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 main() {
  int num[100005];
  int n;
  bool flag2 = false;
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> num[i];
  }
  int temp = num[0];
  int t1 = 1, t2 = 1;
  if (num[1] >= num[0]) {
    t1 = 2;
  } else {
    flag2 = true;
    t2 = 2;
  }
  for (int i = 1; i <= n - 2; i++) {
    if (!flag2) {
      if (num[i] <= num[i + 1]) {
        t1++;
      } else {
        if (temp >= num[i + 1]) {
          flag2 = true;
          t2 = 2;
        } else
          break;
      }
    } else {
      if (num[i] <= num[i + 1] && temp >= num[i + 1])
        t2++;
      else
        break;
    }
  }
  if (t1 + t2 - 1 == n)
    cout << t2 - 1 << endl;
  else
    cout << "-1" << endl;
  return 0;
}
