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
N = int(input())
element = []

hist = list(map(int,input().split()))
hist.append(0)
maxhist = 0
maxrect = 0

for i in range(N+1):
    pos = 0
    if i == 0:
        element.append([i,hist[i]])
        maxhist = hist[i]
    elif hist[i] > maxhist:
        element.append([i,hist[i]])
        maxhist = hist[i]
    elif hist[i] < maxhist:
        for j in reversed(element):
            if j[1]*(i - j[0]) > maxrect and hist[i] < j[1]:
                maxrect = j[1]*(i - j[0])
                element.remove(j)
            elif j[1]*(i - j[0]) <= maxrect and hist[i] < j[1]:
                element.remove(j)
            elif hist[i] >= j[1]:
                pos = j[0]+1
                break
        element.append([pos,hist[i]])

print(maxrect)