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 argc, char **argv) {
  list<int> vec1;
  list<int> vec2;
  int n;
  cin >> n;
  int auxn = n;
  int num;
  for (int i = 0; i < n; i++) {
    cin >> num;
    vec1.push_back(num);
  }
  vec2 = vec1;
  vec2.sort();
  list<int> aux;
  int auxnum;
  int cont = 0;
  int tam;
  for (int j = 0; j < n; j++) {
    if (vec1 != vec2) {
      aux.push_back(vec1.back());
      auxnum = vec1.back();
      vec1.pop_back();
      while (auxnum == vec1.back()) {
        aux.push_back(vec1.back());
        vec1.pop_back();
        n--;
      }
      tam = aux.size();
      for (int s = 0; s < tam; s++) {
        vec1.push_front(auxnum);
        aux.pop_back();
        cont++;
      }
    } else
      break;
  }
  if (cont == auxn)
    cout << -1 << endl;
  else
    cout << cont << endl;
  return 0;
}
