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 a[n];
  for (int i = 0; i < n; i++) cin >> a[i];
  bool flag = 0, alleq = 1;
  int minindex = -1, minelem = INT_MAX;
  for (int i = 0; i < n - 1; i++) {
    if (a[i] != a[i + 1]) alleq = 0;
  }
  if (alleq == 1) {
    cout << 0;
    return 0;
  }
  for (int i = 0; i < n; i++) {
    if (a[i] < minelem) {
      minelem = a[i];
    }
  }
  for (int i = 0; i < n; i++) {
    if (a[i] == minelem) {
      minindex = i;
      break;
    }
  }
  while (a[minindex] == a[(minindex + n - 1) % n])
    minindex = (minindex + n - 1) % n;
  for (int i = 0; i < n - 1; i++) {
    if (a[(i + minindex) % n] > a[(i + minindex + 1) % n]) flag = 1;
  }
  if (flag == 1)
    cout << -1;
  else
    cout << (n - minindex) % n;
  return 0;
}
