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;
long long int INF = 1e18;
long long int h[110000], L[110000], R[110000];
int main() {
  int N;
  cin >> N;
  for (int i = 0; i < N; i++) {
    cin >> h[i];
  }
  stack<int> sta, sta2;
  for (int i = 0; i < N; i++) {
    while (sta.size() > 0 && h[sta.top()] >= h[i]) {
      sta.pop();
    }
    if (sta.empty()) {
      L[i] = 0;
    } else {
      L[i] = sta.top() + 1;
    }
    sta.push(i);
  }
  for (int i = N - 1; i >= 0; i--) {
    while (sta.size() > 0 && h[sta.top()] >= h[i]) {
      sta.pop();
    }
    if (sta.empty()) {
      R[i] = N;
    } else {
      R[i] = sta.top();
    }
    sta.push(i);
  }
  long long int ans = 0;
  for (int i = 0; i < N; i++) {
    ans = max(ans, h[i] * (R[i] - L[i]));
  }
  cout << ans << endl;
  return 0;
}
