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;
const unsigned long long mod = 1e9 + 7;
long long renctanble_in_histgram(vector<long long> &h) {
  long long res = 0;
  int N = h.size();
  stack<pair<long long, long long> > st;
  for (int i = 0; i < (int)N; ++i) {
    if (st.empty()) {
      st.push(make_pair(h[i], i));
    } else {
      pair<long long, long long> top_rect = st.top();
      if (top_rect.first < h[i]) {
        st.push(make_pair(h[i], i));
      }
      if (top_rect.first > h[i]) {
        pair<long long, long long> tmp_rect = st.top();
        while (!st.empty() && (st.top()).first >= h[i]) {
          tmp_rect = st.top();
          res = max(res, tmp_rect.first * (i - tmp_rect.second));
          st.pop();
        }
        st.push(make_pair(h[i], tmp_rect.second));
      }
    }
  }
  return res;
}
int main() {
  int N;
  cin >> N;
  vector<long long> h(N);
  for (int i = 0; i < (int)N; ++i) cin >> h[i];
  printf("%d\n", renctanble_in_histgram(h));
  return 0;
}
