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() {
  ios::sync_with_stdio(false);
  int n, first;
  cin >> n >> first;
  int pos = 0;
  int temp = first;
  bool change = 0;
  int b;
  for (int i = 1; i < n; i++) {
    cin >> b;
    if (b < first) {
      if (change) {
        cout << -1;
        return 0;
      }
      change = 1;
      pos = i;
    }
    first = b;
  }
  if (first > temp) {
    if (change) {
      cout << -1;
      return 0;
    }
  }
  cout << (change == 0 ? 0 : (n - pos));
}
