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 MAX_ = 4000 + 5;
const int INF = 0x3f3f3f3f;
int a[300000];
int max_[300000];
int main() {
  int n;
  cin >> n;
  cin >> a[0];
  int id = n - 1;
  bool flag = false;
  for (int i = 1; i < n; i++) {
    cin >> a[i];
    if (a[i] < a[i - 1]) {
      if (flag == false) {
        flag = true;
        id = i;
      } else if (flag == true) {
        cout << -1 << endl;
        return 0;
      }
    }
  }
  if (flag == false)
    cout << 0 << endl;
  else {
    if (a[n - 1] > a[0])
      cout << -1 << endl;
    else
      cout << n - id << endl;
  }
  return 0;
}
