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 a[100010];
int main() {
  int n, i, pos;
  bool ans;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  pos = 0;
  for (i = 0; i < n - 1; i++) {
    if (a[i] > a[i + 1]) {
      pos = i + 1;
      break;
    }
  }
  ans = true;
  for (i = 0; i < n - 1; i++) {
    if (a[(pos + i) % n] > a[(pos + i + 1) % n]) ans = false;
  }
  if (ans) {
    if (pos)
      printf("%d", n - pos);
    else
      printf("0");
  } else
    printf("-1");
  return 0;
}
