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;
bool check(vector<long long int> v) {
  long long int k = v.size();
  for (long long int i = 0; i < k - 1; i++) {
    if (v[i] > v[i + 1]) return 0;
  }
  return 1;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int n;
  cin >> n;
  long long int p[n];
  for (long long int i = 0; i < n; i++) cin >> p[i];
  vector<long long int> v;
  long long int index = -1;
  for (long long int i = 0; i < n - 1; i++) {
    if (p[i] > p[i + 1]) {
      index = i + 1;
    }
  }
  if (index == -1) {
    cout << 0 << endl;
    return 0;
  }
  for (long long int i = index; i < n; i++) {
    v.push_back(p[i]);
  }
  for (long long int i = 0; i < index; i++) {
    v.push_back(p[i]);
  }
  if (check(v))
    cout << n - index << endl;
  else
    cout << -1 << endl;
  return 0;
}
