9. (22nd All-Soviet Union Mathematical Olympiad, 1988) Determine the minimum value of \( n \) for which the following system of equations
\[
\left\{\begin{array}{l}
\sin x_{1}+\sin x_{2}+\cdots+\sin x_{n}=0 \\
\sin x_{1}+2 \sin x_{2}+\cdots+n \sin x_{n}=100
\end{array}\right.
\]
has a solution.