Histogram Area

Have the function HistogramArea(arr) read the array of non-negative integers stored in arr which will represent the heights of bars on a graph (where each bar width is 1), and determine the largest area underneath the entire bar graph. For example: if arr is [2, 1, 3, 4, 1] then this looks like the following bar graph:



You can see in the above bar graph that the largest area underneath the graph is covered by the x's. The area of that space is equal to 6 because the entire width is 2 and the maximum height is 3, therefore 2 * 3 = 6. Your program should return 6. The array will always contain at least 1 element.

Examples

Input: [6, 3, 1, 4, 12, 4]
Output: 12

Input: [5, 6, 7, 4, 1]
Output: 16