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;
long long int arr[10000000];
bool isSorted(long long int n) {
  int i;
  for (i = 0; i < n - 1; i++) {
    if (arr[i] > arr[i + 1]) return false;
  }
  return true;
}
long long int MinOperations(int n) {
  long long int i, j;
  long long int c = 0;
  if (isSorted(n)) return 0;
  for (i = n - 1; i > 0; i--) {
    if (arr[i] < arr[i - 1]) break;
  }
  if (i == 1) {
    if (arr[0] < arr[n - 1])
      return -1;
    else {
      c = n - i;
      return c;
    }
  }
  for (j = 0; j < i - 1; j++) {
    if (arr[j] < arr[n - 1] || arr[j + 1] < arr[j]) return -1;
  }
  c = n - i;
  return c;
}
int main() {
  long long int n, i;
  cin >> n;
  for (i = 0; i < n; i++) cin >> arr[i];
  long long int ans = MinOperations(n);
  cout << ans;
  return 0;
}
