Problem: Polycarp has a favorite sequence a[1 ... n] consisting of n integers. He wrote it out on the whiteboard as follows:

  * he wrote the number a_1 to the left side (at the beginning of the whiteboard); 
  * he wrote the number a_2 to the right side (at the end of the whiteboard); 
  * then as far to the left as possible (but to the right from a_1), he wrote the number a_3; 
  * then as far to the right as possible (but to the left from a_2), he wrote the number a_4; 
  * Polycarp continued to act as well, until he wrote out the entire sequence on the whiteboard. 

<image> The beginning of the result looks like this (of course, if n ≥ 4).

For example, if n=7 and a=[3, 1, 4, 1, 5, 9, 2], then Polycarp will write a sequence on the whiteboard [3, 4, 5, 2, 9, 1, 1].

You saw the sequence written on the whiteboard and now you want to restore Polycarp's favorite sequence.

Input

The first line contains a single positive integer t (1 ≤ t ≤ 300) — the number of test cases in the test. Then t test cases follow.

The first line of each test case contains an integer n (1 ≤ n ≤ 300) — the length of the sequence written on the whiteboard.

The next line contains n integers b_1, b_2,…, b_n (1 ≤ b_i ≤ 10^9) — the sequence written on the whiteboard.

Output

Output t answers to the test cases. Each answer — is a sequence a that Polycarp wrote out on the whiteboard.

Example

Input


6
7
3 4 5 2 9 1 1
4
9 2 7 1
11
8 4 3 1 2 7 8 7 9 4 2
1
42
2
11 7
8
1 1 1 1 1 1 1 1


Output


3 1 4 1 5 9 2 
9 1 2 7 
8 2 4 4 3 9 1 7 2 8 7 
42 
11 7 
1 1 1 1 1 1 1 1 

Note

In the first test case, the sequence a matches the sequence from the statement. The whiteboard states after each step look like this:

[3] ⇒ [3, 1] ⇒ [3, 4, 1] ⇒ [3, 4, 1, 1] ⇒ [3, 4, 5, 1, 1] ⇒ [3, 4, 5, 9, 1, 1] ⇒ [3, 4, 5, 2, 9, 1, 1].

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class Permutation{
    public static void main(String [] args)
    {
        try{
	       BufferedReader rd=new BufferedReader(new InputStreamReader(System.in));
	       int t=Integer.parseInt(rd.readLine());
	       while(t-->0)
	       {
	       int n=Integer.parseInt(rd.readLine());
	        int arr[]=new int[n];
	       String str[]=rd.readLine().trim().split(" ");
	       
	       for(int i=0;i<n;i++)
	       {
	           arr[i]=Integer.parseInt(str[i]);
	       }
	       int nwr[]=new int[n];int k=0;
	       nwr[n-1]=arr[n/2];
	      for(int i=0,j=n-1;j>i;i++,j--)
	      {
	          nwr[k]=arr[i];
	          nwr[k+1]=arr[j];
	          k=k+2;
	      }
	       for(int i=0;i<n;i++)
	       {
	             System.out.print(nwr[i]+" ");
	       }
	       System.out.println();
	     
	      
	}
	    }
	    catch(Exception e)
	    {
	        return;
	    }
        
    }
}