The solutions to the equations $z^2=4+4\sqrt{15}i$ and $z^2=2+2\sqrt{3}i$, where $i=\sqrt{-1}$, form the vertices of a parallelogram in the complex plane. The area of this parallelogram can be written in the form $p\sqrt{q}-r\sqrt{s}$, where $p$, $q$, $r$, and $s$ are positive integers and neither $q$ nor $s$ is divisible by the square of any prime number. Find the value of $p+q+r+s$.

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