Suggest a data structure for a set of n points {(x1, y)... (In, Yn)}. That is, each point is given by its c-coordinate and by its y-coordinate. Suggest a data structure that supports all the following operations, each in O(log n) time, where n is the current size of the set. (a) Insert(x,y) Insert into S a new points whose coordinates are (x, y). (b) Extract MaxX delete the point of S that has the largest x value. Of course, you need to delete the whole point - don't delete only its x value. (c) Extract MaxY delete the point of S that has the largest y value. Of course, you need to delete the whole point - don't delete only its y value. (d) (Bonus 2 points) Initialize the data structure for a set of n points, in time O(n). Suggest a data structure for a set of n points {(x1, y)... (In, Yn)}. That is, each point is given by its c-coordinate and by its y-coordinate. Suggest a data structure that supports all the following operations, each in O(log n) time, where n is the current size of the set. (a) Insert(x,y) Insert into S a new points whose coordinates are (x, y). (b) Extract MaxX delete the point of S that has the largest x value. Of course, you need to delete the whole point - don't delete only its x value. (c) Extract MaxY delete the point of S that has the largest y value. Of course, you need to delete the whole point - don't delete only its y value. (d) (Bonus 2 points) Initialize the data structure for a set of n points, in time O(n)