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
/*
 * Given N numbers denoting the heights of consecutive bars of a histogram,
 * find the area of the largest rectangle contained within the histogram.
 *
 * N <= 1e5
 * 0 <= h_i <= 1e9
 */

#include <algorithm>
#include <iostream>
#include <iterator>
#include <stack>
#include <vector>
using namespace std;

int A[100010];
int main() {
  int n;
  cin >> n;
  copy_n(istream_iterator<int>{cin}, n, A);
  stack<int> st;
  vector<int> l(n), r(n);
  unsigned long long M = 0;
  for (int i = 0; i < n; ++i) {
    while (!st.empty() && A[st.top()] >= A[i])
      st.pop();
    l[i] = st.empty() ? -1 : st.top();
    st.push(i);
  }
  while (!st.empty())
    st.pop();
  for (int i = n - 1; i >= 0; --i) {
    while (!st.empty() && A[st.top()] >= A[i])
      st.pop();
    r[i] = st.empty() ? n : st.top();
    st.push(i);
    M = max(M, (1ull * A[i]) * (unsigned long long)(r[i] - l[i] - 1));
  }
  cout << M << endl;
}
