For how many primes \( p \), there exist unique integers \( r \) and \( s \) such that for every integer \( x \), the congruence \( x^{3} - x + 2 \equiv (x - r)^{2} (x - s) \pmod{p} \) holds? Find the number of such primes.

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