[Value = 9 points]
Let S be a set of positive integers, such that 1 ∈ S, 2002 ∈ S, and for all n ∈ S, n < 2003.
Suppose S has the following feature: for any n ∈ S, the mean of the elements of S - {n} is an integer.
What is the greatest number of elements S could have?
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