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Consider the following system of equation over positive integers x,y,zx,y,z.

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

Let NN be the number of solution triplets (x,y,z)(x,y,z) and MM the maximum value of xyzxyz.

Find N+MN + M.


Inspiration.

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