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() {
  long n, temp, res = 0, prev, m;
  cin >> n;
  cin >> prev;
  m = prev;
  bool ok = false;
  for (int i = 0; i < int(n - 1); i++) {
    cin >> temp;
    if (temp < prev) {
      if (temp > m) {
        cout << -1;
        return 0;
      }
      i++;
      res++;
      while (i < n - 1) {
        prev = temp;
        cin >> temp;
        if (temp < prev || temp > m) {
          cout << -1;
          return 0;
        }
        prev = temp;
        res++;
        i++;
      }
    }
    if (temp > prev) ok = true;
    prev = temp;
  }
  cout << res;
}
