A set $$\mathcal{S}$$ of distinct positive integers has the following property: for every integer $$x$$ in $$\mathcal{S},$$ the arithmetic mean of the set of values obtained by deleting $$x$$ from $$\mathcal{S}$$ is an integer. Given that 1 belongs to $$\mathcal{S}$$ and that 2002 is the largest element of $$\mathcal{S},$$ what is the greatest number of elements that $$\mathcal{S}$$ can have?

(第二十届AIME1 2002 第14题)