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Consider the following system of equation over positive integers \(x,y,z\).

\[\large \begin{cases} xy + xz = 357 \\xy + yz = 37 \end{cases}\]

Let \(N\) be the number of solution triplets \((x,y,z)\) and \(M\) the maximum value of \(xyz\).

Find \(N + M\).


Inspiration.

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