One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  int ara[n];
  int min_value = 100000000, min_ind;
  for (int i = 0; i < n; i++) {
    cin >> ara[i];
    if (ara[i] < min_value) {
      min_value = ara[i];
      min_ind = i;
    }
    if (i > 0 && ara[i] == min_value && ara[i - 1] > min_value) {
      min_ind = i;
    }
  }
  bool b = true;
  for (int i = min_ind; i < n + min_ind - 1; i++) {
    if (ara[i % n] > ara[(i + 1) % n]) {
      if (ara[i % n] == ara[min_ind]) continue;
      b = false;
      break;
    }
  }
  if (b)
    printf("%d\n", (n - min_ind) % n);
  else
    printf("-1");
  return 0;
}
