Square S1 is 1×1. For i≥1, the lengths of the sides of square Si+1 are half the lengths of the sides of square Si, two adjacent sides of square Si are perpendicular bisectors of two adjacent sides of square Si+1, and the other two sides of square Si+1, are the perpendicular bisectors of two adjacent sides of square Si+2. The total area enclosed by at least one of S1,S2,S3,S4,S5 can be written in the form m/n, where m and n are relatively prime positive integers. Find m−n.[asy]
size(250);
path p=rotate(45)*polygon(4);
int i;
for(i=0; i<5; i=i+1) {
draw(shift(2-(1/2)^(i-1),0)*scale((1/2)^i)*p);
}
label("S1", (0,-0.75));
label("S2", (1,-0.75));
label("S3", (3/2,-0.75));
label("⋯", (7/4, -3/4));
label("⋯", (2.25, 0));[/asy] geometrynumber theoryrelatively prime