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

Let's think step by step and output the final answer within \boxed{}.
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