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 <iomanip>
#include <ios> 
#include <vector>
#include <string>
#include <algorithm>
#include <functional>
#include <queue>
#include <stack>
#include <set>
#include <cmath>
#include <bitset>
#include <map>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define sz(c) ((int)(c).size())

using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair<int,int> P;
const int MAX=1e5+10;



int main(){
	int N;
	cin>>N;
	int h[MAX];
	rep(i,N){
		cin>>h[i];
	}
  	h[N]=0;
	stack<P> st;
	ll ans=0;
	rep(i,N+1){
		while(true){
			if(st.empty()){
				st.push(make_pair(i,0));
				break;
			}
          	else{
				P p=st.top();
				if(h[p.first]<h[i]){
					st.push(make_pair(i, p.first+1));
					break;
				}
				else{
					ans=max(ans, (ll)h[p.first]*(i-p.second));
					st.pop();
                }
			}
		}
	}
	cout<<ans<<endl;
}
