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, sum, idx = -1;
int main() {
  cin >> n;
  vector<int> v(n);
  for (int i = 0; i < n; i++) scanf("%d", &v[i]);
  for (int i = 0; i < n - 1; i++)
    if (v[i] > v[i + 1]) {
      idx = i;
      break;
    }
  if (idx == -1) {
    puts("0");
    return 0;
  } else {
    for (int i = n - 1; i > idx; i--) {
      if (i == n - 1) {
        if (v[i] > v[idx] || v[i] > v[0]) {
          printf("-1\n");
          return 0;
        } else
          sum++;
      } else {
        if (v[i] > v[idx] || v[i] > v[i + 1]) {
          printf("-1\n");
          return 0;
        } else
          sum++;
      }
    }
  }
  cout << sum << endl;
  return 0;
}
