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::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n, a, mx = 0, mn = 0;
  cin >> n;
  deque<int> unsorted, sorted;
  for (int i = 0; i < n; i++) {
    cin >> a;
    unsorted.push_back(a);
  }
  sorted = unsorted;
  sort(sorted.begin(), sorted.end());
  if (sorted == unsorted)
    cout << 0 << endl;
  else {
    int i = 0, cnt = 0;
    while (i < unsorted.size()) {
      if (unsorted[0] < unsorted[unsorted.size() - 1]) {
        break;
      }
      int x = unsorted.back();
      unsorted.pop_back();
      unsorted.push_front(x);
      cnt++;
      i++;
    }
    if (sorted == unsorted)
      cout << cnt << endl;
    else
      cout << -1 << endl;
  }
  return 0;
}
