The solutions to the equations $z^2=4+4\sqrt{3}i$ and $z^2=4+4\sqrt{15}i$, 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. What is $p+q+r+s$?