Given an array of numbers X = {xi,T2, ,xn), an exchanged pair in X is a pair (ri,Tj) such that i j and xi > Xj. Note that an element xi 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(nlogn) 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