A quadrilateral has vertices $P(a,b)$, $Q(b,a)$, $R(-a, -b)$, and $S(-b, -a)$, where $a$ and $b$ are integers with $a > b > 0$. The area of $PQRS$ is $16$. What is the value of $a+b$?

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