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 largest_square(const int N, const vector<int>& in_histo) {
  auto histo = in_histo;
  histo.push_back(0);
  int ans = 0;
  stack<pair<int, int>> s;
  for (int n = 0; n < (int)(N + 1); ++n) {
    auto height = histo[n];
    if (s.empty())
      s.push(make_pair(height, n));
    else if (s.top().first < height)
      s.push(make_pair(height, n));
    else if (s.top().first > height) {
      int last_idx = n;
      while (!s.empty() && s.top().first > height) {
        auto area = (n - s.top().second) * s.top().first;
        ans = max(area, ans);
        last_idx = s.top().second;
        s.pop();
      }
      s.push(make_pair(height, last_idx));
    }
  }
  return ans;
}
int main() {
  int N;
  cin >> N;
  vector<int> histo(N);
  for (int n = 0; n < (int)(N); ++n) cin >> histo[n];
  cout << largest_square(N, histo) << endl;
  return 0;
}
