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;
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[200000];
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> A[i];
  cout << calc(A) << endl;
  return 0;
}
