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
from collections import deque
import sys
input = sys.stdin.readline

n = int(input())
a = list(map(int, input().split())) + [-1]
ans = 0

q = deque([])
for i in range(n + 1):
    ind = i
    while True:
        if not q:
            q.append((a[i], ind))
            break
        if q[-1][0] <= a[i]:
            q.append((a[i], ind))
            break
        else:
            height, l = q.pop()
            ans = max(height * (i - l), ans)
            ind = l
print(ans)
