CGMO 2009 Problem 7

On a $10 \times 10$ chessboard, some $4n$ unit squares are chosen to form a region $\mathcal{R}.$ This region $\mathcal{R}$ can be tiled by $n$ $2 \times 2$ squares. This region $\mathcal{R}$ can also be tiled by a combination of $n$ pieces of the following types of shapes (see below, with rotations allowed).

Determine the value of $n.$ Attachments: