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Let $A = \begin{bmatrix} x & y & z \ y & z & x \ z & x & y \end{bmatrix}$, where $x, y$ and $z$ are real numbers such that $x + y + z > 0$ and $xyz = 2$. If $A^2 = I_3$, then the value of $x^3 + y^3 + z^3$ is ______.
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