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);
  cin.tie(0);
  cout.tie(0);
  long long int n;
  cin >> n;
  vector<long long int> b(n);
  vector<long long int> c(n);
  vector<long long int> v((2 * n), 0);
  for (int i = 0; i < n; i++) {
    cin >> v[i];
    b[i] = v[i];
    c[i] = v[i];
    v[n + i] = v[i];
  }
  sort(b.begin(), b.end());
  if (b == c) {
    cout << 0 << endl;
  } else {
    long long int m = b[0], ans;
    int flag = 0;
    for (int i = 0; i < v.size(); i++) {
      int p = i;
      if (v[i] == m) {
        int j;
        for (j = 0; j < b.size(); j++) {
          if (b[j] == v[i]) {
            i++;
          } else {
            break;
          }
        }
        if (j == b.size()) {
          flag = 1;
          ans = (n - p);
          break;
        }
      }
    }
    if (!flag) {
      cout << -1 << endl;
    } else {
      cout << ans << endl;
    }
  }
  return 0;
}
