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() {
  int n, t;
  vector<int> nums;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> t;
    nums.push_back(t);
  }
  int size = nums.size();
  int count = 0;
  for (int x = 0; x < size; x++) {
    if (nums[x] > nums[(x + 1) % size]) count++;
  }
  if (count <= 1) {
    for (int i = n - 1; i > 0; i--) {
      if (nums[i - 1] > nums[i]) {
        cout << n - i;
        return 0;
      }
    }
    cout << 0;
  } else
    cout << -1;
  return 0;
}
