$ \text{Let } R \text{ be the focus of the parabola } y^{2}=20x \text{ and the line } y=mx+c \text{ intersect the parabola at two points } P \text{ and } Q. $ $ \text{Let the point } G(10,10) \text{ be the centroid of the triangle } PQR. \text{ If } c-m=6, \text{ then } (PQ)^{2} \text{ is:} $