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, i, p, f = 1;
  scanf("%d", &n);
  p = n;
  int a[n];
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  for (i = 1; i < n; i++) {
    if (a[i] < a[i - 1]) {
      p = i;
      f = 0;
      break;
    }
  }
  for (i = p; i < n; i++)
    if (a[i] > a[i + 1]) break;
  if (i == n && a[n - 1] <= a[0]) {
    printf("%d ", n - p);
  } else if (f == 1)
    printf("%d ", 0);
  else
    printf("-1");
}
