A histogram is made of a number of contiguous bars, which have same width.

For a given histogram with $N$ bars which have a width of 1 and a height of $h_i$ = $h_1, h_2, ... , h_N$ respectively, find the area of the largest rectangular area.

Constraints

* $1 \leq N \leq 10^5$
* $0 \leq h_i \leq 10^9$

Input

The input is given in the following format.

$N$
$h_1$ $h_2$ ... $h_N$

Output

Print the area of the largest rectangle.

Examples

Input

8
2 1 3 5 3 4 2 1


Output

12


Input

3
2 0 1


Output

2
def calc_largest_rect_in_hist(heights):
    heights.append(0)
    stack = []
    left = [0] * len(heights)
    ans = 0
    for i, height in enumerate(heights):
        while stack and heights[stack[-1]] >= height:
            idx = stack.pop()
            ans = max(ans, (i - left[idx] - 1) * heights[idx])
        left[i] = stack[-1] if stack else -1
        stack.append(i)
    return ans


def aoj():
    input()
    print(calc_largest_rect_in_hist([int(x) for x in input().split()]))


if __name__ == "__main__":
    aoj()

