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 <cstdio>
#include <stack>
#include <cstring>
#include <algorithm>
using namespace std;
int n;
int h[100000];
int l[100000];
int r[100000];
int main() {
  while(true) {
    scanf("%d",&n);
    if (n==0) break;
    for(int i=0;i<n;++i) {
      scanf("%d", &h[i]);
    }
    long long answer = 0;
    stack<int> S;
    for(int i=0;i<n;++i) {
      while(!S.empty() && h[S.top()] >= h[i]) S.pop();
      if (S.empty()) {
        l[i] = 0;
      } else {
        l[i] = S.top() + 1;
      }
      S.push(i);
    }
    S=stack<int>();
    for(int i=n-1;i>=0;--i) {
      while(!S.empty() && h[S.top()] >= h[i]) S.pop();
      if (S.empty()) {
        r[i] = n-1;
      } else {
        r[i] = S.top() - 1;
      }
      S.push(i);
    }
    
    for(int i=0;i<n;++i) {
      answer = max(answer, 1ll * h[i] * (r[i]- l[i] +1));
    }
    
    printf("%lld\n", answer);
break;
  }
  return 0;
}