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, a[100010], ans = 100010, id;
  bool f = false;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] < ans || (f && a[i] == ans)) {
      ans = a[i];
      id = i;
      f = false;
    } else if (a[i] > ans)
      f = true;
  }
  for (int i = 1; i < n; i++) {
    if (ans > a[(i + id) % n]) {
      puts("-1");
      return 0;
    }
    ans = a[(i + id) % n];
  }
  if (id == 0) {
    puts("0");
  } else {
    cout << n - id;
  }
  return 0;
}
