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;
void answer(vector<int> v) {
  int ck = 0;
  for (long long int i = 1; i < v.size(); i++) {
    if (v[i] < v[i - 1]) ck++;
  }
  if (ck == 0)
    cout << "0";
  else if (ck == 1 && v[0] >= v[v.size() - 1]) {
    int dp = 0;
    long long int count = 0;
    for (long long int i = 1; i < v.size(); i++) {
      if (v[i] < v[i - 1]) dp = 1;
      if (dp == 1) count++;
    }
    cout << count;
  } else
    cout << "-1";
  cout << endl;
}
int main() {
  long long int n;
  cin >> n;
  vector<int> v;
  for (long long int i = 0; i < n; i++) {
    long long int t;
    cin >> t;
    v.push_back(t);
  }
  answer(v);
}
