Problem 4. (25 points) Given an array of numbers X = {x1,x2, ,Zn), an enchanged pair in X is a pair (xi, a) such that i x. Note that an element x, can be part of up to n - 1 exchanged pairs, and that the maximal possible number of exchanged pairs in X is n(n-1)/2, which is achieved if the array is sorted in descending order. Develop a divide-and-conquer algorithm that counts the number of exchanged pairs in X in O(n log n) time. Argue why your algorithm is correct, and why your algorithm takes O(n log n) time. You can assume that n is a power of two