Let A be an array of integers of size n. We call any pair of indices i,j{0,1,,n1} an inversion if iA[j]. For example let A=[3,1,5,10]. This is the list of all inversions in our array: {(0,1),(0,3),(1,3),(2,3)}. In this problem we want to design and algorithm to count the number of inversions in a given array. (a) Here's one strategy: Go over all pairs of indices and check if they make an inversion. Show that the time complexity of this algorithm is (n2). (b) Use divide-and-conquer technique to design an algorithm for this task with time-complexity of O(nlog(n))