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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, a, i;
  cin >> n;
  vector<long long> arr;
  for (i = 0; i < n; i++) cin >> a, arr.emplace_back(a);
  if (is_sorted(arr.begin(), arr.end()))
    cout << 0 << endl;
  else {
    i = 0;
    while (i < n - 1 && arr[i] <= arr[i + 1]) i++;
    if (i < n - 1) i++;
    if (is_sorted(arr.begin() + i, arr.end()) && arr.back() <= *arr.begin())
      cout << n - i << endl;
    else
      cout << -1 << endl;
  }
  return 0;
}
