)recall the problem of finding the number of inversions. as in the text, we are given a sequence of n numbers a1, a2, . . , an, which we assume are all distinct, and we define an inversion to be a pair i < j such that ai > aj . we motivate the problem of counting inversions as a good measure of how different two orderings are. however, one might feel that this measure is too sensitive. let call a pair a significant inversion if i < j and ai > 2aj . give an o(n log n) algorithm to count the number of significant inversions between two orderings.