Let P be a convex polygon whose vertices are p_1...p_n. Assume n is an even number. We mark the vertices {p_1, p_2... p_n/2} as blue vertices, and the others are red vertices. See Figure 3 for an example. Suggest an algorithm for finding a triangulation of T such that the sum square of areas all triangles is as small as possible, and every triangle contains at least one red vertex and at least one blue vertex. Solve this question in O(n^2). (partial credit would be given for an O(n^3) time algorithm.)