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, v[100100], ordV[100100], k = 0;
  scanf("%d", &n);
  for (int i = 0; i < n; i++) {
    scanf("%d", &v[i]);
    ordV[i] = v[i];
  }
  sort(ordV, ordV + n);
  while (ordV[0] != v[k] && k < n) k++;
  if (k == 0 && v[n - 1] == ordV[0]) {
    k = n - 1;
    while (v[k] == ordV[0] && k >= 0) k--;
    k++;
  }
  int i = 0, aux = k;
  for (i = 0; i < n && ordV[i] == v[k]; i++) {
    k++;
    if (k == n) k = 0;
  }
  if (i == n) {
    if (aux == 0)
      printf("0\n");
    else
      printf("%d\n", n - aux);
  } else
    printf("-1\n");
}
