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)