There are n houses on a street that goes in the west-east direction. The locations of the houses are given as an array X = [x1, x2, ..., xn], where the ith house is xi yards east of the start of the street. We want to install fire hydrants to this street, such that all houses will be at most d yards away from at least one hydrant. We would like to minimize the number of the hydrants. What is a greedy choice that is guaranteed to lead to an optimal solution to this problem? Explain why