Let A[1,...,n] be an array of n distinct numbers. If i < j and A[i] > A[j], then the pair (i,j) is called a reverse pair for A. (a) List the five reverse pairs of the array A = [2,3,8,6,1]. (b) What is the relationship between the running time of Insertion in the input array? Justify your answer. (c) Modify Merge sort and the number of reverse pairs sort in order to give an algorithm which determines the number of reverse pairs in an array of n numbers in (nlogn) run time. Fully explain your algorithm and also justify why your algorithms satisfies the required time complexity bound.