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 int maxn = 1e5 + 1;
int arr[maxn], n, cnt = 0;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) scanf("%d", &arr[i]);
  for (int i = 1; i <= n; ++i) {
    if (arr[i - 1] > arr[i]) {
      for (int j = i + 1; j <= n; j++)
        if (arr[j - 1] > arr[j]) {
          printf("-1");
          return 0;
        }
      if (arr[n] > arr[1])
        printf("-1");
      else
        printf("%d", n - i + 1);
      return 0;
    }
  }
  putchar('0');
  return 0;
}
