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
#define _USE_MATH_DEFINES

#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <vector>
#include <queue>
#include <stack>
#include <map>

using namespace std;

typedef pair<long long int, long long int> P;
long long int INF = 1e18;

long long int h[110000], L[110000], R[110000];

int main(){
	
	int N;
	cin >> N;
	
	for(int i = 0; i < N; i++){
		cin >> h[i];
	}
	
	stack<int> sta, sta2;
	
	for(int i = 0; i < N; i++){
		while(sta.size() > 0 && h[sta.top()] >= h[i]){
			sta.pop();
		}
		if(sta.empty()){
			L[i] = 0;
		}else{
			L[i] = sta.top() + 1;
		}
		sta.push(i);
	}
	
	while(!sta.empty()){
		sta.pop();
	}
	
	for(int i = N - 1; i >= 0; i--){
		while(sta.size() > 0 && h[sta.top()] >= h[i]){
			sta.pop();
		}
		if(sta.empty()){
			R[i] = N;
		}else{
			R[i] = sta.top();
		}
		sta.push(i);
	}
	
	long long int ans = 0;
	for(int i = 0; i < N; i++){
		ans = max(ans, h[i] * (R[i] - L[i]));
	}
	cout << ans << endl;
	return 0;
}
