2004 AIME I Problem 12

Let \mathcal{S} be the set of ordered pairs (x, y) such that 0<x \leq 1,0<y \leq 1, and \left\lfloor\log _{2}\left(\frac{1}{x}\right)\right\rfloor and \left\lfloor\log _{5}\left(\frac{1}{y}\right)\right\rfloor are both even. Given that the area of the graph of \mathcal{S} is m / n, where m and n are relatively prime positive integers, find m+n. The notation \lfloor z\rfloor denotes the greatest integer that is less than or equal to z.