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 int MAXN = 1e5 + 20;
int n, vec[MAXN], sec[MAXN];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> vec[i];
  int ind = 1;
  for (int i = 1; i < n; i++)
    if (vec[i] >= vec[i - 1])
      ind++;
    else
      break;
  if (ind == n) {
    cout << 0 << endl;
    return 0;
  }
  rotate(vec, vec + ind, vec + n);
  copy(vec, vec + n, sec);
  sort(sec, sec + n);
  bool fl = 0;
  for (int i = 0; i < n; i++)
    if (sec[i] != vec[i]) {
      cout << -1 << endl;
      return 0;
    }
  cout << n - ind << endl;
  return 0;
}
