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;
bool sortbysec(const pair<long long, long long> &a,
               const pair<long long, long long> &b) {
  return (a.second < b.second);
}
const long long N = (1e5);
string yes = "YES", no = "NO";
void solve() {
  long long tt = 1;
  while (tt--) {
    long long n;
    cin >> n;
    vector<long long> a(n);
    for (long long i = 0; i < n; i++) cin >> a[i];
    bool first = false;
    long long p = 0;
    for (long long i = 1; i < n; i++) {
      if (a[i - 1] > a[i]) {
        if (first) {
          cout << -1 << '\n';
          return;
        }
        first = true;
        p = i;
      }
    }
    if (a[n - 1] > a[0]) {
      if (first) {
        cout << -1 << '\n';
        return;
      }
    }
    if (!first)
      cout << 0 << '\n';
    else
      cout << n - p << '\n';
  }
}
int32_t main() {
  solve();
  return 0;
}
