Let P be a set of points P = {P1 Pn), sorted based on their z-coordinates, from the leftmost to the rightmost point. Assume no two points have the same x-coordinates. That is, Pi.x Pi+1-x. Let P' be a subsequence of P, 1 and assume P, is also sorted by x coordinate. We say that P' is increasingly monotone ifpi.yPi+1,y, where Pi,y is the y coordinate of p. Assume that every point p has a weight (P), and every subsequence P of P has a weight w(P) which defined as the sum of weights of the points in P. Suggest an O(n2) time algorithm to find the max-weight monotone subsequence. Hint: Use the previous problem. Let P be a set of points P = {P1 Pn), sorted based on their z-coordinates, from the leftmost to the rightmost point. Assume no two points have the same x-coordinates. That is, Pi.x Pi+1-x. Let P' be a subsequence of P, 1 and assume P, is also sorted by x coordinate. We say that P' is increasingly monotone ifpi.yPi+1,y, where Pi,y is the y coordinate of p. Assume that every point p has a weight (P), and every subsequence P of P has a weight w(P) which defined as the sum of weights of the points in P. Suggest an O(n2) time algorithm to find the max-weight monotone subsequence. Hint: Use the previous