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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


public class Main {

    public static void main(String[] args) throws IOException {
        // TODO Auto-generated method stub
        BufferedReader b=new BufferedReader(new InputStreamReader(System.in));
        int t=Integer.parseInt(b.readLine());
        
        int a[]=new int[t];
        String aa[]=b.readLine().split(" ");
        
        for(int i=0;i<t;i++)
            a[i]=Integer.parseInt(aa[i]);
        int pos=0;
        int counter=0;
        for(int i=1;i<t;i++)
        {
            if(a[i-1]>a[i])
            {
                pos=i;
                counter++;
            }
            if(counter>1)
                break;
        }
        
        if(counter==0)
            System.out.println("0");
        else if(counter==1)
        {
            if(a[a.length-1]<=a[0])
                System.out.println(a.length-pos);
            else
                System.out.println("-1");
            
        }
        else
            System.out.println("-1");
    
    }
}
