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
if __name__ == "__main__":
    N = int(input())
    hist = list(map(lambda x: int(x), input().split()))

    stack = [(0, -1)]  # (height, x_position)
    ans = 0
    for i in range(N):
        height = hist[i]
        pos = i
        while stack and height <= stack[-1][0]:
            h, j = stack.pop()
            ans = max(ans, (i - j) * h)
            pos = j
        stack.append((height, pos))
    while stack:
        h, j = stack.pop()
        ans = max(ans, (N - j) * h)

    print(ans)

