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 main() {
  int N;
  cin >> N;
  int Arr[N];
  int rotate1 = 0, l = 0;
  int res = 0;
  for (int i = 0; i < N; i++) {
    cin >> Arr[i];
  }
  for (int i = 0; i < N - 1; i++) {
    if (Arr[i] > Arr[i + 1]) {
      l = i + 1;
      res++;
    }
  }
  if (res == 1 && Arr[0] >= Arr[N - 1]) {
    cout << N - l << endl;
  } else if (res == 0) {
    cout << 0 << endl;
  } else
    cout << -1 << endl;
  return 0;
}
