AIME 2002b Problem 9

Let $\mathcal{S}$ be the set $\lbrace1,2,3,\ldots,10\rbrace$. Let $n$ be the number of sets of two non-empty disjoint subsets of $\mathcal{S}$. (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained when $n$ is divided by $1000$.