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 A[1000000];
int main() {
  ios_base::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(0);
  int n, ans, fg, i, j, k;
  cin >> n;
  for (i = 0; i < n; ++i) cin >> A[i];
  k = -1;
  for (i = 1; i < n; ++i) {
    if (A[i] < A[i - 1]) {
      k = i;
      ans = n - i;
      break;
    }
  }
  if (k == -1) k = ans = 0;
  fg = 1;
  for (i = 0; i < n - 1; ++i) {
    j = (k + 1) % n;
    if (A[j] < A[k]) {
      cout << -1 << endl;
      return 0;
    }
    k = j;
  }
  cout << ans << endl;
  return 0;
}
