Problem 1. In a min-heap every node i, other than the root, holds the property, Aparent()) SA such that, the smallest element in a min-heap is at the root. Suppose we have a min-heap containing n = 2' elements in an array of size n, and suppose that we repeatedly extract the minimum element, n times. To make the heap space efficient, we move the heap over to an array of size 21 whenever an extraction decreases the number of elements to 2) for any integer j. Suppose the cost of each such move is 2). What is the total movement cost caused by extract-mins starting from the heap of n elements? (You may ignore the (nign) cost from the heapify operations themselves.)