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 Node {
  int index, value;
  Node(int index = 0, int value = 0) : index(index), value(value) {}
};
int calHistrigramArea(const vector<int>& a) {
  deque<Node> dq;
  int ans = 0;
  for (int i = 0; i < a.size(); i++) {
    int e = a[i];
    while (!dq.empty()) {
      if (dq.back().value > e) {
        int v = dq.back().value;
        dq.pop_back();
        int leftIndex = dq.empty() ? -1 : dq.back().index;
        ans = max(ans, (i - leftIndex - 1) * v);
      } else {
        break;
      }
    }
    dq.push_back(Node(i, e));
  }
  int i = a.size();
  while (!dq.empty()) {
    int v = dq.back().value;
    dq.pop_back();
    int leftIndex = dq.empty() ? -1 : dq.back().index;
    ans = max(ans, (i - leftIndex - 1) * v);
  }
  return ans;
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  int ans = calHistrigramArea(a);
  cout << ans << endl;
  return 0;
}
