Let $N = 30^{2015}$. Find the number of ordered 4-tuples of integers $(A, B, C, D) \in \{1, 2, \ldots, N\}^4$ (not necessarily distinct) such that for every integer $n$, $An^3 + Bn^2 + 2Cn + D$ is divisible by $N$.

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