A polynomial $P$ is called *level* if it has integer coefficients and satisfies the conditions $P(0) = P(2) = P(5) = P(6) = 30$. Find the largest positive integer $d$ such that for any level polynomial $P$, $d$ is a divisor of $P(n)$ for all integers $n$.

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