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 LR {
  long long n;
  vector<long long> a;
  LR(int sz) : n(sz), a(sz + 1) {}
  void Input() {
    for (int i = 0; i < n; i++) cin >> a[i];
    a[n] = 0;
  }
  int solve() {
    long long ans = 0, ls = 0;
    stack<pair<long long, long long> > st;
    for (int j = 0; j < n + 1; j++) {
      if (st.empty())
        st.push(make_pair(a[j], j));
      else if (st.top().first == a[j])
        continue;
      else if (st.top().first < a[j])
        st.push(make_pair(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(make_pair(a[j], ls));
      }
    }
    return ans;
  }
};
int main() {
  int n;
  cin >> n;
  LR L(n);
  L.Input();
  cout << L.solve() << endl;
}
