2. [8 marks The following is the pseudocode of the algorithm maxsubrangesum1 for the maximum subrange sum problem shown in clas;s maxsubrangesuml (x, n) 1: max 0 2: for lower 1 to n do 3: for upper max then 6: max sum 9: return max Show that this algorithm indeed uses S2(n3) time in the worst case. Show the steps of your worlk You can make the following assumptions to simplify the analysis (a) Each line of the pseudocode uses one unit of time if it uses a constant number of primitive operations only; (b) The number of times a loop test is executed is the same as the statement directly inside the loop is executed. For example, you can assume that the statement "for i-1 to n" is executed n times By now you have learned enough to know the above simplifications (even simpler than those used in the analysis of insertion sort given in class) are reasonable Hint: The identity 122 = n(n+162 +1) which can be found in Appendix: Mathe- matical Background of the textbook, may be helpful