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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int n, i, j, k = 0, l;
  cin >> n;
  vector<long long int> numbers(n), duplicate;
  for (i = 0; i < n; i++) cin >> numbers.at(i);
  duplicate = numbers;
  sort(duplicate.begin(), duplicate.end());
  if (duplicate == numbers) {
    cout << "0";
    return 0;
  }
  for (i = 1; i < n; i++) {
    if (numbers.at(i) < numbers.at(i - 1)) break;
  }
  if (numbers.at(i) > numbers.at(0)) {
    cout << "-1";
    return 0;
  }
  for (j = i + 1; j < n; j++) {
    if (numbers.at(j) < numbers.at(j - 1) || numbers.at(j) > numbers.at(0)) {
      k = -1;
      break;
    }
  }
  if (k == 0)
    cout << n - i;
  else
    cout << "-1";
  return 0;
}
