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.*;
public class LittlePony
{
    public static void main(String args[])
    {
        Scanner s=new Scanner(System.in);
        int n=s.nextInt();
        int arr[]=new int[n];
        for(int i=0;i<n;i++)
        {
            arr[i]=s.nextInt();
        }
        int a=0;
        boolean h=false;
        for(int i=1;i<n;i++)
        {
            if(arr[i-1]>arr[i])
            {
                if(h==false)
                {
                    a++;
                    h=true;
                }
                else
                {
                    a=-1;
                    break;
                }
            }
            else if(h)
            {
                a++;
            }
        }
        if(arr[n-1]>arr[0])
            a=-1;

        if(h==false)
            System.out.println(0);
        else
            System.out.println(a);
    }
}