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 <stdio.h>
#include <stack>
#include <utility>
using namespace std;
typedef pair<int,int> pi;
#define F first
#define S second
#define MP make_pair
int main(){
    int n,temp;
    long long int ans=0;
    pi last;
    stack<pi> s;
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&temp);
        while(!s.empty()){
            if(s.top().F>=temp){
                last=s.top();
                s.pop();
                if(s.empty())ans=max(ans,(long long int)i*last.F);
                else ans=max(ans,(long long int)last.F*(i-s.top().S-1));
            }
            else break;
        }
        s.push(MP(temp,i));
    }
    while(!s.empty()){
        last=s.top();
        s.pop();
        if(s.empty())ans=max(ans,(long long int)n*last.F);
        else ans=max(ans,(long long int)last.F*(n-s.top().S-1));
    }
    printf("%lld\n",ans);
}
