For a list of n movies, say n =4, you rank them as {1,2,3,4} and another person ranks them for example as {3,1,4,2}, that is the movie you ranked 1, the other person ranked 4, and so on. A natural way to quantify similarity between two rankings is to count the number of inversions in the second sequence. Suppose the second sequence is {a1, a2,, an}, propose an algorithm in pseudo-code to count the number of inversions with complexity.