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 main(void) {
  long long N;
  cin >> N;
  long long h[100001];
  for (int i = 0; i < ((int)(N)); i++) cin >> h[i];
  long long left, right, max = 0;
  for (int i = 0; i < ((int)(N)); i++) {
    right = N - 1;
    left = 0;
    if (i != N) {
      for (int j = ((int)(i + 1)); j <= ((int)(N - 1)); j++) {
        if (h[i] > h[j]) {
          right = j - 1;
          break;
        }
      }
    }
    if (i != 0) {
      for (int j = ((int)(i - 1)); j >= ((int)(0)); j--) {
        if (h[i] > h[j]) {
          left = j + 1;
          break;
        }
      }
    }
    if (max < (right - left + 1) * h[i]) max = (right - left + 1) * h[i];
  }
  cout << max << endl;
  return 0;
}
