A equa\303\247\303\243o de oscila\303\247\303\243o de flex\303\243o amortecidavon M. P\303\266hlmannEmail: Poehlmann001@aol.comNesta planilha, determinamos uma solu\303\247\303\243o para a equa\303\247\303\243o de vibra\303\247\303\243o de flex\303\243o com uma montagem articulada e amortecimento temporal das vibra\303\247\303\265es.Consideramos uma barra homog\303\252nea de comprimento L, que \303\251 apoiada em dois lugares no eixo x. Esta haste se curva sob a influ\303\252ncia de cargas verticais y (x) e executa vibra\303\247\303\265es longitudinais que diminuem em amplitude com o tempo devido ao amortecimento.A equa\303\247\303\243o de vibra\303\247\303\243o de flex\303\243o com amortecimento ao longo do tempo \303\251: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(); # input placeholderExistem y (x, t) - deflex\303\243o em fun\303\247\303\243o da localiza\303\247\303\243o xe do tempo t E - m\303\263dulo de elasticidade, Ix - momento de in\303\251rcia da \303\241rea \317\201 - densidade, A - se\303\247\303\243o transversal da haste e L - comprimento da haste \316\262 - coeficiente de amortecimentoAs condi\303\247\303\265es de contorno dependem do tipo de suporte da haste. Apenas o mancal articulado (mancal fixo e solto) pode ser resolvido analiticamente, para o qual se aplica o seguinte:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY/LUkjbWlHRiQ2JVEjUkJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ5RidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIwRidGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUZXRmVuLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGaW4vRk5Gam5GZW8tRlM2JC1GIzYnLUYsNiVRIkRGJy9GMEY9RjktRlM2Ji1GIzYnLUZYNiRRIjFGJ0Y5RmVuRmVwRmBvRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GLDYjUSFGJ0Zgb0Y5RjktRlM2JC1GIzYlRk9GYG9GOUY5RlJGYm9GV0ZlbkZlb0ZPLUZTNiQtRiM2Jy1GLDYlUSJMRidGL0YyRmVuRl1vRmBvRjlGOUZib0ZXRmVuRmVvRmlvRmFxRmVxRmJvRldGYG9GOQ==print(); # input placeholderTal como acontece com a equa\303\247\303\243o de onda, as condi\303\247\303\265es iniciais para a solu\303\247\303\243o temporal dependem dos coeficientes de Fourier:
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print(); # input 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(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">1. Separa\303\247\303\243o das vari\303\241veis</Font></Text-field>A fim de encontrar uma solu\303\247\303\243o para a equa\303\247\303\243o de vibra\303\247\303\243o de flex\303\243o, realizamos uma abordagem de separa\303\247\303\243o baseada em uma solu\303\247\303\243o espacial e temporal:
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print(); # input placeholderA inser\303\247\303\243o no DGL parcial e a separa\303\247\303\243o das vari\303\241veis \342\200\213\342\200\213resultam em:
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print(); # input placeholderOs lados direito e esquerdo da equa\303\247\303\243o (1.2) tornam-se um par\303\242metro de separa\303\247\303\243o negativo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSVtc3VwR0YkNiUtSSNtaUdGJDYlUScmIzk1NTtGJy8lJ2l0YWxpY0dGNEYvLUYjNiQtSSNtbkdGJDYkUSIyRidGL0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Yv igualado. Isso d\303\241 duas equa\303\247\303\265es diferenciais ordin\303\241rias, cada uma para tempo e lugar:1. Equa\303\247\303\243o dependente da localiza\303\247\303\243o
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print(); # input placeholder2. Equa\303\247\303\243o dependente do tempo
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print(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">2. L\303\266sung des \303\266rtlichen Eigenwertproblemes</Font></Text-field>Transformamos a equa\303\247\303\243o dependente da posi\303\247\303\243o (1.3) um pouco 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(); # input placeholdere definir o par\303\242metro 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JSFH :
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print(); # input placeholderEstamos procurando uma solu\303\247\303\243o para as condi\303\247\303\265es de contorno de rolamentos articulados em rolamentos fixos e flutuantes. As condi\303\247\303\265es de limite s\303\243o:
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(); # input placeholderA solu\303\247\303\243o geral da equa\303\247\303\243o (2.2) \303\251:
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print(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EjRzhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RKiZjb2xvbmVxO0YnRjJGNS9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkobWZlbmNlZEdGJDYoLUYjNiUtRiw2J1EjUlJGJ0YvRjJGNUY4RjJGP0YyRjVGPy8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRictRjw2L1EiOkYnRjJGNUY/RkFGQ0ZFRkdGSUZLRk1GT0ZSRjJGPw==print(); # input placeholderOs valores pr\303\263prios \316\272 s\303\243o determinados a partir da matriz de coeficiente das constantes:
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(); # input 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print(); # input placeholderOs valores pr\303\263prios s\303\243o determinados a partir da equa\303\247\303\243o (2.6).
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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVExX0VudkFsbFNvbHV0aW9uc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVGMUYvRjItRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0Y9Rjk=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(); # input 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print(); # input placeholderOs valores pr\303\263prios da equa\303\247\303\243o dependente da posi\303\247\303\243o s\303\243o, portanto: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print(); # input placeholderDetermina\303\247\303\243o da fun\303\247\303\243o pr\303\263pria EF: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print(); # input 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print(); # input 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print(); # input placeholderA autofun\303\247\303\243o \303\251 determinada a partir da equa\303\247\303\243o
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(); # input 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print(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVExX0VudkFsbFNvbHV0aW9uc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVGPUYvRjItRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0Y9Rjk=
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">3. Solu\303\247\303\243o geral para o problema de vibra\303\247\303\243o</Font></Text-field>A solu\303\247\303\243o para o problema de vibra\303\247\303\243o de flex\303\243o pode ser representada na forma da seguinte expans\303\243o em s\303\251rie:
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print(); # input placeholder
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">4. Solu\303\247\303\243o do problema do valor inicial temporal</Font></Text-field>Para o problema do tempo, temos que resolver a seguinte equa\303\247\303\243o diferencial ordin\303\241ria:
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(); # input placeholderPara resolver a equa\303\247\303\243o (4.1), precisamos dos seguintes valores iniciais:
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(); # input 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(); # input placeholderIsso d\303\241 a seguinte solu\303\247\303\243o temporal:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EkRzIyRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUSomY29sb25lcTtGJ0YyRjUvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUS1GLDYnUSlzaW1wbGlmeUYnRi9GMkY1RjgtSShtZmVuY2VkR0YkNiYtRiM2KC1GLDYnUSdkc29sdmVGJ0YvRjJGNUY4LUZYNiYtRiM2KS1GWDYoLUYjNiktRiw2J1EkRzE5RidGL0YyRjVGOC1GPDYvUSIsRidGMkY1Rj9GQS9GREYxRkVGR0ZJRktGTS9GUFEmMC4wZW1GJy9GU1EsMC4zMzMzMzMzZW1GJy1GLDYnUSRHMjBGJ0YvRjJGNUY4RmRvLUYsNidRJEcyMUYnRi9GMkY1RjhGMkY/RjJGNUY/LyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0Zkby1GLDYnUSJURidGL0YyRjVGOC1GWDYoLUYjNiUtRiw2J1Eia0YnRi9GMkY1RjhGMkY/RjJGNUY/L0ZjcFEiW0YnL0ZmcFEiXUYnLUZYNiYtRiM2JS1GLDYnUSJ0RidGL0YyRjVGOEYyRj9GMkY1Rj9GMkY/RjJGNUY/RmRvLUYsNidRKXN5bWJvbGljRidGL0YyRjVGOEYyRj9GMkY1Rj9GMkY/print(); # input 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print(); # input placeholderJSFH
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">5. Apresenta\303\247\303\243o da solu\303\247\303\243o geral</Font></Text-field>Ao inserir a solu\303\247\303\243o temporal (4.5) na equa\303\247\303\243o da solu\303\247\303\243o geral (3.1), obtemos a solu\303\247\303\243o geral:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVElTG9lc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRJXN1YnNGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2Jy1GLDYlUSRHMjNGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSNMU0YnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5Rl9vRjk=print(); # input placeholderVamos tamb\303\251m definir os valores pr\303\263prios LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTQ7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYkLUYvNiVRImtGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNQ== na solu\303\247\303\243o, obtemos:
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print(); # input placeholderA equa\303\247\303\243o (5.2) descreve o comportamento de vibra\303\247\303\243o de flex\303\243o da haste el\303\241stica com comportamento de vibra\303\247\303\243o amortecida.
<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">6. Exemplo do comportamento de vibra\303\247\303\243o flexural</Font></Text-field>O comportamento da vibra\303\247\303\243o flexural deve ser ilustrado usando um exemplo anal\303\255tico.Definimos os seguintes par\303\242metros: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print(); # input placeholderO seguinte se aplica \303\240 deflex\303\243o inicial:
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print(); # input 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print(); # input 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(); # input placeholderA solu\303\247\303\243o agora pode ser exibida como uma anima\303\247\303\243o:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmcGxvdHNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2JS1GLDYlUShhbmltYXRlRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRjY2JC1GIzZGLUYsNiVRJHJoc0YnRi9GMi1GNjYkLUYjNiUtRiw2JVEjQjJGJ0YvRjJGPUZARkAtSSNtb0dGJDYtUSIsRidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInhGJ0YvRjItRlc2LVEiPUYnRkBGWi9GZ25GP0ZobkZqbkZcb0Zeb0Zgby9GY29RLDAuMjc3Nzc3OGVtRicvRmZvRmBwLUkjbW5HRiQ2JFEiMEYnRkAtRlc2LVEjLi5GJ0ZARlpGXnBGaG5Gam5GXG9GXm9GYG8vRmNvUSwwLjIyMjIyMjJlbUYnL0Zmb0Zkby1GLDYlUSJMRidGL0YyRlYtRiw2JVEidEYnRi9GMkZbcEZicEZmcC1GY3A2JFEkMC42RidGQEZWLUYsNiVRJ2ZyYW1lc0YnRi9GMkZbcC1GY3A2JFEkMjUwRidGQEZWLUYsNiVRJWF4ZXNGJ0YvRjJGW3AtRiw2JVEmYm94ZWRGJ0YvRjJGVi1GLDYlUSp0aGlja25lc3NGJ0YvRjJGW3AtRmNwNiRRIjJGJ0ZARlYtRiw2JVEmdGl0bGVGJ0YvRjJGW3AtRiw2JVE/YEJpZWdlc2Nod2luZ3VuZ35laW5lc35TdGFiZXNgRidGL0YyRlYtRiw2JVEqdGl0bGVmb250RidGL0YyRltwLUY2NiYtRiM2KS1GLDYlUSZUSU1FU0YnRi9GMkZWLUYsNiVRJlJPTUFORidGL0YyRlYtRmNwNiRRIzE1RidGQEY9RkBGQEZCRkVGPUZARkBGPUZA%;JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEjQjNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSVzdWJzRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiotRiw2JVEieEYnRi9GMi1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRIjFGJ0Y5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEjQjJGJ0YvRjIvJStleGVjdXRhYmxlR0Y9LyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnRjlGOUZmb0Zob0Y5print(); # input 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%;LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH