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;
const int MX = 200020;
const int N = 1000060;
const int mood = ((int)1e9 + 7);
int main() {
  cin.tie(0);
  cin.sync_with_stdio(0);
  int n;
  cin >> n;
  int a[n], b[n];
  for (int i = 0; i < n; ++i) {
    cin >> a[i];
  }
  b[0] = a[0] >= a[n - 1];
  for (int i = 1; i < n; ++i) {
    if (a[i] >= a[i - 1])
      b[i] = b[i] + 1;
    else
      b[i] = 0;
  }
  if (count(b, b + n, 0) > 1) return puts("-1"), 0;
  int res = 0;
  for (int i = 0; i < n; ++i) {
    if (b[i] == 0) {
      res = (0 - i + n) % n;
      break;
    }
  }
  cout << res << endl;
  return 0;
}
