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 cww {
  cww() {
    ios::sync_with_stdio(false);
    cin.tie(0);
  }
} star;
void square() {
  int n;
  cin >> n;
  vector<int> h(n);
  for (int i = (0), i_len = (n); i < i_len; ++i) cin >> h[i];
  deque<pair<int, int> > st;
  st.emplace_back(-1, -1);
  int ans = *max_element((h).begin(), (h).end());
  int pos;
  for (int i = (0), i_len = (n); i < i_len; ++i) {
    if (st.back().first == h[i]) continue;
    pos = i;
    while (st.back().first >= h[i]) {
      if (ans < st.back().first * (i - st.back().second))
        ans = st.back().first * (i - st.back().second);
      pos = st.back().second;
      st.pop_back();
    }
    st.emplace_back(h[i], pos);
  }
  while (st.size()) {
    if (ans < st.back().first * (n - st.back().second))
      ans = st.back().first * (n - st.back().second);
    st.pop_back();
  }
  cout << (ans) << "\n";
}
int main() {
  square();
  return 0;
}
