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 HelloWorld{

     public static void printArray(int a[],int n){
        for(int i=0;i<n;i++){
            System.out.print(a[i]+" ");
        }
     }
     public static void solve(int a[],int n){
        if(n <= 2){
            printArray(a,n);
            return;
        } 
        
        int arr[] = new int[n];
        int i = 0;
        int mid = 0;
        int j = n-1;
        
        while(i < a.length && mid < a.length){
           if(i%2==0){
               arr[i] = a[mid++];
           }else{
               arr[i] = a[j--];
           } 
           i++;
        }
        
        printArray(arr,n);
     }
     
     public static void main(String []args){
       Scanner s = new Scanner(System.in);
       int t = s.nextInt();
       while(t-->0){
           int n = s.nextInt();
           
           int a[] = new int[n];
           
           for(int i=0;i<n;i++){
              a[i] = s.nextInt();
           }
           
           solve(a,n);
           
           System.out.println();
       }
     }
}