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 int sz = 1e5 + 5;
const long long int szz = 1e6 + 6;
const long long int mod = 1e9 + 7;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(nullptr);
  cout.tie(nullptr);
  clock_t startTime = clock();
  long long int n;
  cin >> n;
  long long int ar[n];
  long long int count = 0, last;
  for (long long int i = 0; i < n; i++) {
    cin >> ar[i];
    if (i != 0) {
      if (ar[i - 1] > ar[i]) {
        count++;
        last = i;
      }
    }
  }
  if (!count) {
    cout << "0\n";
  } else if (count == 1 and ar[0] >= ar[n - 1])
    cout << n - last;
  else {
    cout << "-1\n";
  }
  cerr << "\n"
       << setprecision(20)
       << double(clock() - startTime) / (double)CLOCKS_PER_SEC << " seconds."
       << "\n";
}
