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 n, a[100005], flag, start;
int main() {
  while (~scanf("%d", &n)) {
    flag = 0;
    start = n + 1;
    for (int i = 1; i <= n; i++) {
      scanf("%d", &a[i]);
      if (a[i] < a[i - 1] && (!flag)) {
        flag = 1;
        start = i;
      }
    }
    a[n + 1] = 100005;
    if (flag) {
      int i;
      for (i = start; i <= n; i++)
        if (a[i + 1] < a[i] || a[i] > a[1]) {
          printf("-1\n");
          break;
        }
      if (i == n + 1) flag = 0;
    }
    if (!flag) printf("%d\n", n - start + 1);
  }
  return 0;
}
