For each set of five integers $S= \{a_1, a_2, a_3, a_4, a_5\}$, let $P_S$ be the product of all differences between two of the elements, namely:

$$P_S = (a_5-a_1)(a_4-a_1)(a_3-a_1)(a_2-a_1)(a_5-a_2)(a_4-a_2)(a_3-a_2)(a_5-a_3)(a_4-a_3)(a_5-a_4)$$

Determine the greatest integer $n$ such that given any set $S$ of five integers, $n$ divides $P_S$.

Let's think step by step and output the final answer within \boxed{}.
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