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 n;
vector<int> v;
int main() {
  cin >> n;
  v.resize(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  for (int i = 1; i < v.size(); i++)
    if (v[i] < v[i - 1]) {
      int mx = -1e9, mn = 1e9;
      for (int j = i; j < v.size() - 1; j++)
        if (v[j] > v[j + 1]) {
          cout << "-1";
          return 0;
        }
      for (int j = i; j < v.size(); j++) mx = max(mx, v[j]);
      for (int j = 0; j < i; j++) mn = min(v[j], mn);
      if (mn >= mx) {
        cout << v.size() - i;
        return 0;
      } else {
        cout << "-1";
        return 0;
      }
    }
  cout << "0";
  return 0;
}
