Question 59
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 $B$.
$$
S_{1} \subseteq S_{2} \subseteq \cdots \subseteq S_{999} \subseteq \{1,2, \ldots, 999\}
$$
Here $A \subseteq B$ means that all elements of $A$ are also elements of $B$.