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;
int n;
stack<pair<int, int> > S;
long long ans = 0;
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    int h;
    cin >> h;
    while (!S.empty() && S.top().first > h) {
      ans = max(ans, 1LL * S.top().first * (i - S.top().second));
      S.pop();
    }
    if (S.empty() || S.top().first < h) S.push(make_pair(h, i));
  }
  cout << ans << endl;
}
