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);
  cout.tie(NULL);
  long long n;
  cin >> n;
  deque<long long> d;
  long long c = 0, f = 0;
  map<long long, long long> m;
  for (long long i = 0; i < n; i++) {
    long long a;
    cin >> a;
    m[a]++;
    if (m[a] == n) {
      f = 1;
    }
    d.push_back(a);
  }
  if (f) {
    cout << c;
    return 0;
  }
  long long i = 0;
  while (d.front() >= d.back()) {
    if (i == n) {
      break;
    }
    d.push_front(d.back());
    d.pop_back();
    c++;
    i++;
  }
  for (long long i = 1; i < n; i++) {
    if (d[i] < d[i - 1]) {
      cout << -1;
      return 0;
    }
  }
  cout << c;
}
