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
# 入力
N = int(input())
hist = list(map(lambda x: int(x), input().split()))
max_num = 0

stack = [(0, -1)] # 高さと位置, 初期値右隅
for i in range(N):
    # 一番左の位置
    base = i
    # stackが空の時
    if len(stack) == 1 or 0:
        stack.append((hist[i], base))  
        
    # stackの末尾より、高さが大きい
    elif stack[-1][0] < hist[i]:
        stack.append((hist[i], base))
        
    # stackの末尾より、高さが大きい
    elif stack[-1][0] > hist[i]:
        while stack and (hist[i] <= stack[-1][0]):
            h, j = stack.pop()
            max_num = max(max_num, h * (i - j))
        stack.append((hist[i], j))

# 残りのスタックで出力
while stack:
    h, j = stack.pop()
    max_num = max(max_num, (N - j) * h)

print(max_num)
