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.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		long t = sc.nextLong();
		while(t>0){
		    int n = sc.nextInt();
		    long a[] = new long[n];
		    if(n==1){
		        a[0] = sc.nextLong();
		    }
		    else{
		        if(n%2!=0){
		            int cnt=0;
    		        for(int i=0;i<=n/2;i++){
        		        a[cnt] = sc.nextLong();
	        	        cnt+=2;
	    	        }
        		    cnt = n-2;
	                for(int i=1;i<n/2;i++){
    	    	        a[cnt] = sc.nextLong();
	    	            cnt-=2;
		            }
		            a[1] = sc.nextLong();
		        }
		        else{
		            int cnt=0;
    		        for(int i=0;i<n/2;i++){
        		        a[cnt] = sc.nextLong();
	        	        cnt+=2;
	    	        }
        		    cnt = n-1;
	                for(int i=0;i<n/2;i++){
    	    	        a[cnt] = sc.nextLong();
	    	            cnt-=2;
		            }
		        }
		        
		    }
		    for(int i=0;i<n;i++){
		        System.out.print(a[i]+" ");
		    }
		   
            System.out.print("\n");
		    
            
            t--;
		}
	}
}