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_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  long long ar[n];
  for (long long i = 0; i < n; i++) {
    cin >> ar[i];
  }
  if (n == 2) {
    if (ar[0] > ar[1])
      cout << 1 << "\n";
    else
      cout << 0 << "\n";
    return 0;
  }
  long long count = 0;
  for (long long i = 0; i < n - 1; i++) {
    if (count > 2)
      break;
    else {
      if (ar[i] > ar[i + 1]) {
        count++;
      }
    }
  }
  if (count > 1)
    cout << "-1";
  else {
    long long c = *min_element(ar, ar + n);
    long long d = 0;
    for (long long i = 0; i < n; i++) {
      if (ar[i] == c) {
        d = i;
        break;
      }
    }
    if (ar[0] != ar[n - 1]) {
      bool flag = false;
      if (ar[0] < ar[n - 1]) {
        count++;
        flag = true;
      }
      if (flag && count == 1) count--;
    }
    if (d == 0) {
      for (long long i = 1; i < n; i++) {
        if (c == ar[i]) {
          if (c != ar[i - 1]) {
            d = i;
            break;
          }
        }
      }
    }
    if (count > 1) {
      cout << "-1";
      return 0;
    }
    if (count == 0)
      cout << 0;
    else
      cout << n - d;
  }
}
