXGMWWquHmtrmW^DwUTSqPPnDpntjneKNhRp`rHaRP<O;LVCEq`XpIPjQlyO@QjAWNyuEyPIpVWhx^aKTAk^TXglqVqymISSAksIKmaqytmudkmuYE\\qCyodQmPxkwY_u?yoxqEFri`alWbLV[c_f^guNVaOFcBxZZIap?vvwvVPyPglygfc@eAYiapuUguUIcWXl;O_Bik<Hb=I_Z>v<PapAnHniiIrXv]vptUQesxpvhi?oogpwxAtinnLOp<gnJ?_GNx`f]mA];VemogAf`wXiewgsGgwfnNI\\IygkW]?__hGqQob>N`K@w;W^kIo^gqmXcRawXPw?NqKH]]ajBYZlpkCV[NIjKXliqeQ?vYi\\rOkuQvTFbwgi^NqXGnmGo?_gT>]>p[gofkNv:No`nbW?qmW`jNfC>b;>]:vwvga[iqqVr`Yh`xrpWxVOpsyxQvhlhuI?^JOb@PlPofdFqrNdjO`jGaov\\C`a_NnrQkNwlRgpshlLX`MFyQOh<ypKv]w`\\d`k>FlXFxx`dmIlCioeh_<oroifpvhPxx<F]TG]FNdAHu\\fy^agX>]qwZKhbWiw^P`;_ZQAdAg`CY_<^a;PePWZ^>_vVl;pmu>d@fcQxjPy_SfurokuonXHefVnmxpBprNVe@A]m@j;Gyqp`MAsBYu;HrgHsxxw:vmKOmlAyvwed`uvIdXPsoixef]LvtQoyAippvu`?ihnwGOpIqpgOs`Wd@@abFd@GrLXur`xEXaUIahqwg?nuPjSgwD`okan[Pm\\BJ;Md@sa=Ll<o=@ln<yiEnpTj_UndQV]Yt<PrDuvFeP@DW[@ufdV_ltwPORaOk`JFXsqAxULPEPmeaOgXvnPp<LUmXP^DLfPWMasL=s<=J;tVlIUIDmf`RLDyvPmPpxpqSCUveYSbhOPEUP@oFQP>`KfAXdNxIGfNytN`yb?yExh[iulWsH?pxXmGWec_w_aqO`psi^uQbEWhVniTw`PPsQGfNpqj>rfQ[l?h:WaGV\\:qiWFtoYtgHu?GoEvslNv?GeoWeSHfAgmqQcLw^mO]PpGkUuOfn]yOIFgyI:cBTaEtowoqHC]Gh_tfItUmUEmW_KBBAGGSEecdZ=dN[uXGIgAgi_wTiHfqDhobtkCkYG:cV@eR<;SFsDs?RJGi_wixOhjWxLQxpkWEUeb;BiagL]B?Ce=kD^IRN;DACiq]BZsHxye@EFwgfXScvstkUBoYIV_il]T_ubc]F]IFRmeH_f=SiAcrRItL[XeSSguvLkdKovPUHJGHCmE@]b@?SrACN;R:GDPai^QDAaVZWvU?iQ=GeoTlCbPwriES_iI__yjKe_[HgSDOpvuLL:mxTAnuUUpIPHiLq=LddyTUyPYprin[UsbepcqsUDOTiuC\\WFDtRXj>Ill@sgXPFyZ;gZBqrrnZ:x^i_ZcwxQNyfxlLxswnk[@oUOg`GsWWnOGqB@_h^sgHmO^qrHkGpqIguHp[GggbO]`vm\\XeGgg`hrf>`GihgFtA?qqO[lI`qOuRfmEHqC@[rHdM@jdfxwhxOhrGirghqVQ\\Iag;yfGh^FFtLN`=>Zl_nHHigIexP`TVubOwvfa^FgvoggIil?qlqiKI]V`i:akR`b:xhIacVN]:^sPaaCFvGyd>yZUgqEHdQ^fUylRghE?k[WlBiikygC`]]fwh?h;wsvotcHtnVxuGoXQoVgbmOo<?lWgcOVr]Pp\\Pp`PtI>s:YaZooHnctGjVwqC`iqwh`@i\\Xib^`Rx^Maxsao[^taViLXp@fqNhbI^luPcJ@]<XuSpct^f\\AobymJf`GPc]IcMqZO`nAwiyo\\fhjM>D_VDSgUoB>yUoGFFmwQuGZiDHoHTARPwYAMiOwi=cHy]CcuhtgfgosbyRgUWmcyoEvr]vlsDBaIacfFQgLCWdCR@QRY;Y=KExIwjQseOihSroieegfPEtuqXMofkOBQOHdCTKkhv?b>UXZehg_FXWwAADxAvrmBiICruiJiiJ[YqGxb?YJSeBiGgcXcUT\\esfOTCEET_Idmb=;TE=fjiFU?r_yx?YUecSYWUxcWY]s@OTnWuUKx`[DX_XLUgeCigoFEmIYQCIUTs_vGgCO_Sd?IZuCY;YdmRusdMaFvqIL[iuyfWwg?oGocyxMIGaXRMUW]uYuCvaGQuR[AS`mHVUg[;hk[U:?idmHXIGk_GyUdocsXqVQ?R=ArMgrSYh_OIPWyOYxKoh<cFpkDhOb;Eyt=hR[uEyhToxoIFWYe>QiHCyISugiwiyxcAt@?waaG?EFJKHAubsadmWtIOB:kHvgTZ=UrYE=MeiwrnAr\\ucImHBSFl=tW;XssHrEE`EY\\;XlCcoCxZscxit;=erusSEhqOb@yf[UyYawuyGg;u]Qh`CtYsXeChImUlkbsabCqsskrsToemmx`tnuOOLWtaYThknLq`emoyNAiOTqUKTngXwBXN<]L=PXBEr[UQcqs>xPE=rQpWx=MrqQdeK<YKUdS<AyiPT[enQeTh=u@YPsHYPamCYyJ`vJDrp\\vvyNHHoiAxaQrlmuVqUEqKehnWQS:qm[epuUNd<mJ]NiYmsImGPrmPJdUrJxWLtxV@tsDxGqvChOvArvdta@qvPTn_iT^kpNvrft]xc\\vdOH\\jHq>^rBnuHG[]>^jW`vFb]yoQFecOeW`ptoaAp\\wxnYGgjOsIxhmNuvv`M@kNXj_aoUHqZNjrH]>ng]Fg:FwhpyW>ypnvTqtTyv>OkRgo]@iJapiHqOAmmHmUoh___GI^\\GugnvC_miagCIorW[=yhXQ^AxePh[<W_RqgLIyPWuL?q@p\\rhdTi^bGl>ag_qa<OcWXslamH@_uwmNfeAQnsQ`cGlWWbc`jQI^n@qmYfB_icH[:osdXul@tYNqgxsapd;YodG\\vycvHt`?qmFeEan?YihoqTGo;plMW]h@bEqZ^n`CGyp?vo_`:nrrIi[Yn\\Pgt>]G_ecOe?xqSqflpyRYqJvr@viOQrXpf[^cvWq]Oup^iyxhDheAGvpIjc@gk@gqYtrOku?ehgZ<y\\kiZiIm`QZf`nCqviAffPkDI[<ApBAZPqkAXoYyeeOy`imkWGcb@uEkMtUCsGQHG_wdGDAmvRARF[bM?baKdsoG=OF:=xUQBT_fTobUEWEMFhwwn?cvUgUGU_CY_GD<ER`WVQ;FCGFUsvfsRsMVHgiy;BvuxgKVr]Y=egg=W=Ci>UDC]cCIGVUS^GwIuwDYuiOX:MHEAxUSsWeesoGuOfFKs:Kv`=y]CvC_hEcygeGo_hlOYBWEvGWecUZ;UjyrSUdfYbESb>sSc?xRyrE?BgEGvwU[ucimV=UI_iysQt_UXg_fwOyPMV_iw;mIcgEEAIVAd[CSS[RwEtkQT^GTK;rV]HxidLIFkIUQiwxuUish^mu^Id;=GIgunwSqEGs=FQCTuSV=SHcsydKYFmGI[BqqHgiC>IHGWeICU^ARDoyZ_Ds]T^;D@osiGFguuMUtPMBusGdAE`YT>cgWeg^mBVIT`sR^eBSUUcGFO?VJASb?sf;CxiUrqVUOumgTgYvOgGieW]?eKQFPqWKee>mB<]FKqVSsXsmv\\AFi_vPmSGkHs]T^lKpxSAlqJTlNULKeYQ`yGqX?@omMS[aVr\\JIymOTq[mK<USn@YTaUhUNqepXXPZAsh\\qSXOrUvIutoUwrdxb]rmduVMWmtuFEPkTk\\lRhIMpqLILY^iyLYUj<sOTU^ITK<rO`PE=wf`w[XpntPEUYeAYP_rEhp]gb:N_;@u:>Zc`ev?v;PlwNoFOklJGyrZeU<TMwpsTqSLUyIdWCaqUEofqo_xpSTm_lQSIL=@NVAU[=SSxxxUx`]LYpKvUpiAnRAwpHtdAxUIWSUUcXNPqoPQVSQkd@MLExa@mkDVJ]wGxP_]MkiUPdRSb_iFjwX@mWoUSWQSi[CqwxPScDawMcc]YXs;ubKtLwm:ejutm^\\LLEYKeuvHLA]OGamBpOHPkl@PB=vtMjuXTl@oBskSFyMc?UWrMFWufCQTQ?cSoWgog]EufWbZKdEAS`iEBQChaB@Ibssr>UxKYGXisM]yCgIQoIyoI_igg;bHQTRKGqkHbqVTgT^_TD[u=SHrCUf=B\\MH;ixO]fKELkhWvxQ`HR\\YYiHL?uwdLwQqlKUUIIoSPsR@tL<J[TQ;hJI<N<hydqtolNTQWtiqhILbpRlIuXYUCeWkQmBMSTupL]O=DOFLpC\\VJtR]MUS\\L^=TAtpmAViyKWAWtqPIhqNds_MNGewxtmYPU_mjatP:LREqjEYVrLV=uYPXW^`UNHmemkbAS]P^mOqi_jnh_u^eMxdoXpVheyFmq`stplB?vmq[caabHuDhbvPxUAZVQi`Ypi_y=vniXrC^y;>nWoubQm^op`YtvOdSnvBg]mQ`eNsRow_GgNF`angvqk:xdcGl@gBgtnUWR_wf?fmgH<UWu;Y]?e\\KsoOB\\;W;[TI;B@wRoSCrsF=EULAh=kXd_CDK`DWu:qaRvpj`tfXfkHqjNwPwg]?aPpxcO[U?`ZFrMV`M`[ZG`<qbNo[k^kQWb\\HgPQm@wkagnR_bKQeS?bP@x]>cHqdn>ddX[kf^rXZLHcwNw`ibS^\\;vko?ncWlrOmIF\\Eig[^tgio^_pDHfv>jBfe=P`fyZc_^bxv>nk@ika>bMa`wXeOgtf>fPXagPe^omoakHQvA_dB^nc^^iNs:Nr:x[vot@ibSB:uwdYHWyI:kIyYtxKvYKYvwtZovvUIIyI:EwcYExyI:Qyy;RQEhNkHMIiiESWg_jpIyQLU`xrYQxguyZeqxILTXo`pM<QVviQywxxaqnvqwa^gXcpYt`QjUWeRawiH^qNxwqnHIi]PZbOeJ^k^Ha;aZk^ZXVnovjZYieY_UWkoPqvppqpfjXtDFka@eCyYEtAwxBohh=XeMIHySvicnoysGct_rYuVSUCwWb[UTaiFZUGGqXm_so;hxsbGiTsUBqMRG;WPOxacviUxvAeguUyQUJeu=UR:GwRAhHGEWwFWyHwqFQoXAqwMivvsuiYS@kbrGgyshnyGtYScyI:;IMysrIdwGY_yI:=TYYsy;b:=uy;b@QVXGRiOxGiegieQ_Cf]YECxgWfw[rLURiifwUF\\iwJ;S:sxrIIE?TZ?VsuU;ysjidhIt[GhbgiW_VmwScuUEuIqihHUGi_vLCs[GwL[ed=W>cDRERKwBcqhyshn:;A:=<:UCsorwYseSFbQry;bAKtIWyBUuy;RkixHQwPky?eDhyWhcHiabbuTmKGGUUXCsnotFsD@yI:ex_EciUUiawneWTyI:WUTyDwibnyI:[iCyRvAwxaeLyI:;giivy;RZ[sy;R]gbvUrXovA[Y`=D]uU]IRyCXUyQveU]AY=YtkDxqxj`Mthpl\\Et^MLSLTuewDYtGik\\eL_lrWivQxJG<YdHRimty=Jq:bC::ZG<mfXShY]ro=ifwbC[ikqveYtSwBlWYWMBuwFMAisWE<[DP_iW;fFkE:]eP]vtoEGoEioFioT?OfT_cj[wLguggfbiT]WTOQbUMHNMDBwBDwIq_@BrVvA;@>yA:\\lvtuHTuRQwpMypTk@Dkp`OLXkUdqppYPIkqQQJ\\VQik=Qj>YjRUXTmqXttntkI<WPMqXHL_dRgEV[qwPpTKqO]lwpqRDdL@Ys^=xtlMIMyiqx`iLyERwyOyMj[uYTxQq`pi:T<?gq=te]unQi`ScpsgHChheB_oF][Bi[RqeSsMg_kCp?FlUwh=SLArBwgDQREItjgfPUhqewS=YioS=Wtv?bsWyHQWOgFR]S]Sx@usiOt_qyVO<:<j@ykgesepy<LyYmy>XRx]pU=solwN=x_qxKDVypKU=WtiwVPP=qKqIYheXeEy`lMQQVlUs]xLEAshas>QYX<PjhjUeYmirypqlpqv@tfloh]oWpMHEWieoEYUupOP]vgEULyT<tRdywp;::JM:DqK\\TvIqwaQx@ny=J>tWHQq:YkDUycQqnXXptYqqxdYk<yPTyRAtTJUWuHs`tmLSwsxwoRgsg^MtBwv`QVyeHNKvb_gbWVhGsogis::orIiGGYgxQRtyExar=kYnEEpecuysOiHGUTQUsneDnSwegfp=iE;wPQvhiT>Sx[McBEIhEUH=Xu[DxAVO[HI=tcyI:IuTwvA_GoSGy=xC]vVqEUMYiWTO[wQmr;[VTyI:qh`i<lInyV=xiZmkQNXIRiPx`dkw]NcQypIPhdRcanqQuvHloXrGMOUqp>eK<\\nCUxGHpIHm<tysAuX\\qVutoeQMhuLqnLiPgpJAQtjtM<TweYOEEu\\<L@\\K=TOktJ>XJoQjMTIFBZy=xD:xPJXwVIN\\IvZusMtsNly\\<xhiKe>_FAgqyhPNlOPbl?d_Oqa_mnOn`QxDyv@qdxf^TXe@YgEFi[oplP]G@lpXbZ>diyriY[JNos^iH>rTvqwIq_xiJyeEwy:>rRxi@ykgiS:rPKXGOCxgtxKDv;Ioodl_XTGEoYWsywhwvretgmUCgvJsxu=YO?dbKGrOSZOiM]Xvcv;wIQavy;b;gsqsYQIuy;bU:Z]<jyGJ<j@U;@sidPYlKYUwpQmOyv@`xUekDuSypvuplhit^TKwpxWDUWLW[XX[IRftYfyo>`x_`t>lro]QQpLX@wJpn<IVqtVu@YqeleUI::::BoCIyQTryw:QiSEbIybg[W[eUCchU=IgkGfMRYOc[;bMsbGEYxyXZcWsaG^[eKeytkeIgijghjiijoRIeXeCWMUBi_RmKUlSBUEV@cd?qYcMD@iydyxpo>^Y::;a]ybBi`hadmBLwXTiWU=YIKCqMUNKFeEsGgScUG^SR;?tP;f;[sHgUeawrkCLIHp[xYshKyxy;r\\Swy;RuUxD:rYven=T<??`xrMR<LpfALYdyDyuy=jElOLUOYhky=j<ArvHxwhuCxQOunBYN:dUXAUlHuB`t;`VJXJhtXpPxGyTpljqxQq`@:VN::;R]jFUy;@VwTqTQqPaPymjbqxTilPEXkexVpX<Hs=`MrXvy`mXHQc`xc]yapnbuTTpoYDVwPOQaSs\\ka`pDpVOQVQ@x;au[HqBQvgtYhwQ:HhpU_FbwsyD:f_^Q=Ur@oTncUMoSIycK[HeSIE?imKXEYYE]tOsc^;rUodZqXOaHR]YGyH\\ErfMxWauUeBh_bTgTc=U]MrHAu@_WbMFqshv;TtOvaqyVOtyr_Z:rA:lIvPOuJ=YqIDJ[IyiTFKexESi;whog__YsiVNiwEccnmwWieRCy^afkYt:;BV;ReYExSTryI:yFGyqZqrYyiQFeyA::Zx=JjsrE\\MwbxY\\rviaisy>x]wgyAZ?ItyAZC^myVx`ymrI`qD:?ytqsxaeL:@B;::sAXEKuy;bjIu=sYxIgySRUyI:va[Y`ApyvWtyA:xY:lyhXpytpn:n>::B:Uf?fcY>yF[Y<jEXNxULrxY:xVGyQjUviyY:hbiiwGeyby:^XJMbbFo]xy:F;Jv[\\AwyE[WxAmyvYLFhwy=jrQqHqyVQty<GyQZ;:wAh_o^`yGvm:n:jI<yFIvyoacwYAv@yeyWsfywgcKwKvkbqyVQD:VksoZ`xkvq^jka;<Z]pyM>A:<j\\UwuTYmkZJ:D:dkYJw;rU;kbyY:LBvCjrMqyDvmxZs=<:Whyshnv?>vFsrI<FB:dkPb`yCv:r@r]kIMra:<jE`oiiWG;sAtI:;a]iB::>Z?IT`:BxB:hH:RZ>ZGx=:sAXEbj:S:va[=b;Za;cAn>HD:Z:fkP:kAxC:irKZI=>ZE`OUAbyjyJt;G[\\<F;Jv[\\AWLRaka>]UE:PABnJZkA;nYrPjj;n:jI<yFKYZUZmtgNY:pI:j?[v=Y@B:HD:B:Eho:=<;b:b@y;oAZi;LBvCjrMqyDF`IB:nsx=Y;;IMHx]:=<ZTf?vZ@Al;vmkxnxa;J]EWMarqElZll@`LAEY]\\NmYNNdk\\@pHMTAURPyY:ppnyOt]KcyY:n>HdiOcZvopqsRx`F^]W_ryVlIvtnNy;fsvGcyAZQtxIbtyhxGDTOwy;B>YCeWWmkGguWgkwBWTokD\\IuK;s@ATlObMKSeMIuSRvKIyQerEb]KCMoFYQF?Mb@mFWqwSUed=GOgBTMHHABAovQkYMesqUtCyQ<TwImYodROlX:yOvq>:r]kYM:ZD@_l@ZyAZ>XtW_xLyijiccwy:nrbxY::Dt?=lA\\y`::Y>:J?;::xI::??::xB:ZD<::vY::DD::vK::O>::ry::NN::r]::dB::jy;:bb::jA;:NK::Zy=:JK;:ZI<:b\\:::yA:Z\\<::Y>:J?;::xI::??::xB:ZD<::vY::DD::vK::O>::ry::NN::r]::dB::jy;:bb::jA;:NK::Zy=:JK;:ZI<:b\\:::yA:Z\\<::Y>:J?;::xI::??::xB:ZD<::vY::DD::vK::O>::ry::NN::r]::dB::jy;:bb::jA;:NK::jNyj@QMhuKTts:xMsUJTyY:HXd@o\\<s@durUTYqPmPRlHWKaOjEsVlJgpOTmpdXsnhKE=M]@nKHr\\LkdPn>xsyaG::1:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlK2dGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiUhPiVGKi0lKUNISUxEUkVORzYi

Figure 9.10 The Tangent Tutor applied to 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 at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUY1LUkjbW5HRiQ2JFEiMkYnRjlGOQ==

press the Plot Options button and make the settings shown in Figure 9.11.

yIpyIr<K_Tn^T^;FZ;BR<`:rpH^BnZ@vZ@fZBvZAvZCF[BN[F^\\G^[EV[FF]LV\\I^\\WN]Yn]WN]V^]Z^^hv^ZN^fV^V^]bv`c^_jF`n^`nv]aFaw>al^ahV`nN`yYU@j>`j>lj?lJFpj@\\KS@LH@LSDMSD=:::::::vy:U>KR:[R:or:=bBDjB@j;@k:xY\\w=@j<@j:@j:B:;J:Z;NZ=^Z?nZA>[CN[Evy>Ug[J;@j;HJ;Lj;Pj<LJ<R:uU:?r:;B;]R;_RB]SJGr>]TRIbB]E?_SZ]VbKrB?Tf=X?_Tn[ICacR_eZMb<gr?kR@oRCGsCKSDOCGecGiCHmcHADKEdKIDLMdLaDOedOiDPmdPAESEeSIETMeTaEWeeWiEXmeXAF[Ef[IF\\Mf\\_v^cV_gv_kV`ofbAGcEgcIGdMgd_wfcWggwgkWhogjAHkEhkIHlMhl_xncXogxokXpoXr?yrCYsGysKYtOYv_yvcYwgywkYxoyyCpI@Z=F:=R:Z:J:R:?J<:ZoH<?R:?B;Cr:Cr;EB;Cj:DjuFZ<VZK^Z?F^knZLFbKwZ[GhMN^lFjB^\\<Gl[Hp;I[]V`L?xONflGtDn\\^^`[i^ky\\RF=GsCK[on`q::::::Dr;Mr<;::::::Je[\\Yv^=NxmaX:oP@Hj:NZKVZK>ZyruobvUbNWx@uwVgUbCcdwrHceOOF@IhS_ywiGm_uMEC\\WhFETJaGJyqJuqiyiXvYoBd=w_=TgOcmYGC[RkwrkKBmWY?eDO_nL\\r;LLsdQeiVneY]tsBYNPewLpYg]trpM[aQYio;yshuxI\\L^exV\\mFlM@lLedLAEkIqm]Tw\\EoMemSQX?]Lp=wY\\xiXuywryprGPmAfyEnxyExiIxgXKeX_ShXWw\\Ks?GclMEs]SXah?MsxMGVSG@CIv_SeMxBmSHEidYhrmCbcXwkh;oveUubIDAaGlISxmXPiCyMwgsJw<unYo[@K_luD\\nX\\KoEwDYl_qly?vRAwp?gY^xiVuyuryxrGTmAbyEvxyEyqEyQeFUcTwXYwUIUsBkSYkcT?bV[uhQR[ArAUgE=grUrAWTnqtOgfwMBEAHUmTB[uxqxIeEVmUIkewwS_eWn]VcaGJyA:TMnx;:etuYUUSCWmUWmDCgDgWvEqCmSf[SBhKhpoEA]y]UWJEBwAXN?fjwioqSXWYNCygMRDafVWGqGVxGD@WEASr]oeEGvQmHbyEnywUyqAyq@iKTxJwYkpyikywkQoJQgtgeFQhCwgcHeDGl@gfKXnW@e\\^[_IkAFj;yvTYpgaaIgndo`PxdPvdpnsqxh@^ZCwfRwmZ>v[IcCaacXuNqjX^pWGZmXp:wYZXvY::Sd\\QUPWiceg[GY<WSBIx`_BLQrkwv`;FswEGQxTQx<IXDQuXQuHCb=CdNQG>IWb;IwwCgKeBUe`I:ZKYp:wY:rLMUEYyRMUEIe[ceOOcPIC==RAGtKou`Sys_X]hRm@ry=J[pyYuyXtYTlPbyMn;yoLiyVLyKmxmEG:::::::::::::::::::::::::::b\\KCwMtlKFI_sCkHVGH@CEVIGnevmesCkHwYhxcbCyI:;XLygjcGwQc[AvLKb=]CGuxIQybgt_qxQqikavRmsOUd<McOMCigC^KxjOsfEdBgbAqXfoFP?UnWu>uuiEFmMh^iSkYuDWwKkgrcWgmhPCIP`m\\Avy=jbypdLLdQugxN@\\pnMtGHpu@M?Mk_PR_=UsqoaAYNXJ>`qMPyK=T=qqAmnyGn<wgvaZU`ydn\\TNZDGtCGvRQnKpb\\Ql@Aw:QiZAlkgdiipY@kpN]ogtfqlTIaHPuQFm:AZWPo_xkCGsbQ_aYkV`u<_rmqp@yvyES?gwdlpEL>LXbUPZ<YvqolInbIxTaSDqY>\\KTlYnxUtal`yi:XdyU[ednmtukxpEHdqvTsgSoXH?RxasGiIA;IfYHJcDvoe[=YMGVQ?tHmrEeSPGuneBPCg?=HNUXV;CIIYH?RF[X^QXWCR=EGxgfBAwOMdYISdsS=ksm_fuyqIUT<UYS\\PS]n]yNUYS_pucLu`tJteLv<LWXMb\\QjmRIdLr]yHUtgxRKDYe=yhYNsmNkpRuxPHTMhuurlskQm`aP@XWWprkQQK\\l=extaVoyY:DYGtuywoCxanY^W_dTHoOn^jOvcO_ofeo>tnY]rPnp@x?fqvqs]>\\;ygl>ckOxt^lbVrsF]F^\\FPjlnZ;GwKwoD`hy>\\@wrJotgig`ik@^vmi\\KFjdAsFIhRiky@iX>nFp\\RItoIugaxUY_EfgsnwTV[evh`o[]xwZX^cp]APxgx[giwEoy:PhywuRyy:>ythv@Iv[Nka`w`QqYQyNA`oiqFHqOxwwIimvsff`Bi`Yy\\bq`Pxlkfp^x_iVlLv]SxrLxYsWVkhxWrbCCagbpiWb[YKuyqWFIUTGIip=cnYg^shBGxNEenSwXutP?vlAFtiTHuSKguiqhpiVyLxywqkxY]IWyuUOuQcy:afywykfrOAt[P]J>d<@tOWwtNp`yiPioVx\\E`q;NodQqGasTIhRGvrHtGOkj@aTYwb>l=nyEa[hxbDWoc@ie^ePapYn\\lFew`otHmqXieG]WO``@^SHs>>ogVpQi]mnkeGtyugewAoY:MxyxqkbrKiywHoyEtIrCuYyYvyhrPQuR@mTxY:lj^DxyTJhaXmUMUeSoQjJTpomK:Ur:<U^@X:uv>xKgPTIHrylTvis^LwQMmnmP]XSHhVUUOcLPC=NOenpEPU<XI\\UXLyDLwyx`y^x=:RnuYiKwy;BnWrMqyxyryXK]<tvxm[qNGxY:HocmuPpQDxjDPT<Yq?mL\\utMHYL\\Mb@jMPX]unrtvRtSopwUErTixq\\JvXq_dMtprrPto`TTlvH<MrYJuHyETXlmq[yrXYW?MyWhj^MmOAooXTvQpppp[UkBDnbelNXlMn`AnaOXguYiKwy:>nVvmqqxynyhfk@?hXv]jqfqhfgHgk^u>YwXnli_[qhfNXk;Y`hae]omtfm:YhF`fPoeC@vwoiPYs<A`WGgho\\KihBfhB^y_AZfFqRI[>^vYFdVxdcxy:vgdwA::::HQYpjbQmW\\MQpPQmXGeWaqm>]pSmxSLr?pRSMkLhOFDVBIQ:Im`QqI`wMEwGqyXaty<WAx>j]TYuQty=JZ`mYxXpyQxqOG\\ruTynLyKiYTdycxqUQuQF:vI:xUnY:B:Qvb[DfYIuaXtIdwMMMyiisQ::M?:ibK=WRyXpIoAmxcgcxquN=ZEtxqeNyQJswZ<WryXpIgnYFUhC:jEX>::Ev[yeSyfu]XyovYqWMwiq:j?;::rwKeyUxIuhcyALI:::;r?GlklsQLQEYMr]WTDJsaml<m>]W<Xla=l;Usi@XPdQAys<EoRiurMlexsrUm`hMpUTUHvgeMEyjB=RZ@SA]jhiWRUXQuonplu`qT\\vcQQFdketl^QK\\AlutkMESoxKpYky=jIqogxi<>fgxgKNgWokYopdo`KfhwIyyFyDNcIyuvNmx>lpAtCpuPAi_@g>Ht@irxwslN\\vnrJ?hWWiqYotifFPmWOxXo^Qxiv>oBvcxNvLv\\]^ZFH\\TQoxfjQXfXvmc`r>`v@wljfwYGfVPmhVjLga<wwL_qLihEfbLq^IVhc_`Dfcgqn=^af?nYxunGsNfy;oyQigtOifYthVmnQcy>pYoywghi_yCNjhHwpy^Iw\\YFxa^qsx`K>]Vwsvvb^ia:GrWFguFeRAouHcmVlLafMa[LxseX\\f>\\b>gfalY^xa`^jyvZHb;Y^rYpbQ[phjxipeOvEFa`xqcfge@bfptMqrA`feQlvwj=^a^gmg`ysvsqYjr@yl^[WppTOrh@iKwh@vZox^vI^jwYYheawy@RrXOCHTLltwDQ]ApMuLupwy=jQxNdAUj]Py`wu`THYPoHNxMXQImf\\keQq:`xsXLyMro@WtDQI=kSaSKEWqTebi^XHi]phaVaN_iapnUWtwHiiAkNv_Ch`?g]?^u]xYyRGehJWSFaGIsWQedOcwcuR`KiiuryxREyijhgIpyEPgbYgX@xiayvwpwYjfwinYeQWbDWeR@^\\Pkc>ZKgbNRNE<mTNQy>WDSgcpeCy]IcYw?kV]KB=]d\\sfU[FAEuM]dNUbMEUhgg[IYLuWgibFkrr_fOCfe;I]kyHCuC?gacXxmDIKXn?g\\MC?cRNELD@o\\::::::ffrWlxAbLxiQAgy_xdwdQ@yEpy@ggUoyyp^yAZJistwjCxa^I[afypwjyAZ@gnswiBxq^qfOyqeQxigyFntn`rIabjywv=:stwIvYAYsyGuqrRyQKeWWeKaio@QJD@O^DJ?]LJEJ?]\\HNiXic`wtFWcGp^PYaox`qHpEY[jwhoVr>xgZhas?wyG\\dgcdVvEwj@w\\QhcoGikGonXtBQiio`LakiVyZ>_=FwUAnR@gPPkHYfPpyZnwLi\\DpyngeFYckN[hTlCSvQyMYFLgwLKvS_cqOHv]GTsyxmXceTCOtsQUHmrj]rnugEKtxItHaW;MtvaeG[utgB_yqBPmeduX=YdYo;IoUEYKyUTaoQhkxuK@`QaLPc`uVhj<]MptSw@O=xuQiOnekhpV]atmqvNaX;@YlUMnaRp@vPYWr<vvYOplXaqXXulhAVUHrFLYo`lGusbPPkikOqUs<WoeQo]o]mpUUu]Eo\\XohaKEDoO`q@EK]@jmFaFX_h>tlFeVGkiXwk_pLIskgg]hp^Yww^wQY`gPnAyaRaokp\\cQfNPZq?spg\\Vaiy`qp>lwoeD@bmwltgrOqlWHveYwsIvoPkSwduqcLojrFlG_qAxmjnZG`iYa_G>usF^Iw^OnsqNkigvHptZYwYgfAGqt@e[AiPFa_W[o_^kGjMnnaOrdpZDp`H@dmvxS@tInb\\@mXffb@yY`rjfch@sThkVPdUgbvodEisI^_cN\\BOfQHslyh`nh@Wu^@l]xZZaibyZWGoYWwTncM@hJ@uVOwqGpSistfu^FhB`c[hePxaf>aMH];>b;nkDfvCHsgPybVZDqwoWqBi`UHyngstW]EyhDPsQfta@g[Ac\\yy:^cfGm>hgKfyZadXY^eVxfWyZipC_oVOgqNefw\\qQi<`enNAQGV]GcMUEcWewBoMdIke[_iNwDP;ReWHn]BpiCd]DLWb:AIQ]Y=uvZOIFsXyoWTYWgQsLquAaW=kG[uDGyuWIySSh<sG>OBaUUqaI`SCyATdqFUsDxOVmcgsmg]mSgqtTKfewclGWHkdsYeBksOWC^Wg<]gA=UlmyrIxb]DMWr>WticXBkiYigGiUDuBuoxnIxsMdTOxisGoOfG?uRmWJSbY_tJSrr;C]chXWwiQWTwEDgGgUtJUh\\qs`QdO?VYOvvCS]oBGEh??SPaUBwBRkE^kSpcW^IvuKIbYRHiwoeytuu>EThmWossweHGKhuWWCqiH?cpYS`Su]?CR;eRmSqkhiEilAR[sTeet`Eh@AxLsSFQewQHRif^Gh`uvlIHSSwdUrfGthwX@]r\\mifwgJUvxiUBct@QenYUEAciewXMe`EU]]y^CrmQBvauj=G=ocWwCoUxIWTgaHBKUU]DjGeqYIEUGE_fG;rlqc^SHV;RlIC:=Bn=BLWbKUsW_dHwY`UbqUG=_TmcR:SYRIVTWclQra?CKabFuEuKdegCAIBMITBWgrOVD;VNE<E<FZOPvIGy<FcyAZWGnyAZKIoXwe\\y_sI]oxgtayUxy:VboNwX^^yAZJ`^YhxTy]wQ]OhvxQ^yU^qfOyI:YWlyGwacPax>us>Axi]ivyhwURfyaggeGVhXi]y=<eIpYO]sngn^\\KCBORDaVMeBg_rMsSdcRFMSXCS^?fdKS@Cs^;H:iEbUh>WH^mBNSdtWXfgv@mFO;FLuBLEr_ICqoEnABt?W`CSnCTvCc^?GGUgfecS;rh;egIRd?XfIHbISg;bIOFD;g:`lC;:::IRnEtL=USURpmWXsgjgTQAGUSGbUb\\ou:WIT?bDOCuoeYqvFSX^qsH?xxESOogV]dgGvjsEquBeIw;]w;uWLuy]IUymxi[iBYdyOS_;hm?GgyUfSyy;rhicyCRLyq\\Aoxyrm:r\\=VaEDTyI:AUpyI:guUsI<avydROYMEAUgtOZ<uv=RXtPfLM@awZmotXLd=w;\\LKeRjLkb>ZN^djHeRyb]hbuGievbTVuCpfTXcQhdKwpf^rhAr=VlL?eUAgtimVxhPx\\\\nwPacfQmEnrKX]>Vj@h[=PjB^yc^eD^tPwkpiaYxx`wy:>rCxarQoyFpf=Z?EVaCdUwASyXycuUxy;RZ_rY]IOyuRmxyTAvYDTjYpbpnRltUXqb@lp`RJdjFhrkLxcLwsMWGQQRdJNDT:EMXany?^CwaeapyNyoV_Eay?wYAcGUwyxoCyQnUpXIN\\ySsMjCWq=wYAgNswiCxQ_yFOuqeYxicyGvTodRIebkuWwiIqdy=hgycxUsd=gequjyWv:Zag_@QjD@_^XZ`flg?vLxfHndon_>?gW?k=^adRLgI:aFQYgZcwpuH@stPOeGWi^WXfQXUYfqUSgogbOcpmf;_eRECZYxqsHQCu_qho]HJwrX=coaTkGVLWHeSUSwfsQCoWvDGV>=XsOtRKctqY<UUfefvAe=Ig<YHiyfF]hywxvSCyYYuyfguYcswqQcSss]_GqmEPIhuiuuqxiieAWuIEyaeVQEH?=BmkIHWDfuDcYFdMd@_W[gVtWS>sDr_VOWsLOtc;wBaUB?X_;s_[TywumCxgiBtoYGIy^WeB=r_UYVEx_MXlAhPOhXAUaAXtsHwcENGrOMfyexy;B<wvfgy=qSuyVRyFl_yFGYXqf=uHhIiW]E]ae`AYgkGIMTTUudQrDugS;Icawp=HZMTFuVIEwvGRomrRaEgGBAMS:aBTEsMAWN;DAgu`Ued=xYAuWCcxsv]]udwxjoCMSyRWFoqb_SF;Ky?_EkAT^qG=cbG_h?qWuybuuxy;royUy]fDef?itG[Xi_xpMuy\\p[\\lLlylmnHhR]qJJDLrUTDeu\\XX>=X=eW^pliIof@lQ\\uv=TgiW=qq`iVCAXsMVCiOu`nVtTCEUYywOyQbYky=JMDsAYUoyWtQjyGs^hnZGqehb_giypdyAZZx_xic_v]igty@wEvYaVLEdZGYeCetyWvuyTyI:sDswYTQdwuyPwIZyWxcS_WdrqUhYIbqYOiVp]GAqvYouAiUDwVaqcYcEnKvbqg]md?eSP=vUaS;=WWyrBERHCCR_EXwIvEiVGrT;fhAFk]vpyxMEbq_GS_YgQE\\AI:[wv?ChyI:CD]URhoxJaS;sBh?XaKh:YfK?oaqMBixNDx[MlmUOUDmaIqDdx]Pk[]JjEyLAMDQqxLRU]W_ayRXrcPrmtwa`sc]qupxy=jnyMgyUphyqhVyiUqxvOxsQhKYpNvyvFuruXxIhUsiTsdR:HUY]KXQmoPm\\MsEAs\\mKS\\kK]R^HvnTOAXkNeLZlQ@Xu_EY;]W=xr;ExFApdulLhYh`rshQmQnthq:TrwPSBLvGMxAePp@lB=S:`rDQNV`MhIWfuOoapMiWPdq]\\S;QL?xY:`pb\\Uj<pkQUfhYypty=JZxOxeS_DnT\\PP]ptqP[XpFELcItuPRuenO]Q<ItppJ=MyW`OaxJkxJwHspeyUqy:xQsapN\\ouPMnltQYUokykKqXw;\\LRmoPYMxMrqxqoEty=JnMUL]TcanLaUWaQjEYLDM@XVXUMYPNqeL_<T?\\\\:<<<bxVSrBjiBtpu[J<:NDLvi:myGbPX@:Z[<Zk\\g[gnRO^?feDWcRapSivMIvCow]iekQraQZLGaSam:hn:P_R>xC^Z<pZGfcufdwodxyboxcrql?A\\XVh@QsLacC_u:p`D^w:nZByamflsQepf\\ehdngyxf_pFuZijWhlaQml_e<xhCW^BWr;XthFhgqknHZF`icwnywgEQnfX`oNwiAe\\x[JFiW`ds@d?de?TfSbtKGVKBU_s^CcaMSgMUUoB;mwTMuS]CGyFSGeq?X@CESeDl[ulEIrsYeaIYkFqqBRwy>iwG]WqEDdOE>myFUxVYE?Weasd>OdfMB@MsNkw^QsGYxhIR[?h^Ews?hg=RbMRGCIVAXDmfBqd[?iKOFLuvjuIvSXCCC^;h_qbi]iR;x>KiPSiHeYdkgZwHTAgtSWusR\\?CsSFe]vH=WskD>qrBsRZ]V`eS=WunUTa=eauRJmx_keGoHYaie_sKwX]kr:IHMIyvAgL_h;kvw_SiUYmCywSSeSsfKFosF=Yb_eSOWh;isR]E:?BLeD:cHIycbOynSgxgv]IgqStd[WLaEU_FFst^SFfIS@Is]oE:yvNchB_HWqVmOTWge[_x;wVKSf:EXNQD>_CJWx;UwViiqmCf?fleioQClGsgOvNmVuqr<?cjGUOOcLEi`EcFUEl;C=mcK;cAAvNahreHgqVmgcWee[Wy;?fKSFZ=XQOd^_C<Wx=EWSOeY[rneITYi>meecTQWxvMXs_G]acpqfNGBO]IfIYyWiX]EJYbf]YKUWuoypUScCILiyFmTcCXfEV]II\\wGswdVwEPuxZAeUGbFqrDudMYvwWuyhxYuY^QSaQVJeo[UyXDU`tq_qqXDylXRShNmux=xRWmmuYVyXjMlSteoYpwWceyqwELcHjUPVwTwJQTYyS=xSHdRqNueWl_`uY_^BWoqqh:Wbiof_orB?]QwvZVZsHfqNunVwcoyMiZQe>ysaWUFsRh;bu=d_myM]Tl;YwusTSCxodloXq=CnCy^;d<SykqiEKsbiDq;rHAGSCuCEyQqfU=I]?R:;ctkDPqXtoVWeW[sfYuTeSWLSRDkWaKGbER@sCa;bH_h:EH?]DJEBSOyipiyAZVkndodISOyiAixihymWlsinnfZdovYwrT_e@wilvuJgb;po=Faph^D?r_y^jwbU>d[GkiAqdnwv?nYqkCN\\?ofuPm:_aFYn>FrVArFHv;GyAOss>wxggAQmAym<Q]wgrn@xvvt[nf<Py@F^QH^h_vL>cAWsNI\\lQyHFq``ZaorTxhpaytP_=Y`XoooQkZFxAFmOYcO@[VOa^Y_Jnsdxj:nj=I_tNqpWo@Vo`iad`c[wk=nsrOsevau>l@Vrhoe=^fjGcY_qfx\\s^yangiWftXkJ_t[NxaOm`qubfuv>q^fl^O\\jNdaHh`ndiwmpw[Efj_ncHhm_Hb_HiCPgmA[^Grlqe<OwipsaiZlXuUPjSaaJXeiY`P>ZUyjgymjqkUY[I>^W?]]>[Myv\\_VkTZQHRCUuKXqSfUsdusRugwiYwQOuakHVUdcEgpuSloS^cwW?VWIFlSb>=CD;s[kGDYD`kHTsrRIS<sgoURdkiOqC?wwh]wFohbueb]X_EUJ=VaEWZ;rrSvrASHkBH?C]wU>_YUUi?urV_d\\?Ymor@qE`?Yggd]GR<kfJKBYuW`Uv=sHqgCr[bFOCJIGrUrMqiUurSgdvsuaiWQqHQmyPiGUyXRKupaUZsvSmBjWgjmO:hJnySfEmoTkbiovUkPXqE\\wEuqqmwLQTXINHIsZqr=mmrusvuT;=R?\\<[cSyI:[V]YYycuQui?cF_awYKhKiiyowEwy\\OdL;g<K[lRLyQJZyRGhF<jKfOxoCyAH>:yAs?jtw@jmDdq;=@htJutw::po@XpPTFFZ?_\\JGZ?_<:RNuCg_RFIeZgsRchf?bToDD?r=]gpyI:YHgysw;xbSiWywvUy=uIvOcXKc::::::rcIxUSRMoGHAuJSVScd<_f\\\\LKeR:Z=`wp;>_ui]i`yuYbyEYObaOF:A>:::::::SUVId>UY]eb;aU[krc]TKLkbRSku^wA\\@OuOi>G\\xyq`B:[@MvICqMnhAxy:nBmuYKviTpdyuowGTGLNr_YVjfwIq<iy[yurEyiSqkxY:DDoZGhZNBL?b\\KCb>?<UPMyhhMcTwT`SqLywio=YKn@TmQRh@RlMnrDSWDqoTqSqpy=jTMqwqY[hnohmO\\RQYpfPSLiUn\\WkLL`<kKtPnyNiLydQyREmgloAeOrUyBIPMQvsppLao[dMidwpDsWLQe`KVmRH<kS<WGUsHDnflm_pQMQsaTl?hmvPW:im?]nsal=lsk@KQ\\Mqyq<LwMTwThMfpXlHWp=lAqXBdNcqloau:Ple\\mi\\LlpSVeXWLwedwJduYYMUeuHUxI=qrmLSpURaRXMWcPv:DkK@R;yxcaKhIQHmjUhQo\\lLqQ@ptCTvn\\t]MtZQMLqvvPqkPJdqX;tT^my\\uO[TkseJq<pUdTSmRsIvoppI=nrUuAEx_XYT=uEMQ;ILTXp`qRx]vZ=JUAkfIsqyl_=L]`YW=QfusYhJgIvTxrBYqvPkHYSEAPSEK=prfHKk<S`mj?EYj=KQIJ@tx=hQqys^<wc]NgAsito`xP@DnGhpnpOxhUvTVRdtD^g?>dSVsjVZih_S`_;`qKWgYNu`plLIxnVwi?axFn_qjE`hU_q;ij_nrD>aEA_>no;VaQ`hL>y<Y]sWnoHqLihrvg_il]VcwFlCY^iGcSW]b^w[xcMP^^ypDqbUOgvitu>iXotIgp=g_WYvcytxFhwwaFY[PFwqGiAP_=^mQXh@Pf;^g:p`hPtI^[<Om>P]Ghswiv_awlVoCxvlatO@e_ib<G\\OnhIpa=Wtsb^;B?=r:kimEHScW\\UsECc_AImuh@OwUSfkShfKcN;hlKXN_YBay=QHa=MtdkUlRLpuwhpopUMDyOhvGiS^EX\\Lnl@kZ]M@IUBMXQHJ@DSrdNRlolIjgXS[UQsQNlutJ]t\\HJaIy`eJWPKBMu`YmtPL>XPV\\P_]uvuQkPO^xsa<yluuH]t?LvVauDQSQaSCDnG=OhdNC]UF<Or`KSDm^`yAYL@gfavknXseHoffwEirlWl<Ij^F\\Basg`ajGpbNph_k=P^F@cOnjxWwOffaxnI`x]hn`fnwfq_innptEYhhwtbFpsQwS?\\]i_lIv_iklWyNowFF[F?pK`aIvn^ptHxgowZUg`Bgo\\HgQ_fk^^kPcKHjq@nj>_VQh^Q\\SnkN^ogIvGfaf`pUyet^vGn`FQeU?a__uuPeQFeIVs<PsJqbAW]tgvB?a^`ZPnesVto>]]Vibn_hgfg>^PX]io_`Gk]?[WOxHhd:Q\\Aarf_wq?vcF^:`iXG_Ewg>FwTpy]x\\Gihg_Zh@pO`bH>wR^yLA`NoeHW[j`wl>e:xfy_[^pmFOldQqUhu`hxuwoondCW^wWm]IyNO_cNx]qvj^kD^vJVcM^atO]U?wPOaOgnoivbHpD@a[@qCxtFIZQ>fVQ[N`gF`vOV^v>jB^Zj>^iW\\ZFl\\gceVdPhdBhcoO]>WqgAdm@_ffn;pi]WlXndviwBAs_guOhovAbkXtUpdlhjpOwpnpMIs<nsCIk^nk`Vl@>`xAgVG_uFmO?cS^[qG_g?_vy^iogJhn`HnbPe?HjgonlieNvsTnld^ngasZw\\vGiXoeJAuVgZJ?pdo]AVtoI^fVhXOwEngGAhcygVNo]FkaHcLNd@^uLprP_gkhgahj<Uc=b@kiqgxGsg]qtTMhiIhsQxVccO=yRGF;wFTQVfWsViWlms:GYROxcwXOuwAOVECUoUEugdnaYUUHmgGfsTxAel_FLgvJ;cm_uhSDUyGFxrO`uZ<pZAx@lmghPB`qeimt\\OLDrs`UsdTsynJhLs=ys<QvuVvhjqeSUtWGLw=`RJiUBMTGpqLMxuUqrQlken?\\NSiLyxX_mNEDmEQLIqNLQKhhLG<jo]PKeRjLkbB?]<RSk=vTNGJ]VETlyKwXBv>XBFIZy<BkY@lqUqIVeQCQXryriSADD:\\><dD<::::::::^[iP\\y?sLvctiwInyGPclyy:F\\y?sGYoywt^yutI]i@dky^vIj^vy:noJyy:>wNyoiFxQ^yFPuqhyxsy;RbofokV`KiauryxRE?Zjt]wQo\\hXtusA:`o_AQJET?aL:@o\\>::RRkY\\eGGqyFoTLmU?kFqWESaxrOvLEFIUUBCeOSBZYEqcr?IcS[XXcR:mWK]uVkenQt:EReuWgWHgMH:wVX?WgkFL[th?geKxr;eCwrNGvO_i[=IysC[=FIauWUECgwqmxgoC][xm_uvkRReF`CdEIg\\eSJcBMEgg?xKWxRIr:GYH?EbuRqerkQeaCcoitjofq=WcMIvKVE?ghKdUoDsmU^Mh=eySKel]BgcSUiG=Eh]SX[Eb\\WeToWagy`AWC_XtyHToWxCD^?hmMY@ucM_dGgENkU;AuC[FL]d^;g@cwOir?OVwCDoesDqw`qsUSydUeI_HumyO?UMKgnKHCmFLYTaguBkS@MHPah<mblMWdkimqTEaTmQtW_VkgbskRn=rRaeDYtTKBUEbE=WSgFO;c;CSD;u@OCDABg?GfSCyStQAhPGVfyucsdpQV;]VsYvl]FYEHKwHMweTGDm[SV_vdai:oC=sVqIEkoDsgrWgSVkXpqhtQVEof^iF]]IeitFkROeF]yDY_sgEb<=f[mYx?T:kXnkdY?soGWnwWmuRgYfpIyaaE;Sx[OBhMxpcbVmSsiVaqvKgE;KgSmDXmVgIrngxqYDYOEFITXOumKs:SIs=S^yVdgdJOiGUVpWC`kcqAE:yhbmWEASkitgAUKUFgiXFwTp=xEyFIkh^?DtkBuChRIsB_vlmwAKBuACjuTqcdCgdZacH?CMcT@_rGWcdkHsGBB_rFyx:KID=Bw]TKL;::P@rY:::[@:XBG<jdyelyGTg>]i=:l?:bbjgB?:?:ZbPwtfbXHo_YmKP`Cq\\pWciGh^N\\:FhOxuUV_g?a>^kZilA^]Fvc_fwfpcLWcRHdAidc?Z\\VmwYn]wy:vaPxYiYwyekuF`Wg\\_BXqtK]fBGTg[EdqW@gTXcbMCg_?CUisu=FECY\\iCSqw^iy`CcigRnEYHQuO=R`oXKMDset`qEgSff;BjKthufmihlUFu;Rj?seyI:KEpyI:YXsyWyuyQ]ybqiKIhyyUEyI:YityI:Uf?=EW[ta?hpusnsX`UYQgXsCuOKvmIC_sCjeTpAUqeW@AfGmDJAUimWxWVUsTtgrWgF>mhmGCT=ypEILWCCmDN=V]?HNqxj;E^WDu[FLCCsGyQUy@yRxsygyI:ywdwIGyETkxy:NnFq_D@hbo\\pO\\CWh`xnSywGvpSqtAGi^VbmY`@`hVy`pxx`__HWvspqhgclv_EFwconRIeCW\\FqppNfHI]XNbV>^lqsl?q=qfb>ujFr?FbRVoyepgsIaYxYuy;rYiDyKey]XfyI:yvlyuxoyiAYKkVQ]rPKewgbgaRPScACu>WyvExjcWmgcKaXisf^yI:Ks<ay>;x:;g:;w[Ah`CEFsgYcdnYi_McPQt\\mfS[FgWdA]SikhgeXR[VhGXLAismShuybA=:xrpi;:Fe?HtPVn]@udouYWuZWxv^q;xj__uaX]K@p@_vfg[BIuP?rBAaOfZqpjnYmBGvBg_pFyXvcLpy]wlF`buHdOGkBAd_pj;FrXIyAVi`wvpikI`yxYeyuqexy;b@yCgSuYIivyhywyekYnGu?ED<sSEAgpuWf?Vo]XUgVGKD[_YXItl=RNwVIqXQcfD=I`gr@iracvRgD@gfqKRr?TsAEN;FlEIp;VFQXFCsa_ULes=gY]Y>::xG:ofDowqmxhErPkW@MFj?BJMTG?U_IFV?g\\KC:?g\\:r:QCkyfvCJy[]<DidwuoMyCosSLyI:`^eapyNyoV_E]:V^pfOxoCya`gp`p^tw^Axi]MpWFDDXXXimyw]gvY;upyRygRo[ho_EqKED?g\\;D?]TK;B?:PoSYWpMqhMpnXspLLsxW`qX@hsyTQ?ll?PuG]y_LMNYKXDkrlsDYJ]xJD\\PsmLYPQtUKCmohxvmxpDLwNik`MLc\\SF=lMTxvYRFXXmmK;@QfXn[yqgeSPEy_YlEePRmOgIU]]WGaMLTkAmkBmSB`K@Pl;QQ@LkAep><xPeqPhMeHunLyfywgXUIEWs=qq=kUYOVeUBaNGpppXxp@wviJQdjkhqm@l_V^nXlWGt\\yu`QgpH__qwYQq[qZWqq`_wmqrvFmmGw_yqqqc^FqOapUY_uWmEhq<OtBf_Vg^>QlFQojHpD>blocN>lbAbynuXNnsXqyoZsyiSqqfo`g^vrOjiydrHymovswmbOxUpwmQ^sAllQif?vvQnkhwxn]YIwtqhYh\\rHpWIga@u:At=aaPpufGpEFlcFeKx`?qlrx[wpb`Yre@ZVNtS^uSWwpvhtakpphipvfap<@xF_jnNhAG`JH^PwZYhxFgijnbCfw[`eyOjvH_yGveXkAiqsPj]qsBpbXn`JplyNguXmaFigNsVy^PWfJHuaFofA_:NN<:Z=vaO?[gafL@jKa`aQiX^k>ng=Y^y@^Y>rP_gtvoAx^egrI`wF^gUhgIQsZ`bkWlrpxWFicAlA?dkwiS?aPvfrfyeYveaVsdAaGrqYIQUNWfv=EGWDViwD]bDWCN;U[seX[BieIjIHRETCcuBiENmgneWAysLcHGeWZ?g^WIB_Gk;WSWdVYbrswZ[h\\aHeQE_kDUSYbcT>?gQ;HdOFFeBJ=EZus;erfUtd;sPEF?]ljPND<o:PND:Gj>yMlSyJ]J>_VbvY]QAorWlxmyXGJviBJMBnUxTSDMcyMWry;rkQxYkhGIxy;RKeGWesmkuWwA=pYdyPFnfhvr@tKgbN>jbNN;BD:LrgutuQQCMQQDQimOq=RHAJHEj=<nNlqAeYvluy=JZatY\\YOUS?YQkDUKDyY`XkIyyOZ^xY?Id_yIMA:OgPKshQbBYsBwiaYsI[iDYdyOs]AcyBvjLEt?=USELs;:K?:bd::jAI<>XRc::Zb<:NOJTUwRlO]HpHuxLlrtYoVAs:my?PoylxPXMyqqaqYxy`gP]bnv[_fJwk?Wt\\il^?cBfhZVj`y`]wmYGfQ?w\\XlggjLP[bNn;hjNFd:gZNFDjFtOLxY:<SLxstewIpYGPsluiyAZKXmPwy:voCyqneQ=grYTx?RL<jh@ty=jbadYOviFYxPwWmyAZ=g`gH`mFtvVayuA:ui?<weqmjyWvayqhY=\\wy=JnUuPitg]UpmlmlUFASD@KTur]Pp;TlSUsj=WIeR^aOxiNKll>ItfPJj\\k>xLLljS\\wpMR@qy>tKtyxSLvy=Jt]jcyY:<YSxPyAmdlxLqYTxNTyRtasOQnl`QIYly=JJUnIyi;XlyGxDhcxA_yAZZTayI:=>pMHyUMIRgYNwmNeETSYQvITyARGXQyUj`xY:TVNxWkyRwMjnxWvakUxY:\\kKaw_eYnpMLyQLqVohLOhmxen?hxopPcDv?@QtlvBmmSLU:]Uc\\wJ@S>`y[tkSHWHAQexpqMLUUmrio[YXhmw_Qx[`kp@tGapkHSfQJe`mZax^PvMUpTLldiVDQoYHUvXTyARwYMymjlxi]a\\wWm?yany[KyqjYfivy:>]_PsyAZ``]BIq?Wduy`Dxiby]]xiZqrYoykvbSaqMwY;Tyqry;b;_sy@Y?amiLy[asE\\LOyol@ya>ybwurI`Qxy:^kKoxY_\\yumGV]yI:AV@yExEHAYgxKUH]fWOVcgyUcry<wYTny=jZmrYmYkhr_hTMmUVAuYYUAiJVQkHTsNlJ>]vwERREPDPYelk:EWAUOH\\vWQnJ\\M<dYepPHeUqGgOfx@xmaXmC_tvf_mOikYq[`vkfdC@jByvgH[pn`La`bQoyofkycwYZnygvA]Eyy:nRqyGO>jijOtYFauBEQ?QTuyODrmGny=:rAEUvlI:Nsym;asE\\PO=Mhyw[]tPUrMiP<Hk^Hk`HkgtvlXnddlGDSOAn<XS@YqLiuWaug\\WPlppHXIuXt`qDPPBUV?iR:mV`AjKTsb<vX\\plYQRayDuthDtNqyGQF:rbSiqMsy;BbwU]yI:ZVJkTx\\dVOxsfmuc:yQ=:wSm?yaoy;KyqkAZ:BAKXhDowyL?yqmIV]xIjAEUvYTymQTxPx[@Usyun=DmQFgetEaGXFJRSjoijVup\\Lvu<K>uppPTsUp@iOrpJT=mZ=V^eL_Iq:UWAUoTLL_uULxiJ<jluI@CvoC=:<jh::xPwmIHnTPTRXPK]ARjJOYW?yY:LXbTwYiX]ypx=jdyOAxIxAxi?gpUGx<_`XX\\PI\\NVpo^l:IZNim@hnv?gL?ySWtT_udHuUQjAOy^xarAwdPq@AqtpdTpgPG`nfkf>d?G]gGn^Pl?gkq^]Vn_aI]ZN\\@>c>>xs?yvib`Xmro`Xob:Qb=Tv[Fbybo?GieHWQvxidgmW`wrC=xB]E;[bVkR>OHf;C>GD<;C>=T?QwjUxiEVyCXdGxpoVeUgtoDIOd`YWpeYDWYC]RpGWaYB^_iighSUdfKDOUEOGEqCU@CIR[rG]t\\IXvQhdUtUuBaax:crDEBeOebgEhYCWagKQDHYFsgRmWHuuReGFUWWVmBEES]otY]rQUXXsbbkdEuxbyX<Orl_IbSvKOXl;CC=wCiuQefW;hhWU[cbZ?Y=gdsqRjeg_EYPQBe=vcGE^?R[iuGohSKxDcgUmiJ;iRwueaTxyDqwCXiyHurHGh_odcKghuUiEwuwfBaiSUC>mh;wBPmXQiwR_UlQbEGrV[vO_e[EeqqiNoi\\aYqMCgudB?yTKvEuTswVCMdPGt;me>QTBwE:AxFSHsAy:;G:=bPyGv[VTVxnymWxae`txydqyZvViP`yC?_MHejqtI^yxhsyEc_xy;R]IdXgutwhAws__wAsY_wvfWSWQSUIDQ[IwgunSs]eBo_iHWVbwemAyISDawuBgheQi>Sg@WV\\cS]gGGqG^gRI=rTME_wEU;hYccLWSEISpwIcIsXeWqwu[mdwEWweR`wSgtoM<ucMo]LXh`OhlwW<kuTj@=xdHJHIPCTUvlxYdkYlPIPyDaTfyQnxOgtw[aTi\\Whho\\ML_TY[IlVMLN\\oBDLRhXGLy\\YP^ePoxWvIY_HWxPN=hrtpUM`sKqRlXp@Unm]MZ<KVAsZMl@\\V@=tCESUtUhqvUDxh`SrqVIQTPio`aPLTwBpW=LpBXvWxkPlk]`USeTLPsELqGAN@\\kRlORYtUXrpupM`olLwTHjw]YQPtZDLOqVXPNUdVj]l^ElTDoKaJ]EN=IV>pLxXlMiof@noTy`ENlPu:AlSapLUoopPPyrVuNiuNvITptmliKZ<JQToE=LG<QxlNRiUEampYsxDSgpw^DQOavKLtRQMVQOCHLFUuDysLXuptoUDmpmPtdU]pUE@uMQTgANT@jRMrGaP^=LSDUSImK`Tc\\jlTPHHxVLJAXnweKM@SQPldQmVxLC`lKXKMPOAXMTqNBQK[lrv`LsQR?tqpdvgisULUNELcqTiPKIaQgaNg`OLXSnlLpEQaLW?hTIYTolRHISEMlC=SAxupiNoiLIQs;]Y]qy=qQWHwy=J]lobUyZyxdlPMioAEkiduH@VPptkHPnuwlHvkhX=IOveRQiOMhnhekPYyADwGAx^PWXhkJalKpRWxwy=j\\plVtujeYexk=yxCtyBpsJPKSIpRERUXVm\\Od=MwER>lyNPnh@mYarypOAySdTWJEWThrhe^ii[Vx[kO^@IZ\\?o_@kS>^aWZPIqWxh?QaYqjnXmUXsyAZfIuXYguojopkXy^<F[]PjCOjsf_uat\\n`U>rF`vIvl`Yahfcfv\\jFc>Fxf>pDin^nk?_uh`nZOjI^ZKNukp_vvaeWicWhegibPgQ>hCaZJPbaFlRWueFn@?_pgvUHg@IyqnpmvsFYuHHbWp`IPvrgxeYyAIprosU@gXIbKHlqxcc^djGsJIi[_][GqYYq]N[ZpqQQuQ`tQo^]FjowfNId^He^HjZGl;GyWgdEp^r?sdFekQjm^qaAaVWeuAfqYnJxZdQlC^aQgnKxy:naqVjyeBqDO]DFYd@mXFUicuxYKypoudIYcIX\\SWOWbPQsD?wrqYbwvqWeYqwP_IGwDMgfyKcfiUU=GuWsRstwAECIrAstDyBjaxLcDiyftAttOyiATeqiNoQ\\yudQy?pSipnM`NGEWg]PJtRmiq?]UGPpgILWDTOilJYlR`UP\\okdJ:pP\\mtYlPIfmy?gqXlghswhwOijRyegnognhh_h>>lfh]S?c>NlCF]S^gJF]lHqEn_VAipYrIotf`xwGcvVkCay^PfmH^;_^RHZJG`S_fW_rGVwSnesX^egwHXt\\q_Uhh]gZYUgKbNWI;wVlGU\\edeiGGMUgGbuKRXAEMwWoqsj?rNScFGCveI]axdQVi=dBaRj_EnMbv_WMMRMWFu;xhuRf?C^ktZUFpyxv[dqsrnovlUTgaie;vnUU;UwfGVQQXg=WWaev;ifcW>]fkwXhCBA_DsArQaDxMvcKewgYuKWPuhPuHMWib_hsKTB;E?MSEGII?gCybHuuoIcsGhFYggyI:IFiYdAsWWmRbkeqWxDKfogXKGtNCsMUE==H`wrVmvM=ekkcmQEauuBiU_[coeUGyw]kuxgEtofJYvg_UUKEmOuiqw]WIbEyVeH`eWuocpqxLQubAbmyXTeVSyeG?DseR\\?sA]CssYfMGC_VLCcsWFJosy;RgYCdWgUShugHi;TYYE^yQlqtXympIRiitnEKPXYWMwbqsbqUo=rharg\\pDxUMDoYdJuDUlpUbuSLxICkteGPsl[KlywO:YL;`>u\\:FtctQ?AewUVMHnTLO_YPK]AJUkOATQyMaLWyXvlyN<dWlhtPpRPQplLwk`rBESX<kZ`VoAqgQtixY:LR?yPq]py=Jv]mAmYOdkp@rxlyW@T_lXs]PwhoWmKEiPN`vMlwpUty=J[QMJyQbYj^xi:A]y@yThnyU<crqsXnyI:[YVyBx]ty;R<:[AaDiqy\\gVIQvipbY^x;Nty?x@v_xq^QpyKfq=ny:PaIoy:fR;BkexAkILGgyGy]yI:AF\\yI:?x]kIL:ZExsrPhAIpuoyKfQ:jbyY:\\JiAry=JZpkMxY:NfyerOu]sICatYauKyI:=HkyUrIDyCsN:RKIIqmsRkxo_wncUycshkTTgiWSvrSRUUin_sj[X_?rcgF@WgBKucOVH?UVGVLcbF[wwIRe;uyDv\\XmuMmylYHXNyMkyDv\\X=:SgqAwn?uusyBot;uI:cuasY:Qvy;R\\Agy]ReAby:RoYCxK<:vK::uvssHQ]GuutyLro<ny=JJujC?Z:H`yGxnvqjiK:JNyY:fB:vI:Jipq[UsXhri=y@]xILI:YFxGDwYbx;RtyCxAr?yI:aBOyUr?s`qi`ycyWrByI:OrI=iBZHV>v_xFvEq]?ywrqB:ZQgoghofio?iq_`pP>x=HlVF\\dp_w?h:f\\Axy:F;J:<yrRNyq>:<IDOxxVr`nP@SbQw>LyPdKoUPGYx]HWMQSAeo^ppKTpYDO]hpUtYC`lYauKyY:<XkyMrITyEkN:jJalPTRciqEyqjeKbyMnIJLyY:<X@xOxqnI<y@]@:FoyOr?;Zy;:xXYDxlyRkXYxILwXjx;R\\Ri::y::jA;:VkI=ewSAuSIGk]Ipmxpotbsffqhj]g[wsx;Tmocsghp_y>URqcwG]bAStVGTAYDrGtDYby_RD:?a]<:fnaWiIXcRWqyE<gXZyQZZ:NF>gyAZ>ly?NBZRGQdy_RDZZ]]<:vnswxQ^_uw\\yGV:^;v_vY>:j>etY<yBqnxqvIxiAF\\yAZ?x]jIL:jExSrPxAE@::HTys::E@:vYA>?x]::hBXfu;:JemrbXN<`J<@k]LkRlRL@QJQoblx=DJRymjE<o^HV>djY@XK:WrBrMmfuMRC]wVCxa_I;afyqwJ<jKEOXyE_yFOuqeYxiK=iPWMwT`othk[lp`MT\\lTnQV]qtG<kDHVt<VtQYQyJi@SM@YEXTPtnQikheV_eXs\\kE\\MJXyD<QehkYxyf;:4:\"\{\}LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlP0dGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiU/RkYqLSUpQ0hJTERSRU5HNiI=

Figure 9.11 Plot Options for the Tangent Tutor

Figure 9.10 shows a tangent line (in green) at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7L0Y/RjFGQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGNS1JI21uR0YkNiRRIjJGJ0Y5Rjk=, and five secant lines (in blue) emanating from the same point. The slopes of these secant lines and the points where they intersect the graph of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== are listed to the right of the Plot Window. Pressing the Animate button will provide an animation of the secant lines approaching the tangent line.

At the extreme right of the Tangent Tutor, both the slope and the equation of the tangent line are given. Recall that the Tangent command gave the slope of the tangent line as 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.

O ponto destes exemplos \303\251 que a reta tangente \303\251 a linha reta que aparece quando enfocamos, no gr\303\241fico da fun\303\247\303\243o, em um ponto particular. A mesma reta pode ser obtida como o limite de retas secantes.

Quando o gr\303\241fico da fun\303\247\303\243o f tem uma reta tangente no 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, a inclina\303\247\303\243o da reta tangente \303\251 a derivada de f em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. A derivada pode ser escrita de v\303\241rios modos, inclusive

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtRiw2JVEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjtRJ25vcm1hbEYnLUYjNiQtRiw2JVEjZHhGJ0Y3RjpGPS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGSS8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrRj0= = 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 = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYsNiVRJHRhbkYnL0Y2USZmYWxzZUYnL0Y5USdub3JtYWxGJ0ZCLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZC = 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 = 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