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;
const int N = 1e5 + 5;
int n, m, cnt;
deque<int> dq;
int sorted() {
  deque<int>::iterator it = dq.begin();
  deque<int>::iterator x = dq.begin() + 1;
  for (; it < dq.end() - 1, x < dq.end(); it++, x++) {
    if (*it > *x) return 0;
  }
  return 1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x;
    cin >> x;
    dq.push_back(x);
  }
  if (sorted()) {
    cout << 0 << endl;
    return 0;
  }
  deque<int>::iterator last = dq.end() - 1;
  deque<int>::iterator first = dq.begin();
  while (*first >= *last) {
    cnt++;
    dq.push_front(*last);
    dq.pop_back();
    last = dq.end() - 1;
    first = dq.begin();
  }
  if (sorted()) {
    cout << cnt << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}
