A large square region is paved with $n^2$ gray square tiles, each measuring $s$ inches on a side. A border $d$ inches wide surrounds each tile. The figure below shows the case for $n=3$. When the gray tiles cover $64\%$ of the area of the large square region, and the ratio $\frac{d}{s}=\frac{3}{13}$, what is the value of $n$?