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.*;
import java.io.*;
public class a {
    static boolean stdin = true;
    static Reader in;
    static PrintWriter out;
    static String filename = "";
    static class Solver {
        Solver(){
            int n = in.nextInt();
	    int[] a = new int[n];
	    for(int i=0; i < n; i++){
		    a[i] = in.nextInt();
	    }
	    int[] b = new int[n];
	    int cnt = 0;
	    for(int i=0; i<n; i++){
		    if(i%2==0){
			    b[i] = a[cnt];
		    }else {
			    b[i] = a[n-cnt-1];
			    cnt++;
		    }
		    
	    }
	    for(int i=0; i<n; i++){
		    out.print(b[i] + " ");
	    }
	    out.println("");
        }
    }
    public static void main(String args[]) throws Exception {
        if(stdin){
            in = new Reader();
            out = new PrintWriter(System.out);
        } else{
            in = new Reader(filename+".in");
            out = new PrintWriter(filename+".out");
        }
	int tc = in.nextInt();
	while(tc-- > 0) {
		 new Solver();
	}
        out.close();
    }
    static class Reader{
        BufferedReader br;
        StringTokenizer st;
        Reader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        Reader(String filename)throws Exception {
            br = new BufferedReader(new FileReader(filename));
        }
        String next() {
            while(st==null||!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(Exception e) {}
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
    }
}