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;
void solve() {
  long long n;
  cin >> n;
  vector<long long> v, s;
  for (long long i = 0; i < n; i++) {
    long long x;
    cin >> x;
    v.push_back(x);
  }
  for (long long i = 0; i < 2; i++) {
    for (long long j = 0; j < n; j++) {
      s.push_back(v[j]);
    }
  }
  vector<long long> ans(2 * n, 1);
  for (long long i = 1; i < s.size(); i++) {
    if (s[i] >= s[i - 1]) {
      ans[i] = 1 + ans[i - 1];
    }
  }
  long long idx = -1;
  for (long long i = 0; i < ans.size(); i++) {
    if (ans[i] == n) {
      idx = i;
      break;
    }
  }
  if (idx == -1)
    cout << -1;
  else {
    long long id = idx - (n - 1);
    cout << (n - id) % n;
  }
}
void init() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int32_t main() {
  init();
  { solve(); }
  return 0;
}
