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 a[200020];
int main() {
  int n, i;
  int min, flag;
  int mark;
  while (scanf("%d", &n) != EOF) {
    scanf("%d", &a[0]);
    min = a[0];
    flag = 0;
    for (i = 1; i < n; i++) {
      scanf("%d", &a[i]);
      if (a[i] <= min && a[i] != a[i - 1]) {
        min = a[i];
        flag = i;
      }
    }
    mark = 0;
    for (i = n; i < n + flag; i++) {
      a[i] = a[i - n];
    }
    for (i = flag; i < n + flag - 1; i++) {
      if (a[i + 1] < a[i]) {
        mark = 1;
        break;
      }
    }
    if (mark == 1) {
      printf("-1\n");
    } else {
      if (flag == 0)
        printf("0\n");
      else
        printf("%d\n", n - flag);
    }
  }
  return 0;
}
