Let $n = p_1p_2... p_{2017}$ be the positive integer where $p_1, p_2, ..., p_{2017}$ are $2017$ distinct odd primes. A triangle is called nice if it is a right triangle with integer side lengths and the inradius is $n$. Find the number of nice triangles (two triangles are consider different if their tuples of length of sides are different)