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;
  cin >> n;
  int arr[n];
  int temp = INT_MAX;
  int ind;
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
    if (temp > arr[i]) {
      temp = min(temp, arr[i]);
      ind = i;
    }
  }
  int var = ind;
  while (arr[(ind % n)] == arr[(ind - 1 + n) % n]) {
    ind = (ind - 1 + n) % n;
    if (ind == var) break;
  }
  int flag = 0;
  for (int i = ind + 1; i != (((ind) + n) % n);) {
    int start = i;
    if (start >= n) start = start % n;
    int last = start - 1;
    if (last < 0) {
      last = (last + n);
    }
    if (arr[start] < arr[last]) {
      flag = 1;
      break;
    }
    i++;
    if (i >= n) i = i % n;
  }
  if (flag == 0) {
    cout << ((n - ind) % n) << endl;
  } else {
    cout << -1 << endl;
  }
  return 0;
}
