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 int n, i;
  cin >> n;
  long long int a[n];
  for (i = 0; i < n; i++) cin >> a[i];
  long long int k = n, o = 0;
  for (i = n - 1; i > 0; i--)
    if (a[i] < a[i - 1]) {
      k = i;
      o = n - k;
    }
  long long int b[n];
  long long int z = k;
  i = 0;
  while (z < n) {
    b[i] = a[z];
    z++;
    i++;
  }
  for (long long int j = 0; j < k; j++) {
    b[i] = a[j];
    i++;
  }
  int f = 0;
  for (i = n - 1; i > 0; i--) {
    if (b[i] < b[i - 1]) {
      f = 1;
      break;
    }
  }
  if (f == 0)
    cout << o << endl;
  else
    cout << -1 << endl;
  return 0;
}
