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<iostream>
#include<stack>
#include<algorithm>
using namespace std;
int n;
stack<pair<int,int> >S;
long long ans=0;
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		int h;cin>>h;
		int j=i;
		while(!S.empty()&&S.top().first>h)
		{
			ans=max(ans,1LL*S.top().first*(i-S.top().second));
			j=S.top().second;
			S.pop();
		}
		if(S.empty()||S.top().first<h)S.push(make_pair(h,j));
	}
	while(!S.empty())
	{
		ans=max(ans,1LL*S.top().first*(n-S.top().second));
		S.pop();
	}
	cout<<ans<<endl;
}

