AUSTRIAN-POLISH 1980 Problem 7

Find the greatest natural number $n$ such there exist natural numbers $x_{1}, x_{2}, \ldots, x_{n}$ and natural $a_{1}< a_{2}< \ldots < a_{n-1}$ satisfying the following equations for $i =1,2,\ldots,n-1$: $$x_{1}x_{2}\ldots x_{n}= 1980 \text{and} x_{i}+\frac{1980}{x_{i}}= a_{i}.$$