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, c = 0;
  cin >> n;
  int r = n;
  int arr[n];
  deque<int> d;
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
    d.push_back(arr[i]);
  }
  sort(arr, arr + n);
  for (int i = 0; i < n; i++) {
    if (d[i] == arr[i]) {
      c++;
    }
  }
  int mid = (n + 1) / 2 - 1;
  if (c == n) {
    printf("%d\n", 0);
    ;
    return 0;
  } else {
    c = 0;
    while (r--) {
      int t = 0;
      d.push_front(d.back());
      d.pop_back();
      c++;
      if (arr[0] == d.front() && arr[n - 1] == d.back() && arr[mid] == d[mid]) {
        if (mid + 1 < n) {
          if (d[mid + 1] >= d[mid] && d[mid - 1] <= d[mid]) {
            printf("%d\n", c);
            ;
            return 0;
          }
        } else {
          printf("%d\n", c);
          ;
          return 0;
        }
      }
    }
  }
  printf("%d\n", -1);
  ;
  return 0;
}
