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() {
  long long n;
  cin >> n;
  vector<long long> v(n);
  long long ar[n];
  for (long long i = 0; i < n; ++i) {
    cin >> v[i];
  }
  long long index_max = max_element(v.begin(), v.end()) - v.begin();
  long long index_min = min_element(v.begin(), v.end()) - v.begin();
  long long val_min = *min_element(v.begin(), v.end());
  if (index_min < index_max) {
    auto it = find(v.begin() + index_max, v.end(), val_min);
    if (it != v.end()) {
      index_min = it - v.begin();
    }
  }
  for (long long i = index_min, j = 0; i < n + index_min; ++i) {
    ar[j] = v[(i + n) % n];
    j++;
  }
  for (long long i = 0; i < n - 1; ++i) {
    if (ar[i + 1] < ar[i]) {
      cout << -1;
      exit(0);
    }
  }
  if (ar[0] == ar[n - 1]) {
    cout << 0;
  } else {
    cout << min(n - index_min, n - index_max - 1);
  }
}
