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<vector>
using namespace std;
 
int main(void){
	int n;cin >> n;
	long long a[n];
	for(int i=0;i<n;i++){
		cin >> a[i];
	//a[i] = i;
	}
	stack< pair<long long,long long> > st;
	long long max_area=0;
	st.push(make_pair(0,a[0]));
	for(int i=0;i<n;i++){
		pair<long long,long long> v = st.top();
		if(a[i] == v.second)continue;
		if(a[i] > v.second){
			st.push(make_pair(i,a[i]));
		}else{
			long long k;
			while(v.second > a[i] && !st.empty()){
				v = st.top();
				k = v.first;
				max_area = max(max_area,(i-v.first)*v.second);
				st.pop();
				if(!st.empty())v = st.top(); 
			}
			st.push(make_pair(k,a[i]));
		}
	}
	
	while(!st.empty()){
		pair<long long,long long> v = st.top();
		//cout << "v.first" << v.first << "v.second " << v.second << endl;
		max_area = max(max_area,(n-v.first)*v.second);
		st.pop();
	}
	cout << max_area << endl;
	return 0;
}
