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() {
  long long int n;
  int a[200001], p[200001];
  cin >> n;
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
    a[i + n] = a[i];
  }
  for (int i = 1; i < 2 * n; ++i) {
    p[i] = p[i - 1] + (a[i - 1] > a[i]);
  }
  for (int i = 0; i < n; ++i) {
    if (p[n - i] == p[2 * n - 1 - i]) {
      cout << i << "\n";
      return 0;
    }
  }
  cout << "-1\n";
  return 0;
}
