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;
int a[100086];
bool judge(int pos) {
  int i;
  for (i = pos + 1; i <= n; i++) {
    if (a[i] < a[i - 1]) return false;
  }
  return true;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  int pos = -1;
  for (int i = 2; i <= n; i++) {
    if (a[i] < a[i - 1]) {
      pos = i;
      break;
    }
  }
  if (pos == -1) {
    cout << "0" << endl;
    return 0;
  }
  if ((!judge(pos)) || a[n] > a[1]) {
    cout << "-1" << endl;
    return 0;
  } else {
    cout << n - pos + 1 << endl;
  }
}
