# Pain and gain

Algebra Level 4

$\large x^2y^2z^2$

Let $$x,y$$ and $$z$$ be reals number satisfying the conditions $$x+y+z=0$$ and $$x^2+y^2+z^2=1$$.

Let the maximum of the expression above is $$P$$, submit your answer as $$\left \lfloor 10000P \right \rfloor$$.

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