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 LittlePonyNdSortByShift {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int a[] = new int[n];

        boolean f =true;
        for(int i=0; i<n; i++)
            a[i] =sc.nextInt();
        int ind =0;
        int count =0;
            for(int i=1; i<n; i++){
                if(a[i]<a[i-1]){
                    count++;
                    ind = i-1;
                }
            }
            if(count==0)
                System.out.println(0);
            else if(count==1 && a[0]>=a[n-1])
                    System.out.println(n-(ind+1));
            else
                System.out.println(-1);






    }
}
