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 x;
  cin >> x;
  int temp = x;
  int start = x;
  int res = 0;
  int index = -1;
  for (int i = 1; i < n; i++) {
    cin >> x;
    if (index >= 0) {
      if (x < temp) {
        res = -1;
      } else {
        if (x > start) {
          res = -1;
        }
      }
    } else {
      if (x < temp) {
        if (x > start) {
          res = -1;
        } else {
          index = i;
        }
      }
    }
    temp = x;
  }
  if (res != -1) {
    if (index != -1)
      cout << n - index << endl;
    else
      cout << 0 << endl;
  } else {
    cout << res << endl;
  }
}
