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>
int main() {
  int n;
  scanf("%d", &n);
  int arr[n], asc = 1;
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
    if (i) {
      if (arr[i] < arr[i - 1]) asc = 0;
    }
  }
  if (asc)
    printf("0\n");
  else {
    int asc = 0;
    for (int i = 1; i < n; i++) {
      if (arr[i] < arr[i - 1]) asc++;
    }
    if (asc == 1) {
      int ans;
      if (arr[0] >= arr[n - 1]) {
        for (int i = 1; i < n; i++) {
          if (arr[i] < arr[i - 1]) {
            ans = n - i;
            break;
          }
        }
        printf("%d\n", ans);
      } else
        printf("-1\n");
    } else
      printf("-1\n");
  }
}
