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.io.*;
import java.util.*;

public class A {
    public static void main(String args[]) throws Exception {
        BufferedReader br = new BufferedReader (new InputStreamReader (System.in));
        Scanner sc = new Scanner(System.in);
        int T = sc.nextInt();
        // int T = Integer.parseInt(br.readLine());
        while(T-->0){
            int N = sc.nextInt();
            int arr[] = new int[N];
            for(int i=0; i<N; i++) arr[i] = sc.nextInt();
            int brr[] = new int[N];
            for(int i=0; i<N; i+=2){
                brr[i] = arr[i/2];
            }
            int j = 1;
            for(int i=N-1; i>N/2; i--){
                brr[j] = arr[i];
                j+=2;
            }
            if(N%2 == 0){
                brr[N-1] = arr[N/2];
            }
            // int start = N - (N%2) -1;
            for(int i=0; i<N; i++){
                System.out.print(brr[i] +" ");
            }
            System.out.println();
        }
    }
}