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;
void largest_rectangle_in_a_histogram() {
  int N;
  cin >> N;
  vector<int> h(N);
  for (int i = (0); i < (N); i++) {
    cin >> h[i];
  }
  using P = pair<int, int>;
  stack<P> st;
  st.emplace(-1, -1);
  int ans = 0;
  for (int i = (0); i < (N); i++) {
    if (st.top().first == h[i]) continue;
    int pos = i;
    while (st.top().first >= h[i]) {
      if (ans < st.top().first * (i - st.top().second))
        ans = st.top().first * (i - st.top().second);
      pos = st.top().second;
      st.pop();
    }
    st.emplace(h[i], pos);
  }
  while (st.size()) {
    if (ans < st.top().first * (N - st.top().second))
      ans = st.top().first * (N - st.top().second);
    st.pop();
  }
  cout << ans << endl;
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  largest_rectangle_in_a_histogram();
  return 0;
}
