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 vec[100000 + 5];
int main(void) {
  bool flag = true;
  int n, middle;
  cin >> n;
  vec[0] = -1;
  for (int i = 1; i <= n; i++) {
    cin >> vec[i];
    if (vec[i] < vec[i - 1] && flag) {
      middle = i;
      flag = false;
    }
  }
  if (flag) {
    cout << "0";
    return 0;
  }
  if (vec[middle] > vec[1]) {
    cout << "-1";
    return 0;
  }
  for (int i = middle + 1; i <= n; i++) {
    if (vec[i] < vec[i - 1] || vec[i] > vec[1]) {
      cout << "-1";
      return 0;
    }
  }
  cout << n - middle + 1;
  return 0;
}
