In triangle A B C, A B=125, A C=117, and B C=120. The angle bisector of angle A intersects \overline{B C} at point L, and the angle bisector of angle B intersects \overline{A C} at point K. Let M and N be the feet of the perpendiculars from C to \overline{B K} and \overline{A L}, respectively. Find M N.