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 100010
using namespace std;
typedef pair<int,int> P;
int n,A[N];


signed main(){
  
  P Idx[N];
  cin>>n;
  for(int i=0;i<n;i++)cin>>A[i],Idx[i] = P(A[i],i);
  sort(Idx,Idx+n);
  Idx[n] = P(-1,-1);  

  set<int> S;
  S.insert(-1);
  S.insert(n);

  int ans = 0;
  vector<int> ls;
  for(int i=0;i<n;i++){
    int h = Idx[i].first;
    int idx = Idx[i].second;
    int l =idx-(*(--S.upper_bound(idx)))-1;
    int r =(*S.upper_bound(idx)) -idx-1;
    ans=max(ans,(r+l+1)*h);
    ls.push_back(idx);
    if(Idx[i+1].first!=h){
      for(int j:ls)S.insert(j);
      ls.clear();
    }
  }
  cout<<ans<<endl;
  return 0;
}