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[100010];
int i, j, ok, n;
int main() {
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  for (i = 0; i + 1 < n; i++)
    if (a[i] > a[i + 1]) break;
  ok = 1;
  for (j = i + 1; j < n; j++) {
    if (a[j] > a[0]) ok = 0;
    if (j + 1 < n && a[j] > a[j + 1]) ok = 0;
  }
  if (ok)
    printf("%d\n", n - 1 - i);
  else
    puts("-1");
  return 0;
}
