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 t, n, m, k, arr[100010];
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
  }
  int flag = 0;
  int temp = n;
  for (int i = 0; i < n - 1; i++) {
    if (arr[i] > arr[i + 1]) {
      flag++;
      temp = i + 1;
    }
  }
  if (flag > 1) {
    puts("-1");
  } else {
    flag = 0;
    for (int i = temp; i < n; i++) {
      if (arr[i] > arr[0]) {
        flag = 1;
      }
    }
    if (flag)
      puts("-1");
    else
      printf("%d\n", n - temp);
  }
  return 0;
}
