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:
//package javdir;
import java.util.*;
import java.io.*;

public class classCC {

	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		java.util.Scanner scanner=new java.util.Scanner(new java.io.BufferedReader(new java.io.InputStreamReader(System.in)));
		int t=scanner.nextInt();
		while(t-->0) {
			int n=scanner.nextInt();
			
			java.util.List<Integer> list=new java.util.ArrayList<>();
			for (int i = 0; i <n; i++) {
				//arr[i]=scanner.nextInt();
				list.add(scanner.nextInt());
			}
			int arr2[]=new int[n];
			int index=0;
			while(!list.isEmpty()) {
				try {
					int removed=list.remove(0);
					arr2[index]=removed;
					int removed1=list.remove(list.size()-1);
					index++;
					arr2[index]=removed1;
					//System.out.println(removed+"  "+removed1);
					index++;
				}
				catch (Exception e) {
					break;
				}
			}
			String anString="";
			for(Integer s:arr2)anString=anString+s+" ";
			System.out.println(anString.trim());
			
		}

	}
	static int gcd(int a, int b) {
	    while (b != 0) {
	        int t = a;
	        a = b;
	        b = t % b;
	    }
	    return a;
	}
	
}