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;
struct Rect {
  int height;
  int pos;
};
int HistgramRectangle(vector<int> &hist) {
  hist.push_back(0);
  int n = hist.size();
  stack<Rect> st;
  Rect tmp_rect, past_rect;
  int Max = 0;
  for (int i = 0; i < n; i++) {
    tmp_rect.height = hist[i];
    tmp_rect.pos = i;
    if (st.empty()) {
      st.push(tmp_rect);
    } else {
      if (st.top().height < hist[i]) {
        st.push(tmp_rect);
      } else if (st.top().height > hist[i]) {
        int stp = i;
        while (st.top().height >= hist[i] && !st.empty()) {
          past_rect = st.top();
          st.pop();
          Max = max(Max, past_rect.height * (i - past_rect.pos));
          stp = past_rect.pos;
          if (st.empty()) {
            break;
          }
        }
        tmp_rect.pos = stp;
        st.push(tmp_rect);
      }
    }
  }
  return Max;
}
int main() {
  int n;
  cin >> n;
  vector<int> hist;
  int tmp;
  for (int i = 0; i < n; i++) {
    cin >> tmp;
    hist.push_back(tmp);
  }
  cout << HistgramRectangle(hist) << endl;
}
