A Tricolor Triangulation

Each side of a convex $2019$-gon is colored red, green, or blue, with exactly $673$ sides of each color. Prove that one can draw $2016$ diagonals of the polygon, pairwise non-intersecting in the interior, that partition it into $2017$ triangles, and color each of these diagonals red, green, or blue, so that in every triangle of the partition the three sides are either all the same color or of three distinct colors.