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1. Maximum size of a set with integer means ●●●○○ 50 ptsLet $S$ be a set of positive integers with the property that for any $x \in S$, the arithmetic mean of the remaining numbers in $S$ after removing $x$ is a positive integer. Suppose $1 \in S$ and $2016$ is the largest element of $S$. Find the maximum value of $|S|$.