Santa's elves are troubled by the following problem: They are given n present boxes with widths and lengths specified by arrays X[1.n] and Y[1n] (that is, the i-th box has width X[i] and length Y[i] ), and their task is to form a proper stack of as many boxes as possible. Here, proper means that we can put box j above box i only if X[j]X[i] and Y[j]Y[i] (see Figure 1 for an illustration). Help the elves and design an algorithm which computes the maximum proper stack size in time O(n2). Hint: First find an appropriate order of the presents. Then design a dynamic programming algorithm similar to the algorithm for Longest Increasing Subsequence from the lecture. Figure 1: A proper stack of four presents, se- Figure 2: An example of the broadcasting problecting the 1st, 4th, 3rd and 5th presents from lem which can be solved in four rounds. The bottom to top, in the instance X=[8,5,4,6,3], node labels indicate in which round the respecY=[6,8,4,5,3] tive node has learned the message in an optimal solution