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 ht;
  int pos;
};
int tb[100001];
int area_rect(int size, int buf[]) {
  stack<rect> st;
  int mx = 0;
  buf[size] = 0;
  for (int i = (0); i < (size + 1); ++i) {
    rect r;
    r.ht = buf[i];
    r.pos = i;
    if (st.empty())
      st.push(r);
    else {
      if (st.top().ht < r.ht)
        st.push(r);
      else if (st.top().ht > r.ht) {
        int ti = i;
        while (!st.empty() && st.top().ht >= r.ht) {
          rect pre = st.top();
          st.pop();
          int area = pre.ht * (i - pre.pos);
          mx = max(mx, area);
          ti = pre.pos;
        }
        r.pos = ti;
        st.push(r);
      }
    }
  }
  return mx;
}
int main() {
  int n;
  cin >> n;
  for (int i = (0); i < (n); ++i) cin >> tb[i];
  int mx = area_rect(n, tb);
  cout << mx << endl;
  return 0;
}
