Square S_{1} is 1 \times 1. For i \geq 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.