Take a stick of length $\mathcal{l},$ and remove the middle third. Then remove the middle third from each of the remaining two pieces. Then remove the middle third from each of the remaining four pieces, and so on, forever. Let the final object have mass m, and let the axis be through the center, perpendicular to the stick; see fig. If moment of inertia of such a stick is $\frac{1}{n}m{\mathcal{l}}^2,$ find n = ?