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 round_690_div3;

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class A {
	public static void main(String[] args) throws Exception{
		IOA io = new IOA();
		int T = io.readInt();
		
		while(T > 0) {
			int n = io.readInt();
			int[] ary = io.readIntAry();
			
			for(int i = 0 ; i < (n/2 + n%2) ; i++) {
				int a = i;
				int b = n-1 - i;
				
				System.out.print(ary[a]+" ");
				
				if(a!=b) System.out.print(ary[b]+" ");
			}
			System.out.println();
			T--;
		}
	}
}

class IOA{
	BufferedReader br;
	int[] intAry;
	
	public IOA() {
		br = new BufferedReader(new InputStreamReader(System.in));
	}
	
	public int[] readIntAry() throws Exception {
		String[] ip = br.readLine().split(" ");
		intAry = new int[ip.length];
		
		for(int i = 0 ; i < ip.length ; i++) {
			intAry[i] = Integer.parseInt(ip[i]);
		}
		return intAry;
	}
	
	public int readInt() throws Exception{
		return Integer.parseInt(br.readLine());
	}
}