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Algebra Level 4

Let $$x,y,z$$ be real numbers satisfying $$x+y+z = 0$$ and $$x^2 + y^2 + z^2 = 8$$. If the minimum value of $$|x| + |y| + |z|$$ is $$S$$, find $$\left\lfloor 10000S \right\rfloor$$.

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