There are n people standing in a line. The ith person p i , for 1 ≤ i ≤ n, has a height h i . All the people in our line have a unique height. We also know that the ith person has exactly f i number of people in front of them with height taller than h i (although is it not known which people, only the number). You are given as input a list of n pairs (h i ,f i ), for all 1 ≤ i ≤ n, but the list has been shuffled and is no longer in the correct order. Give an algorithm that reconstructs the original ordering of people. Your algorithm should run in O(nlogn) time.