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.IOException;
 
 import java.util.*;

    public class Training {

      
       
            public static void main(String[] args) throws IOException {
 		Scanner input = new Scanner(System.in);
              int n = input.nextInt();
              int c = 0;
              int d = 0;
              int arr[]= new int[n];
               for(int i =0;i<n;i++){
                   arr[i]= input.nextInt();
                   if(i>0 && arr[i]<arr[i-1]){
                       c++;
                       d= i;
                   }
               }
               
               if(c==0){
                   System.out.println(0);
               }else if(c==1 && arr[n-1]<=arr[0]){
                   System.out.println(n-d);
               }else{
                   System.out.println(-1);
               }
             
             } // end main
 
     
       
    } // end Class
