# That seems nice! (Updated)

$\Large{ A = 1! \cdot 2! \cdot 3! \cdots 16! }$

Find the number of all positive cubic divisors of $$A$$. If the answer is $$p$$, enter the remainder of $$p$$ when divided by $$1000$$.

Assumption: A cubic divisor of $$A$$ is a divisor of $$A$$ that is also a cubic number; that is, a perfect third power.

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