6. Consider a stick of length m meters that has to be cut at s₁, s₂, , and s_n meters from left end, where mand s_i are all integers and the cut order of s_i can be any permutation. The cost of each cut s_i is the length of stick prior to the cut (see slide), and thus different permutation of cut order leads to different cost. Illustrate a dynamic programming algorithm for finding the minimum cut cost of a stick of length 40, which will be cut at 5, 7, 13, 29, 32, and 37 meters from left end. You should write down the recurrence, bottom-up computation, and the entire solution by backtracking.