A finite set \(\mathcal{S}\) of distinct real numbers has the following properties: the mean of \(\mathcal{S}\cup\{1\}\) is \(13\) less than the mean of \(\mathcal{S}\), and the mean of \(\mathcal{S}\cup\{2001\}\) is \(27\) more than the mean of \(\mathcal{S}\). Find the mean of \(\mathcal{S}\).
(第十九届AIME1 2001 第2题)