Consider using mergesort to sort a sequence of points in the plane, according to their x-coordinate, breaking ties in the merge step by picking the point in the left list. Prove that the sorted sequence preserves the order of they-coordinates of points whose x-coordinates are equal. For example, mergesort on the sequence (2,2),(1,1),(2,1),(1,2)yields (1,1),(1,2),(2,2),(2,1). (Hint: Use a proof by induction.)