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() {
  int n, min, cur, prev, res = 0;
  cin >> n >> min;
  bool p = 0, f = 1;
  prev = min;
  int i = 0;
  for (; i < n - 1; i++) {
    cin >> cur;
    if (cur < prev) {
      p = 1;
      i++;
      break;
    } else
      prev = cur;
  }
  if (!p) {
    cout << 0 << endl;
    return 0;
  }
  if (cur > min)
    f = 0;
  else {
    prev = cur;
    res++;
  }
  for (; i < n - 1 && f; i++) {
    cin >> cur;
    if (cur < prev || cur > min)
      f = 0;
    else {
      prev = cur;
      res++;
    }
  }
  if (f)
    cout << res << endl;
  else
    cout << -1 << endl;
  return 0;
}
