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;
const double pi = acos(-1.0);
void solve() {
  long long int n;
  cin >> n;
  vector<long long int> v;
  for (long long int i = 0; i < n; i++) {
    long long int x;
    cin >> x;
    v.push_back(x);
  }
  long long int i = 0;
  while (v[i] <= v[i + 1] && i < (n - 1)) {
    i++;
  }
  vector<long long int> ans;
  for (long long int j = (i + 1); j < v.size(); j++) {
    ans.push_back(v[j]);
  }
  for (long long int j = 0; j <= i; j++) {
    ans.push_back(v[j]);
  }
  for (long long int j = 0; j < ans.size() - 1; j++) {
    if (ans[j] <= ans[j + 1]) {
      continue;
    } else {
      cout << "-1" << endl;
      return;
    }
  }
  cout << (n - i - 1) << endl;
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  solve();
  return 0;
}
