Square \(S_{1}\) is \(1\times 1.\) For \(i\ge 1,\) the lengths of the sides of square \(S_{i+1}\) are half the lengths of the sides of square \(S_{i},\) two adjacent sides of square \(S_{i}\) are perpendicular bisectors of two adjacent sides of square \(S_{i+1},\) and the other two sides of square \(S_{i+1},\) are the perpendicular bisectors of two adjacent sides of square \(S_{i+2}.\) The total area enclosed by at least one of \(S_{1}, S_{2}, S_{3}, S_{4}, S_{5}\) can be written in the form \(m/n,\) where \(m\) and \(n\) are relatively prime positive integers. Find \(m-n.\)

(第十三届AIME1995 第1题)