Let \( a_1,\, a_2,\, a_3, \ldots \) be a GP of increasing positive numbers. If the product of fourth and sixth terms is \( 9 \) and the sum of fifth and seventh terms is \( 24 \), then \( a_1 a_9 + a_2 a_4 a_9 + a_5 + a_7 \) is equal to ________.
