This problem is about building a dam with the largest possible volume of its reservoir. To keep things manageable, we will make the following two simplifications: We will do this only in a 2-dimensional space, and instead of dealing with various angles as typically happens in nature, we discretize our landscape as follows: we measure the height of the land at every meter and pretend that the land is at this height until the next measurement. Therefore, our input is a sequence of n heights, forming an outline of our landscape. As an example, consider input 1,3,3,6,2,2,4,4,1,8,8,3,3,7,7,2,2, where n=17. This input is shown in the following figure on the left: We aim to find the volume of the largest possible reservoir if we fill one of the valleys with water. Two possible reservoirs are shown in the figure on the right. The larger reservoir has volume 17 square meters, which is the largest possible volume we can get for our landscape. A reservoir is a horizontal line connecting two vertical segments in our landscape without crossing or touching any intermediate landscape segment. The polygon below this line and above the landscape defines the reservoir. Give an O(n) algorithm that finds the volume of the largest reservoir