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;
int N;
long long int H[100000];
int L[100000], R[100000];
stack<int> S;
int main() {
  scanf("%d", &N);
  for (int i = 0; i < N; i++) scanf("%lld", &H[i]);
  for (int i = 0; i < N; i++) {
    while (S.empty() == false && H[S.top()] >= H[i]) S.pop();
    if (S.empty()) {
      L[i] = 0;
    } else {
      L[i] = S.top() + 1;
    }
    S.push(i);
  }
  while (!S.empty()) S.pop();
  for (int i = N - 1; i >= 0; i--) {
    while (S.empty() == false && 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++) {
    printf("L[%d]:%d R[%d]:%d\n", i, L[i], i, R[i]);
  }
  long long int ans = 0;
  for (int i = 0; i < N; i++)
    ans = max(ans, H[i] * (long long int)(R[i] - L[i] + 1));
  printf("%lld\n", ans);
  return 0;
}
