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 a[n];
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  int count_g = 0;
  bool fl = 0;
  int minn = 10000000, maxx = -10000000;
  int p = -1;
  for (int i = 0; i < n - 1; i++) {
    if (fl == 0) {
      if (a[i] < minn) minn = a[i];
    } else {
      if (a[i] > maxx) maxx = a[i];
    }
    if (a[i] > a[i + 1]) {
      count_g++;
      fl = 1;
      p = i + 1;
    }
  }
  if (fl == 0) {
    if (a[n - 1] < minn) minn = a[n - 1];
  } else {
    if (a[n - 1] > maxx) maxx = a[n - 1];
  }
  if (count_g == 0) {
    printf("0\n");
  } else if (minn >= maxx && count_g <= 1) {
    printf("%d\n", n - p);
  } else {
    printf("-1\n");
  }
  return 0;
}
