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 n, i;
  cin >> n;
  int a[n];
  vector<int> v, w;
  for (i = 0; i < n; i++) {
    int b;
    cin >> b;
    v.push_back(b);
    w.push_back(b);
  }
  int count = 0;
  int flag = 1;
  sort(w.begin(), w.end());
  for (i = 0; i < n - 1; i++) {
    if (v[i + 1] < v[i]) {
      flag = 0;
      break;
    }
  }
  int mm = i;
  vector<int> q;
  for (i = mm + 1; i < n; i++) q.push_back(v[i]);
  for (i = 0; i <= mm; i++) q.push_back(v[i]);
  if (q == w)
    cout << n - mm - 1;
  else
    cout << -1;
  return 0;
}
