2002 AIME II Problem 13

In triangle A B C, point D is on \overline{B C} with C D=2 and D B=5, point E is on \overline{A C} with C E=1 and E A=3, A B=8, and \overline{A D} and \overline{B E} intersect at P. Points Q and R lie on \overline{A B} so that \overline{P Q} is parallel to \overline{C A} and \overline{P R} is parallel to \overline{C B}. It is given that the ratio of the area of triangle P Q R to the area of triangle A B C is m / n, where m and n are relatively prime positive integers. Find m+n.