Let's write \(p\), \(q\), and \(r\) as three distinct prime numbers, where 1 is not a prime. Find the smallest positive perfect cube that leaves \(n = pq^2r^4\) as a divisor. The original answer is in the form \((p^a q^b r^c)^3\), please give the value of a + b + c.

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