HMMT November 2014 U20

Determine the number of sequences of sets $S_{1}, S_{2}, \ldots, S_{999}$ such that

$$S_{1} \subseteq S_{2} \subseteq \cdots \subseteq S_{999} \subseteq\{1,2, \ldots, 999\}$$

Here $A \subseteq B$ means that all elements of $A$ are also elements of $B$.