2002 AIME II 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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.