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. What is p+q+r+s ?
Answer Choices
A. 20
B. 21
C. 22
D. 23
E. 24