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;
void faster() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
}
int n, a[123456];
int main() {
  faster();
  int a[100010], n;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  int i, j, t = n - 1;
  for (i = 0; i < n - 1; i++) {
    if (a[i] > a[i + 1]) {
      t = i;
      break;
    }
  }
  if (t == n - 1) {
    cout << 0;
    return 0;
  }
  for (j = t + 1; j < n - 1; j++) {
    if (a[j] > a[j + 1]) {
      cout << -1;
      return 0;
    }
  }
  if (a[0] < a[n - 1]) {
    cout << -1;
    return 0;
  }
  cout << n - i - 1;
}
