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>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;

int main(){
  int n;
  cin >> n;
  ll h[n];
  rep(i,n) cin >> h[i];
  ll l[n], r[n], st[n];
  ll t = 0;
  rep(i,n) {
    while(t > 0 && h[st[t-1]] >= h[i]) t--;
    l[i] = (t == 0 ? 0 : st[t-1]+1);
    st[t++] = i;
  }
  t = 0;
  for(int i = n-1; i >= 0; i--) {
    while(t > 0 && h[st[t-1]] >= h[i]) t--;
    r[i] = (t == 0 ? n : st[t-1]);
    st[t++] = i; 
  }
  ll ans = 0;
  rep(i,n) ans = max(ans,h[i]*(r[i]-l[i]));
  cout << ans << endl;
  return 0;
}

