2002 AIME I Problem 14

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?

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.