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 h, w, a[200001], ls, ans;
int main() {
  cin >> h;
  memset(a, 0, sizeof(a));
  for (int i = 0; i < h; i++) cin >> a[i];
  stack<pair<int, int> > st;
  for (int j = 0; j < h + 1; j++) {
    if (st.empty())
      st.push(pair<int, int>(a[j], j));
    else if (st.top().first == a[j])
      continue;
    else if (st.top().first < a[j])
      st.push(pair<int, int>(a[j], j));
    else {
      while (!st.empty() && st.top().first > a[j]) {
        ans = max(ans, (j - st.top().second) * st.top().first);
        ls = st.top().second;
        st.pop();
      }
      st.push(pair<int, int>(a[j], ls));
    }
  }
  cout << ans << endl;
}
