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 \(1000\).
(第二十届AIME2 2002 第9题)