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
#include <cstdio>
#include <algorithm>
#include <stack>
using namespace std;
typedef long long ll;
const int M = 200000;
// SMAX = 10^14 
struct Rectangle {int hei, ind;};

stack<Rectangle> s;
ll Area(int w, int a[])// 返回值 
{
	while (!s.empty()) s.pop();
	a[w] = 0;
	ll maxs = 0;
	
	for (int i = 0; i <= w; ++i)
	{
		Rectangle cur;
		cur.hei = a[i];
		cur.ind = i;
		
		if (s.empty()) 					s.push(cur);
		else 
		{
			if (s.top().hei < cur.hei) 	s.push(cur);
			else if (s.top().hei > cur.hei)
			{
				int tmp = cur.ind;
				while (!s.empty() && s.top().hei >= cur.hei)
				{
					Rectangle pre = s.top(); s.pop();
					ll area = 1ll * pre.hei * (i - pre.ind);
					maxs = max(maxs, area);
					tmp = pre.ind;					
				}
				cur.ind = tmp;
				s.push(cur);
			}
		}		
	}
	
	return maxs;
}

int main()
{
	int w = 0, a[M] = {0};
	scanf("%d", &w);
	for (int i = 0; i < w; ++i)
		scanf("%d", a+i);
	
	printf("%lld\n", Area(w, a));
	return 0;
}
