An inversion in an array A$[1...$ n$]$ is a pair of indices $\{$i$,$ j$\}$ such that i $<$ j and A$[$i$]>$ A$[$j$].$ The number of inversions in an n$-$element array is between $0($if the array is sorted$)$ and n$2($if the array is sorted backward$).$ Give an O$($n log n$)$ time algorithm that returns the number of inversions in a given array A$[1...$ n$].[$Hint: Modify the code for MergeSort$]$