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, i, j;
  scanf("%d", &n);
  int arr[n];
  for (i = 0; i < n; i++) scanf("%d", &arr[i]);
  int t = 0;
  int index = -1;
  for (i = 0; i < n; i++)
    if (arr[i] - arr[(i + 1) % n] > 0) {
      t++;
      index = i;
    }
  if (t > 1) {
    cout << "-1\n";
    return 0;
  }
  if (index == -1)
    cout << "0\n";
  else
    cout << (n - index - 1) << endl;
  return 0;
}
