[8] 7. Consider the following somewhat "inventive" algorithm to find the largest element of a list with n items define find maximum(a list) if a_list contains a single element return this element Select a random integer x from 1 to n-1 (inclusive) Let 11 - the list with the first x elements of a list Let 12 = the list with the remaining elements of a-list Let x1 -find maximum(11) Let x2 -find_maximum (12) Return the larger of x1 and x2 Assume that an invocation to function find_maximum performs c steps, not counting the steps performed inside the recursive calls. Prove that the total number of steps executed by a call to the function with a list with n elements will be at most c(2n-1) Hint: use mathematical induction