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<cstdio>
#include<cmath>
#include<algorithm>
#include<string>
#include<vector>
#include<map>
#include<stack>
#include<queue>

using namespace std;

struct Rect{long long h; int w_pos;};

int main(){
	int N;
	long long c[100001]={};
	scanf("%d",&N);
	for(int i=0;i<N;i++){
		scanf("%lld",&c[i]);
	}
	
	long long ans=0;
	stack<Rect> s;
	for(int j=0;j<=N+1;j++){
		Rect rect;
		rect.h = c[j];	
		rect.w_pos = j;
		if(s.empty()) s.push(rect);
		else{
			if(s.top().h < rect.h) s.push(rect);
			else if(s.top().h > rect.h){
				int t=j;
				while(!s.empty() && s.top().h >= rect.h){
					Rect pre=s.top();
					s.pop();
					long long area=pre.h * (j-pre.w_pos);
					ans = max(ans,area);
					t=pre.w_pos;
				}
				rect.w_pos=t;
				s.push(rect);
			}
		}
	}
	printf("%lld\n",ans);
}
