Let X be a set of n intervals on the real line. A proper coloring of X assigns a color to each interval, so that any two overlapping intervals are assigned different colors. Describe and analyze an efficient algorithm to compute the minimum number of colors needed to properly color X. Assume that your input consists of two arrays L [1 .. n] and R [1.. n], where L [i] and R [i] are the left and right endpoints of the ith interval. As usual, if you use a greedy algorithm, you must prove that it is correct