Rectangle A B C D is given with A B=63 and B C=448. Points E and F lie on \overline{A D} and \overline{B C} respectively, such that A E=C F=84. The inscribed circle of triangle B E F is tangent to \overline{E F} at point P, and the inscribed circle of triangle D E F is tangent to \overline{E F} at point Q. Find P Q.