APMO 1998 Problem 1

Let $F$ be the set of all $n$ -tuples $(A_1, \ldots, A_n)$ such that each $A_{i}$ is a subset of $\{1, 2, \ldots, 1998\}$ . Let $|A|$ denote the number of elements of the set $A$ . Find $$\sum_{(A_1, \ldots, A_n)\in F} |A_1\cup A_2\cup \cdots \cup A_n|$$