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 <bits/stdc++.h>
#define int long long
#define N 200000
using namespace std;
int n;
struct dat{int h,i;};

int calc(int A[]){
  stack <dat> S;
  int res = 0;
  for(int i=0;i<=n;i++){
    int h = A[i];
    if(S.empty() || S.top().h < h) S.push((dat){h,i});
    else if(S.top().h > h){
      int ni = i;
      while(!S.empty() && S.top().h > h){
        dat t = S.top(); S.pop();
        ni = t.i;
        int area = (i - t.i) * t.h;
        res = max(res,area);
      }
      res = max(res,(i-ni)*h);
      S.push((dat){h,ni});
    }
  }
  return res;
}

int A[N];
signed main(){
  cin>>n;
  for(int i=0;i<n;i++)cin>>A[i];
  cout<<calc(A)<<endl;
  return 0;
}