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
#!python3

from collections import deque

iim = lambda: map(int, input().rstrip().split())

def calc(dp):
    ans = 0
    dq = deque([[0, 0]])
    #print(dp)
    for i, hi in enumerate(dp):
        j = i
        while dq[-1][1] > hi:
            j, h1 = dq.pop()
            ans = max(ans, (i - j) * h1)

        if dq[-1][1] < hi:
            dq.append([j, hi])

    i = len(dp)
    for j, hi in dq:
        ans = max(ans, (i - j) * hi)
    #print(i, dq, ans)
    return ans

def resolve():
    N = int(input())
    H = list(iim())

    print(calc(H))

if __name__ == "__main__":
    resolve()

