Let $$S$$ be the set of ordered pairs $$(x, y)$$ such that $$0 < x \le 1, 0 < y \le 1,$$ and $$\left[\log_2{\left(\frac 1x\right)}\right]$$ and $$\left[\log_5{\left(\frac 1y\right)}\right]$$ are both even. Given that the area of the graph of $$S$$ is $$m/n,$$ where $$m$$ and $$n$$ are relatively prime positive integers, find $$m+n.$$ The notation $$[z]$$ denotes the greatest integer that is less than or equal to $$z.$$

(第二十二届AIME1 2004 第12题)