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>
const int inf = 0xfffffff;
using namespace std;
int num[100005], n;
int test(int t) {
  for (int i = t + 1; i < n; i++) {
    if (num[i - 1] > num[i]) return -1;
  }
  if (num[n - 1] > num[0] && t != 0) return -1;
  for (int i = 1; i < t; i++) {
    if (num[i - 1] > num[i]) return -1;
  }
  return 1;
}
int main() {
  while (~scanf("%d", &n)) {
    int minn = inf, temp = 0;
    scanf("%d", &num[0]);
    int ok = 1;
    for (int i = 1; i < n; i++) {
      scanf("%d", &num[i]);
      if (ok && num[i - 1] > num[i]) {
        temp = i;
        ok = 0;
      }
    }
    if (test(temp) == -1)
      puts("-1");
    else if (n - temp == n)
      printf("0\n");
    else
      printf("%d\n", n - temp);
  }
  return 0;
}
