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 check(int a[], int j, int n) {
  int temp = a[n - 1];
  for (int i = 0; i <= j; i++) {
    if (a[i] < temp) return 0;
  }
  return 1;
}
int main() {
  int n;
  cin >> n;
  int a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  int index, flag = 0;
  for (int i = 0; i < n - 1; i++) {
    if (a[i] > a[i + 1]) {
      index = i;
      flag++;
      if (flag > 1) {
        cout << "-1";
        return 0;
      }
    }
  }
  if (flag == 0) {
    cout << "0";
  } else {
    if (check(a, index, n)) {
      index++;
      cout << n - index;
    } else {
      cout << "-1";
    }
  }
  return 0;
}
