JBMO 2010 Problem 4

A $9 \times 7$ rectangle is tiled with tiles of the two types shown in the picture below (the tiles are composed by three, respectively four unit squares and the L-shaped tiles can be rotated repeatedly with $90^{\circ}$ ).

Let $n \geqslant 0$ be the number of the $2 \times 2$ tiles which can be used in such a tiling. Find all the values of $n$.