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
# -*- coding: utf-8 -*-
N = int(input())
H = tuple(map(int, input().split()))

def calc(stack, i, h):
    tmp_max = 0
    while stack[-1][1] > h:
        pi, ph = stack.pop()
        tmp_max = max(tmp_max, (i-pi)*ph)
        if len(stack) == 0:
            break    
    if len(stack) == 0:
        stack.append([pi, h])
    elif stack[-1][1] < 0:
        stack.append([pi, h])
    
    return stack, tmp_max

stack = [] # loc, height
S_max = 0

for i, h in enumerate(H):
    if len(stack) == 0:
        stack.append([i, h])
    elif h > stack[-1][1]:
        stack.append([i, h])
    elif h == stack[-1][1]:
        pass
    else:
        stack, tmp_max = calc(stack, i, h)
        S_max = max(S_max, tmp_max)

stack, tmp_max = calc(stack, i+1, 0)
S_max = max(S_max, tmp_max)
print(S_max)