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
import java.util.Scanner;
public class littlepony {
    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] arr = new int[n];
        int[] temp = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
        }
        int start = 0, wrong = 0;
        for (int i = 0; i < n-1; i++) {
            if(arr[i] > arr[i + 1]){
                wrong++;
                start = i;
            }
        }
        if(arr[n - 1] > arr[0]){
            start = n -1;
            wrong++;
        }
        if(wrong == 0)
            System.out.println(0);
        else if(wrong > 1)
            System.out.println(-1);
        else
            System.out.println(n-1-start);
    }
}
