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
import sys
readline = sys.stdin.readline
n = int(readline())
def largest_histogram(histogram):
    if len(histogram) == 0: return 0
    histogram = list(histogram)
    max_h = max(n, max(histogram))
    for i in range(n):
        for j in range(2, histogram[i] + 1):
            m = 1
            for k in range(i + 1, n):
                if histogram[k] >= j:
                    m += 1
                else:
                    break
            if max_h < j * m:
                max_h = j * m
    return max_h
li = list(map(int, readline().split()))
print(largest_histogram(li))