(Challenge) Coloring Triangulations

After solving the $64 \times 64 \times 64$ Rubik's cube, Chef Ada moved to arts. For her next masterpiece, Ada drew an abstract painting as follows: - $N$ points (numbered $1$ through $N$) are painted on a 2D canvas. Some of these points are red ('R'), some are blue ('B') and the rest are green ('G'). No three points are collinear. - A triangulation, i.e. a maximum set of non-intersecting triangl