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() {
  int N;
  cin >> N;
  vector<int> hist(N + 1, 0);
  for (int i = 0; i < N; ++i) {
    int h;
    cin >> h;
    hist[i] = h;
  }
  int maxv = 0;
  stack<pair<int, int>> S;
  for (int i = 0; i <= hist.size(); ++i) {
    auto rect = make_pair(hist[i], i);
    if (S.empty()) {
      S.push(rect);
    } else {
      if (S.top().first < rect.first) {
        S.push(rect);
      } else if (S.top().first > rect.first) {
        auto pos = i;
        while (!S.empty() && S.top().first >= rect.first) {
          auto pre = S.top();
          S.pop();
          auto area = pre.first * (i - pre.second);
          maxv = max(maxv, area);
          pos = pre.second;
        }
        rect.second = pos;
        S.push(rect);
      }
    }
  }
  cout << maxv << endl;
  return 0;
}
