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;
bool sieve[100005];
void sieve_func() {
  sieve[0] = sieve[1] = true;
  for (long long int i = 2; i < 100005; i++) {
    if (!sieve[i]) {
      for (long long int j = i + i; j < 100005; j += i) {
        sieve[j] = true;
      }
    }
  }
}
void solve(long long int test) {
  long long int n;
  cin >> n;
  long long int a[n], m = 0, k = 0;
  for (long long int i = 0; i < n; i++) cin >> a[i];
  for (long long int i = 0; i < n; i++) {
    if (a[i] > a[(i + 1) % n]) {
      m++;
      if (m > 1) {
        cout << -1;
        cout << endl;
        return;
      }
      k = i + 1;
    }
  }
  cout << (n - k) % n;
  cout << endl;
}
int main() {
  long long int t = 1, test = 1;
  while (t--) solve(test++);
  return 0;
}
