[5 points] We are given an array of integers. We want to design an algorithm that pairs the largest element with the smallest one, the second largest one with the smallest one and so on. Obviously this is easy if you sort the array, but you want to do it in O(n) time. You cannot do all of them, so you are required to design an algorithm that can generate the maximum number of pairs possible. You should prove that your algorithm takes O(n) time. The number of pairs generated by your algorithm should be asymptotically the best possible but you need not prove this