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 long long N = 1e5 + 5;
long long a[N];
void solve() {
  long long n;
  cin >> n;
  for (long long i = (0); i < (n); ++i) cin >> a[i];
  ;
  long long c = 0, idx, mn = a[0], mx = INT64_MIN;
  for (long long i = (1); i < (n); ++i) {
    if (a[i - 1] > a[i]) {
      ++c;
      idx = i;
    }
    if (c > 0) mx = max(mx, a[i]);
  }
  if (c > 1 || mx > mn)
    cout << -1 << '\n';
  else if (c == 0)
    cout << 0 << '\n';
  else
    cout << n - idx << '\n';
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout.precision(10);
  cout << fixed;
  ;
  solve();
  return 0;
}
