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, c = 0, num;
  cin >> n;
  int arra[n];
  for (int i = 0; i < n; i++) {
    cin >> arra[i];
  }
  for (int i = 0; i < n - 1; i++) {
    if (arra[i] > arra[i + 1]) {
      c++;
      if (c > 1) {
        break;
      } else {
        num = i + 1;
      }
    }
  }
  if (c == 0) {
    cout << '0';
  } else if (c > 1 || (c == 1 && arra[0] < arra[n - 1])) {
    cout << "-1";
  } else {
    cout << n - num;
  }
  return 0;
}
