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;
int32_t main() {
  long long n;
  cin >> n;
  long long arr[n];
  for (auto &i : arr) cin >> i;
  long long dis = 0;
  long long c = 0;
  for (long long i = 0; i < n; i++) {
    if (arr[i] > arr[(i + 1) % n]) {
      dis++;
      if (dis > 1) {
        cout << -1 << endl;
        return 0;
      }
      c = i + 1;
    }
  }
  cout << (n - c) % n << endl;
  return 0;
}
