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, l = 0, r = 0, p = 0;
  cin >> n;
  vector<long long> a(n), b, arr;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    b.push_back(a[i]);
  }
  if (a[0] >= a[n - 1]) {
    for (int i = 1; i < n; i++)
      if (a[i] >= a[i - 1])
        continue;
      else {
        l++;
        r = i;
      }
    if (l == 0)
      cout << 0 << "\n";
    else if (l == 1)
      cout << n - r << "\n";
    else
      cout << -1 << "\n";
  } else if (n == 2)
    cout << 0 << "\n";
  else
    cout << -1 << "\n";
  return 0;
}
