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() {
  long long n;
  cin >> n;
  deque<long long> dq;
  for (int i = 0; i < n; i++) {
    long long a;
    cin >> a;
    dq.push_back(a);
  }
  long long count1 = 0;
  while (count1 < n - 1 && dq[count1] <= dq[count1 + 1]) count1++;
  for (int i = n - 1; i > count1; i--) {
    long long p = dq.back();
    dq.push_front(p);
    dq.pop_back();
  }
  if (is_sorted(dq.begin(), dq.end()))
    cout << n - count1 - 1;
  else
    cout << -1;
  return 0;
}
