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;
vector<long long> v;
int main() {
  long long bg = -1, ind = 0, ans = 0, n;
  cin >> n;
  long long ar[n], ar1[n];
  for (int i = 0; i < n; i++) {
    cin >> ar[i];
    ar1[i] = ar[i];
  }
  for (int i = 0; i < n - 1; i++) {
    if (ar[i] > ar[i + 1]) {
      ind = i;
      break;
    }
  }
  sort(ar1, ar1 + n);
  int sum1 = 0;
  for (int i = 0; i < n; i++) {
    if (i + 1 == n && ar[i] == ar1[i] && sum1 == i) {
      cout << "0";
      return 0;
    }
    if (ar1[i] == ar[i]) {
      sum1++;
    }
  }
  ans += (n - (ind + 1));
  for (int i = ind + 1; i < n; i++) {
    v.push_back(ar[i]);
  }
  for (int i = 0; i <= ind; i++) {
    v.push_back(ar[i]);
  }
  int sum = 0;
  for (int i = 0; i < n - 1 && v[i] <= v[i + 1]; i++) {
    sum++;
  }
  if (sum == n - 1) {
    cout << ans;
  } else {
    cout << "-1";
  }
  return 0;
}
