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<cstring>
#include<vector>
#include<queue>
#include<algorithm>
#include<cmath>
#include<climits>
#include<string>
#include<set>
#include<numeric>
#include<map>
#include<iostream>
using namespace std;
#define rep(i,n) for(int i = 0;i<((int)(n));i++)
#define reg(i,a,b) for(int i = ((int)(a));i<=((int)(b));i++)
#define irep(i,n) for(int i = ((int)(n)-1);i>=0;i--)
#define ireg(i,a,b) for(int i = ((int)(b));i>=((int)(a));i--)
typedef long long ll;
typedef pair<ll, ll> mp;

// ll M=1000000007;

//
//???????????°?????????????´¢???????????????
//

int main(void){
	int N;
	cin>>N;
	ll h[100001];
	rep(i,N)cin>>h[i];
	ll left[100001],right[100001];
	ll max=0;
	int j=0;
	rep(i,N){//?????????????´¢
		j=i-1;
		while(true){
			if(j==-1){
				left[i]=0;
				break;
			}
			if(h[j]>=h[i]){
				if(j==left[j]){
					j--;
				}else{
					j=left[j];
				}
			}else{
				left[i]=j+1;
				break;
			}
		}
	}
	irep(i,N){//?????????????´¢
		j=i+1;
		while(true){
			if(j==N){
				right[i]=N-1;
				break;
			}
			if(h[j]>=h[i]){
				if(j==right[j]){
					j++;
				}else{
					j=right[j];
				}
			}else{
				right[i]=j-1;
				break;
			}
		}
	}
	rep(i,N){
		if(max<(right[i]-left[i]+1)*h[i])max=(right[i]-left[i]+1)*h[i];
	}
	cout<<max<<endl;
	return 0;
}