Triangle A B C has lengths A B=20, A C=14, B C=22. The median from B intersects A C at M and the angle bisector from C intersects A B at N and the median from B at P. Let \frac{p}{q}=\frac{[A M P N]}{[A B C]} for positive integers p, q coprime. Note that [A B C] denotes the area of triangle A B C. Find p+q.