Note: Figure not drawn to scale.
In quadrilateral KLMN shown, KL=3,LM=3,KN=27, and MN=27. Diagonals KM and LN (not shown) intersect at point G (not shown), where GK=1 and GM=1. If the length of diagonal LN is p+w, where p and w are integers, what is the value of p+w?