$n$ $2 \times 2$ squares are drawn on the Cartesian plane. The sides of these squares are parallel to the coordinate axes. It is known that the center of any square is not an inner point of any other square. Let $\Pi$ be a rectangle such that it contains all these $n$ squares and its sides are parallel to the coordinate axes.
Prove that the perimeter of $\Pi$ is no smaller than $4(\sqrt{n} + 1)$.