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 = INT_MAX, x, s, count = 0, k;
  cin >> n;
  int arr[100001], arr1[100001];
  for (int i = 0; i < n; i++) {
    cin >> arr[i];
  }
  for (int i = 0; i < n; i++) {
    if (min >= arr[i]) {
      min = arr[i];
      if (i == 0)
        k = i;
      else {
        if (arr[i - 1] != min) k = i;
      }
    }
  }
  s = 0;
  for (int i = k; i < n; i++) {
    arr1[s++] = arr[i];
  }
  for (int i = 0; i < k; i++) arr1[s++] = arr[i];
  for (int i = 0; i < s; i++) {
    if (i != s - 1) {
      if (arr1[i] <= arr1[i + 1]) count++;
    }
  }
  if (count != s - 1) {
    cout << "-1" << endl;
  } else {
    x = n - k;
    if (x == n)
      cout << "0" << endl;
    else
      cout << x << endl;
  }
}
