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;
const double PI = acos(-1.0);
int arr[2 * 100000], l, r, n;
int main() {
  cin >> n;
  for (int i = (0), _b = (n - 1); i <= _b; i++) {
    cin >> arr[i];
    arr[n + i] = arr[i];
  }
  for (int i = (1), _b = (2 * n - 1); i <= _b; i++) {
    if (arr[i] >= arr[i - 1])
      r++;
    else
      l = r = i;
    if (r - l + 1 == n) {
      cout << (l == 0 ? 0 : n - l) << endl;
      return 0;
    }
  }
  cout << -1 << endl;
  return 0;
}
