Given a sorted array A of n (possibly negative) distinct integers, you want to find out whether there is an index i for which A[i] = i. Give a divide-and-conquer algorithm that runs in time O(logn). Provide only the main idea and the runtime analysis. You can assume that n is a power of 2 for simplicity. (Hint: Look at the value of A[ n/ 2 ] and decide how to recurse based on that)