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 "bits/stdc++.h"
using namespace std;
int main()
{
	long long n, mx = 0;
	scanf("%lld", &n);
	priority_queue<pair<long long, long long>> q;
	for(long long i = 0, h, hor = 0; i < n; hor = ++i)
	{
		scanf("%lld", &h);
		for(long long t, u; !q.empty(); )
		{
			t = q.top().first;
			u = q.top().second;
			if(t > h)
			{
				mx = max(mx, t * (i - u));
				hor = min(hor, u);
				q.pop();
			}
			else if(t == h)
			{
				hor = min(hor, u);
				q.pop();
			}
			else
			{
				break;
			}
		}
		q.push(make_pair(h, min(hor, i)));
	}
	for(; !q.empty(); )
	{
		mx = max(mx, q.top().first * (n - q.top().second));
		q.pop();
	}
	printf("%lld\n", mx);
}

