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.io.*;
import java.util.*;
public class b
{
        public static void main(String[]args)throws IOException
        {
                Scanner N=new Scanner(System.in);
                int n=N.nextInt();
                int ar[]=new int[n];
                
                for(int i=0;i<n;i++)
                        ar[i]=N.nextInt();
                        
                int st=0,pos=n;
                
                for(int i=1;i<=n;i++)
                {
                        if(ar[i%n]>=ar[i-1] && st==0)
                        continue;
                               
                        else if(ar[i%n]<ar[i-1] && st==0)
                        {
                                pos=i;
                                st++;
                        }
                        
                        else if(ar[i%n]<ar[i-1] && st==1)
                        {
                                st++;
                        }
                }
                if(st==2)
                System.out.println("-1");
                else
                System.out.println(n-pos);
                
        }
}
