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, data[100001];
  cin >> n;
  int min = 0, max = 0;
  int change = 0, cp = 0;
  for (int i = 0; i < n; i++) {
    cin >> data[i];
  }
  for (int i = 0; i < n - 1; i++) {
    if (data[i] > data[i + 1]) {
      change = 1;
      cp = i + 1;
    }
    if (n > 2) {
      if (i != n - 2) {
        if (change && (data[i + 1] > data[i + 2] || data[i + 1] > data[0])) {
          cout << -1;
          return 0;
        }
      } else {
        if (change && (data[i + 1] > data[0])) {
          cout << -1;
          return 0;
        }
      }
    }
  }
  if (cp == 0) {
    cout << cp;
  } else {
    cout << (n - cp);
  }
}
