A permutation (or ranking) is an array of N integers where each of the integers between 0 and N-1 appears exactly once. The Kendall tau distance between two rankings is the number of pairs that are in different order in the two rankings. For example, the Kendall tau distance between 0 3 1 6 2 5 4 and 1 0 3 6 4 2 5 9 is four since the pairs 0-1, 3-1, 2-4 and 5-4 are in different relative order in the two rankings but all the other pairs are in the same relative order. Develop a O(n log n) algorithm for computing the Kendall tau distance between two rankings.