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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