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 argc, char const *argv[]) {
  int n;
  cin >> n;
  int j, i = 0, ind, arr[n];
  for (i = 0; i < n; i++) cin >> arr[i];
  i = 0;
  while (i < n - 1 && arr[i] <= arr[i + 1]) i++;
  i++;
  ind = i;
  if (i == n) {
    cout << "0\n";
    return 0;
  }
  while (i < n - 1 && arr[i] <= arr[i + 1]) i++;
  if (i == n - 1) {
    if (arr[n - 1] <= arr[0])
      cout << n - ind << endl;
    else
      cout << "-1\n";
  } else
    cout << "-1\n";
  return 0;
}
