14.5.23 ** If for a natural number $n(\geqslant 2)$, there are integers $a_{1}, a_{2}, \cdots, a_{n}$ satisfying
$$
a_{1}+a_{2}+\cdots+a_{n}=a_{1} \cdot a_{2} \cdot \cdots \cdot a_{n}=1990 \text {, }
$$

find the minimum value of $n$.