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;
long long n, m = 0, i, j, a[100000], f = 0, d = 1, e = 0, c;
int main() {
  cin >> n;
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (i = 0; i < n - 1; i++) {
    if (a[i] > a[i + 1]) {
      f++;
      d = i;
    }
  }
  if (!f)
    cout << 0;
  else if (f > 1)
    cout << -1;
  else if (f == 1 && a[n - 1] <= a[0])
    cout << n - d - 1;
  else
    cout << -1;
}
