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;
struct cmp {
  bool operator()(pair<long long, long long> a, pair<long long, long long> b) {
    pair<long long, long long> ca = {abs(a.first), abs(a.second)};
    pair<long long, long long> cb = {abs(b.first), abs(b.second)};
    return ca < cb;
  }
};
int main() {
  std::ios::sync_with_stdio(false);
  long long n;
  cin >> n;
  vector<long long> a(n);
  cin >> a[0];
  long long idx = -1;
  for (__typeof(n) i = (1) - ((1) > (n)); i != (n) - ((1) > (n));
       i += 1 - 2 * ((1) > (n))) {
    cin >> a[i];
    if (a[i] < a[i - 1]) {
      if (idx == -1) {
        idx = i;
      } else {
        cout << -1 << "\n";
        return 0;
      }
    }
  }
  if (idx == -1) {
    cout << 0 << "\n";
    return 0;
  }
  long long first = a[idx];
  for (int i = (idx + 1) % n; i != idx; i = (i + 1) % n) {
    if (a[i] < first) {
      cout << -1 << "\n";
      return 0;
    }
    first = a[i];
  }
  cout << n - idx;
}
