You're gonna love this (Part-2)!

Algebra Level 5

{x2+y2+z2=901x2z2+y2z2=152100\begin{cases} x^2+y^2+z^2&=901\\ x^2z^2+y^2z^2&=152100\\ \end{cases}

How many ordered triplets (x,y,z)(x,y,z) of integer solutions are there to the system of equations above?

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