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, c = 0, past = 0, max = 0, min = 99999999, l = 0, pos = 0;
  scanf("%d", &n);
  while (n != 0) {
    scanf("%d", &c);
    if (past > c) {
      pos++;
      past = 0;
    }
    if (pos > 1) {
      printf("-1");
      return 0;
    }
    if (pos == 0) {
      min = min > c ? c : min;
    } else {
      max = max > c ? max : c;
    }
    if (pos == 1 && past <= c) {
      l++;
    }
    past = c;
    n--;
  }
  if (min < max) {
    printf("-1");
  } else {
    printf("%d", l);
  }
  return 0;
}
