# Will you integrate? (2)

Calculus Level 5

Let $${V}_{1}$$ be the volume generated by all the possible positions of $$P(x,y,z)$$ such that $\left\lfloor \left| x \right| \right\rfloor +\left\lfloor \left| y \right| \right\rfloor +\left\lfloor \left| z \right| \right\rfloor =n$ And let $${V}_{2}$$ be the volume enclosed by the surface $\left| x \right| +\left| y \right| +\left| z \right| =\frac{n+1}{\sqrt{2}}$ If $${V}_{1}+{V}_{2} =800 \text{ unit}^{3}$$. Find $$n$$

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