<Text-field style="Heading 1" layout="Heading 1">Question 1</Text-field>

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

A Solid body is thrown from the floor with initial speed LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EnYHZfXzBgRicvJStmb3JlZ3JvdW5kR1EqWzEyOCwwLDBdRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn. A spring (with coefficient LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy9GM1Enbm9ybWFsRic=) is located at a height of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy9GM1Enbm9ybWFsRic= above the floor.

How much will the spring flex?

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>

We write the energy equations:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJFR0YoLywkKigtSSVVbml0R0YoNiNJI2tnR0YoIiIiLUYyNiNJIm1HRigiIiMtRjI2I0kic0dGKCEiIyIjYSwmKigtRjI2I0kiTkdGKEY1RjZGNUkieEdGKEY5IiM4KipGMUY1RjZGNUY6Rj0sJkY2IyIiKiIjNSomRkRGNUY2RjVGNUY1IiNJNyMvLCQqKC1JJVVuaXRHNiQvSSttb2R1bGVuYW1lR0YoSSZVbml0c0dGJUYmNiM2Iy5GNEY1LUZSNiM2Iy5GOEY5LUZSNiM2Iy5GPEY9Rj4sJiooLUZSNiM2Iy5GQ0Y1RlpGNUZERjlGRSoqRlFGNUZaRjVGaG5GPSwmRlpGSComRkRGNUZaRjVGNUY1Rkw=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEpc2ltcGxpZnlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJFRidGL0YyL0YzUSdub3JtYWxGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMvLCQtSSVVbml0R0YoNiNJIkpHRigiI2EqJiwoKiRJInhHRigiIiMiIzhGNiIjSSIjRiIiIkY7Ri5GOzcjLywkLUklVW5pdEc2JC9JK21vZHVsZW5hbWVHRihJJlVuaXRzR0YlRiY2IzYjLkYxRjIqJkY0RjtGP0Y7

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

NiQjIiIqIiM4ISIk

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We can eliminate the the negative solution, thus,

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kieEc2IiQiJCNwISIk

JSFH

<Text-field style="Heading 1" layout="Heading 1">Question 4</Text-field>

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Particles motion is restrict to the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiWEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJm10ZXh0R0YkNiRRIllGJy9GM1Enbm9ybWFsRictRiw2I1EhRidGOQ== plane, a force is being applied to the particle depending its position on the plane:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRIkZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0Y0L0Y2USdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRL0ZORjQtSShtZmVuY2VkR0YkNiQtRiM2Ji1GLzYlUSJ4RidGMkY1LUY5Ni1RIixGJ0Y+L0ZBUSZmYWxzZUYnL0ZERjQvRkZGW28vRkhGW28vRkpGW28vRkxGW28vRk5GW29GTy9GU1EsMC4zMzMzMzMzZW1GJy1GLzYlUSJ5RidGMkY1Rj5GPi1GOTYtUSI9RidGPkZqbi9GREZbb0Zdb0Zeb0Zfb0Zgb0Zhby9GUFEsMC4yNzc3Nzc4ZW1GJy9GU0ZccC1GVjYkLUYjNiYtRi82JVEnJiM5NDU7RicvRjNGW29GPi1GOTYtUScmc2RvdDtGJ0Y+RmpuRmpvRl1vRl5vRl9vRmBvRmFvRk9GUkZkb0Y+Rj4tRiw2JS1GIzYlRlpGMkY1LUY5Ni5RLCZPdmVyQnJhY2U7RidGPEY+RkBGQ0ZFRkdGSUZLRlRGT0ZSRlQtRjk2LVEiK0YnRj5Gam5Gam9GXW9GXm9GX29GYG9GYW8vRlBRLDAuMjIyMjIyMmVtRicvRlNGZHEtRlY2JC1GIzYmLUYvNiVRJyYjOTQ2O0YnRmVwRj5GZnBGWkY+Rj4tRi82I1EhRictRiM2J0Zdci1GIzYlRl1yLUYsNiVGZG9GXXFGVEY+Rl1yLyUrZm9yZWdyb3VuZEdRKlsxMjgsMCwwXUYnRj5GXXJGZnJGPg==

Given:

QyY+SSZhbHBoYUc2Ii1JIipHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYpSShfc3lzbGliR0YlNiQiIiUtRic2JC1JJVVuaXRHRiU2Iy5JI2dyR0YlKiQtRjQ2Iy5JInNHRiUhIiMhIiI+SSViZXRhR0YlLUYnNiQiIipGMUY+

Calculate the work of the force (in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYoLUYjNigtSSNtaUdGJDYlUSRlcmdGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNC8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy8lLHBsYWNlaG9sZGVyR0Y2LyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR0Y2RjcvRjhRJ25vcm1hbEYnL0krbXNlbWFudGljc0dGJFElVW5pdEYnLyUlb3BlbkdRKCZsb2JyaztGJy8lJmNsb3NlR1EoJnJvYnJrO0YnRkMtRjE2I1EhRidGOkZB) according to the next routs, between the points:

QyYtSSIqRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkvVmVjdG9yQ2FsY3VsdXNHNiRGJkkoX3N5c2xpYkdGKTYkLUkmcG9pbnRHRik2JUkiQUdGKSIiIUYyLUklVW5pdEdGLDYjLkkjY21HRikhIiItRiQ2JC1GLzYlSSJCR0YpIiIiIiIjRjNGOA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The first rout is along the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy9GM1Enbm9ybWFsRic= and then parallel to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy9GM1Enbm9ybWFsRic= axis:

<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>

We use the definition of work:

JSFH

PiZJIldHNiI2IyIiIi1JIitHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYrSShfc3lzbGliR0YlNiQtSSRpbnRHRiU2JC1JIipHRio2JEkmYWxwaGFHRiVJInlHRiUvSSJ4R0YlOyYtSSxjb29yZGluYXRlc0dGJTYjSSJBRz1GJUkmZmFsc2VHRitFXFtsI0ksZ2VvbTJkL2Zvcm1HRiVJKHBvaW50MmRHRiVJLmdlb20yZC9jb29yZHNHRiU3JCIiIUZJRiYmLUY/NiNJIkJHPUYlRkNFXFtsI0ZFRkZGRzckRiciIiNGJi1GMzYkLUY2NiRJJWJldGFHRiVGOy9GOTsmRj42I0ZRJkZLRlo=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiV0dGKDYjIiIiLCYqKC1JJVVuaXRHRig2I0kjZ3JHRihGMC1GNDYjSSJzR0YoISIjSSJ5R0YoRjAiIiUqKEYzRjBGN0Y6SSJ4R0YoRjAiIz03IywmKigtSSVVbml0RzYkL0krbW9kdWxlbmFtZUdGKEkmVW5pdHNHRiVGJjYjNiMuRjZGMC1GRDYjNiMuRjlGOkY7RjBGPCooRkNGMEZMRjpGPkYwRj8=

We know the values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy9GM1Enbm9ybWFsRic= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= :

LUklZXZhbEclKnByb3RlY3RlZEc2JCZJIldHNiI2IyIiIjwkL0kieEdGKC1JJVVuaXRHSShfc3lzbGliR0YoNiMuSSNjbUdGKC9JInlHRigtSSIqRzYkRiQvSSttb2R1bGVuYW1lR0YoSS9WZWN0b3JDYWxjdWx1c0c2JEYkRjA2JCIiIUYu

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJCooLUklVW5pdEdGKDYjSSNnckdGKCIiIi1GLzYjSSJzR0YoISIjLUYvNiNJI2NtR0YoRjIiIz03IywkKigtSSVVbml0RzYkL0krbW9kdWxlbmFtZUdGKEkmVW5pdHNHRiVGJjYjNiMuRjFGMi1GPzYjNiMuRjVGNi1GPzYjNiMuRjlGMkY6

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We got a solution but we need the change it to LUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXJvd0dGJDYlLUkjbWlHRiQ2JVEkZXJnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUwZm9udF9zdHlsZV9uYW1lR1ElVGV4dEYnL0Y2USdub3JtYWxGJ0Y7L0krbXNlbWFudGljc0dGJFElVW5pdEYnLyUlb3BlbkdRKCZsb2JyaztGJy8lJmNsb3NlR1EoJnJvYnJrO0YnRj0=

We know that 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

therefore,

PiZJIldHNiI2IyIiIi1JIipHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYrSShfc3lzbGliR0YlNiQiIz0tSSVVbml0R0YwNiMuSSRlcmdHRiU=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiV0dGKDYjIiIiLCQtSSVVbml0R0YoNiNJJGVyZ0dGKCIjPTcjLCQtSSVVbml0RzYkL0krbW9kdWxlbmFtZUdGKEkmVW5pdHNHRiVGJjYjNiMuRjVGNg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The second rout is along

L0kieUc2Ii1JIipHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSS9WZWN0b3JDYWxjdWx1c0c2JEYoSShfc3lzbGliR0YkNiQiIiMqJEkieEdGJCMiIiJGLw==

L0kieUc2IiwkKiRJInhHRiQjIiIiIiIjRio=

<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>

We find the expression to the new route:

PkkneV9fbmV3RzYiLUkiKkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiRJL1ZlY3RvckNhbGN1bHVzRzYkRihJKF9zeXNsaWJHRiQ2JCIiIy1JJXNxcnRHRiQ2I0kieEdGJA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSd5X19uZXdHRigsJCokSSJ4R0YoIyIiIiIiI0YzNyNGLg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

PkkneF9fbmV3RzYiLUkmc29sdmVHRiQ2JC9JInlHRiQtSSIqRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEkvVmVjdG9yQ2FsY3VsdXNHNiRGLUkoX3N5c2xpYkdGJDYkIiIjLUklc3FydEdGMTYjSSJ4R0YkRjg=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSd4X19uZXdHRigsJCokSSJ5R0YoIiIjIyIiIiIiJTcjRi4=

Now we can write the Work equation like we did previously:

PiZJIldHNiI2IyIiIy1JIipHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSS9WZWN0b3JDYWxjdWx1c0c2JEYrSShfc3lzbGliR0YlNiQtSSIrR0YqNiQtSSRpbnRHRi82JC1GKTYkSSZhbHBoYUdGJUkneV9fbmV3R0YlL0kieEdGJTsmLUksY29vcmRpbmF0ZXNHRiU2I0kiQUc9RiVJJmZhbHNlR0YrRVxbbCNJLGdlb20yZC9mb3JtR0YlSShwb2ludDJkR0YlSS5nZW9tMmQvY29vcmRzR0YlNyQiIiFGSzYjIiIiJi1GQTYjSSJCRz1GJUZFRVxbbCNGR0ZIRkk3JEZNRidGTC1GNjYkLUYpNiRJJWJldGFHRiVJJ3hfX25ld0dGJS9JInlHRiU7JkZARiYmRk9GJiokLUklVW5pdEdGMDYjLkkjY21HRiVGJw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+JkkiV0dGKDYjIiIjLCQqKC1JJVVuaXRHRig2I0kjZ3JHRigiIiItRjQ2I0kic0dGKCEiIy1GNDYjSSNjbUdGKEYwIyIjTSIiJDcjLCQqKC1JJVVuaXRHNiQvSSttb2R1bGVuYW1lR0YoSSZVbml0c0dGJUYmNiM2Iy5GNkY3LUZGNiM2Iy5GOkY7LUZGNiM2Iy5GPkYwRj8=

JSFH

So our answer is:

LSZJJmV2YWxmRyUqcHJvdGVjdGVkRzYjIiImNiMtSSVzdWJzR0YlNiQvLUkiKkc2JEYlL0krbW9kdWxlbmFtZUc2IkkvVmVjdG9yQ2FsY3VsdXNHNiRGJUkoX3N5c2xpYkdGMjYkLUYuNiQtSSVVbml0R0Y1NiMuSSNnckdGMiokLUY6NiMuSSNjbUdGMiIiIyokLUY6NiMuSSJzR0YyISIjLUY6NiMuSSRlcmdHRjIsJCooLUklVW5pdEc2JC9GMUkmVW5pdHNHRjRGJUY7IiIiLUZRRkZGSS1GUUZARkMjIiNNIiIk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMsJC1JJVVuaXRHRig2I0kkZXJnR0YoJCImTDgiISIkNyMsJC1JJVVuaXRHNiQvSSttb2R1bGVuYW1lR0YoSSZVbml0c0dGJUYmNiM2Iy5GMEYx

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=