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() {
  vector<int> vec1;
  int n, ret = 0, ll, rr;
  cin >> n;
  vec1.resize(n);
  ll = -1, rr = n - 1;
  for (int i = 0; i < n; i++) {
    cin >> vec1[i];
    if (i > 0 && vec1[i] < vec1[i - 1] && ll == -1) ll = i;
  }
  if (ll == -1) {
    puts("0");
    return 0;
  }
  rr = vec1[ll];
  for (int i = 0; i < n; i++) {
    if (vec1[(i + ll) % n] < rr) {
      puts("-1");
      return 0;
    }
    rr = vec1[(i + ll) % n];
  }
  cout << n - ll << endl;
}
