ABCD is a quadrilateral such that AD = 9 cm, BC = 13 cm and ∠DAB = ∠BCD = 90°. P and Q are two points on AB and CD respectively, such that DQ : BP = 1 : 2 and DQ is an integer. How many values can DQ take, for which the maximum possible area of the quadrilateral PBQD is 150 sq.cm?