Let $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ be points with integer coordinates satisfying the system of homogeneous equations:
$$
\begin{array}{r}
3 x-y-z=0 \\
-3 x+z=0 \\
-3 x+2 y+z=0
\end{array}
$$
Then the number of such points for which $x^2+y^2+z^2 \leq 100$ is
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