# This works - I don't know why

Let $$a_0, a_1, \cdots, a_7$$ be any $$8$$ distinct integers. Let $$P$$ be the product of their pairwise differences, that is:

$P = \prod _ {i < j} {(a_i - a_j)}$

What is the greatest integer which always divides $$P?$$

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