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 Mainka {
    public static void main (String ar[]) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int [] a = new int [n];
        for (int i = 0; i<n; i++)
            a[i] = sc.nextInt();
        //
        int count = 0, index=-1;
        for (int i = 1; i<n; i++)
            if (a[i]<a[i-1])
                {
                    count++;
                    index = i;
                }
        if(count==0)
        System.out.println(0);
        else if(count>1)
        System.out.println(-1);
        else
        {
            if(a[n-1]<=a[0])
            System.out.println(n-index);
            else
            System.out.println(-1);
        }
    }
}
