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)