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, i, j, c = 0, ind = -1;
  cin >> n;
  int a[n];
  for (i = 0; i < n; i++) {
    cin >> a[i];
  }
  for (i = 1; i < n; i++) {
    if (a[i] < a[i - 1]) {
      c++;
      ind = i;
    }
  }
  if (c == 0 && ind == -1) {
    cout << "0\n";
  } else if (c == 1 && ind != -1 && a[0] >= a[n - 1]) {
    cout << (n - ind) << "\n";
  } else {
    cout << "-1\n";
  }
}
