In python implement the dynamic programming algorithm to solve the chain matrix multiplication problem with minimum number of operations. Given: a sequence of matrices A_1,..., A_n and dimensions D_O,...,D_n where A_i is of dimension D_{i-1} x D_i, determine the optimal order of multiplications. Demonstrate your algorithm on this input as well as several other ones to show that it works. A 1 10x20 (dimensions) A 2: 20x30 A_3: 30x40 A 4: 40x50 A_5: 50 x40 A_6: 40 x10 A_7: 10 x 50 A_8: 50 x 20