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;

long long n;
vector<long long> a;

long long solve();
long long calc(int u, int d, int lef);

int main() {
  cin >> n;
  a.resize(n);
  for (auto& p : a) cin >> p;
  cout << solve() << endl;
  return 0;
}

long long solve() {
  long long res = 0;
  stack<long long> len, id;
  len.push(0);
  a.push_back(0);
  ++n;
  for (int i = 0; i < n; ++i) {
    int nextid = i;
    while (a[i] < len.top()) {
      nextid = id.top();
      res = max(res, len.top() * (i - id.top()));
      len.pop();
      id.pop();
    }
    if (a[i] > len.top()) {
      len.push(a[i]);
      id.push(nextid);
    }
  }
  return res;
}

