Given that $a_m$ (m<2016) are nonegative integers, how many distinct sets of $a_m$ are there such that:

$\prod_{n=1}^{403}\sum_{k=0}^4 a_{5n-k}=2015$

Add the digits of the big number up.

Details: In this case, 'distinct' means that all elements in two sets cannot be equal to each other in a fixed order. (i.e. $a_k$ in set a $\not=$ $a_k$ in set b when 0<k<2016, or else set a and set b are not distinct. Otherwise, they are.)

The answer is 1323.

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