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 Rectangle {
  long long h;
  long long p;
};
int max_area_of_histgram(long long n, vector<long long>& height) {
  stack<Rectangle> S;
  long long maxv = 0;
  height[n] = 0;
  for (int i = 0; i <= n; i++) {
    Rectangle rect;
    rect.h = height[i];
    rect.p = i;
    if (S.empty()) {
      S.push(rect);
    } else if (S.top().h < rect.h) {
      S.push(rect);
    } else if (S.top().h > rect.h) {
      long long now = i;
      while ((!S.empty()) && (S.top().h >= rect.h)) {
        Rectangle pre = S.top();
        S.pop();
        long long area = pre.h * (i - pre.p);
        maxv = max(maxv, area);
        now = pre.p;
      }
      rect.p = now;
      S.push(rect);
    }
  }
  return maxv;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  long long N;
  cin >> N;
  vector<long long> dp(N + 1, 0);
  for (int i = 0; i < N; i++) cin >> dp[i];
  cout << max_area_of_histgram(N, dp) << endl;
  return 0;
}
