(20 points) (Counting inversions) An inversion in an array A[1... n] of numbers is a pair of indices (i, j) such that iAljIn other words, an inversion describes a pair of elements that are not in sorted order. a. Find an array of length n over the elements [1, .., n that maximizes the number of inversions and explain why it is optimal b. By modifying Merge Sort, design an algorithm that counts the number of inversions in an array of length n in (n lg n) time. (Note: There can be (n inversions in an n-element array, so your algorithm cannot explicitly list them and achieve the time bound. It is possible to count inversions without listing them.)