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 <iostream>
#include <stack>

using namespace std;
typedef unsigned long long ull;

int N;
ull h[100002];

ull solve() {
  ull ans = 0;
  int last_j;
  stack<pair<int, ull>> s;
  pair<int, ull> tmp;
  for (int j = 1; j <= N+1; ++j) {
    if (s.empty() || (s.top().second < h[j])) {
      s.push(make_pair(j, h[j]));
    }
    else {
      while (!s.empty() && s.top().second >= h[j]) {
        last_j = s.top().first;
        ans = max(ans, (j-last_j)*(s.top().second));
        s.pop();
      }
      s.push(make_pair(last_j, h[j]));
    }
  }
  return ans;
}

int main () {
  cin>>N;
  for (int i = 0; i < N; ++i) {
    cin>>h[i+1];
  }
  cout<<solve()<<endl;
}

