Not Too Colourful

You have a grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). Initially, the grid is empty. You also have $N \cdot M$ tiles with three colours: $R$ tiles are red, $G$ tiles are green and $B$ tiles are blue. Find a way to place these tiles in the grid such that for each tile, there are at most two distinct colours among the tiles that share a side with it. F