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;
const int MAX_N = 100005;
int L[MAX_N], R[MAX_N], st[MAX_N];
long long renctangle_in_histgram(vector<long long> &h) {
  int N = h.size();
  int t = 0;
  for (int i = 0; i < (int)N; ++i) {
    while (t > 0 && h[st[t - 1]] >= h[i]) t--;
    L[i] = t == 0 ? 0 : (st[t - 1] + 1);
    st[t++] = i;
  }
  t = 0;
  for (int i = N - 1; i >= 0; i--) {
    while (t > 0 && h[st[t - 1]] >= h[i]) t--;
    R[i] = t == 0 ? N : st[t - 1];
    st[t++] = i;
  }
  long long res = 0;
  for (int i = 0; i < (int)N; ++i)
    res = max(res, (long long)h[i] * (R[i] - L[i]));
  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", renctangle_in_histgram(h));
  return 0;
}
