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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
 
public class S {
    
    //************************Main Code*****************************//
    
	public static void main(String args[]) throws IOException{
		S.init(System.in);
		int tt=S.nextInt();
		while(tt-->0) {
			int n=S.nextInt();
			int a[]=readArray(n);
			int l=0,r=n-1,k=0,f=0;
			int ans[]=new int[n];
			while(l<=r) {
				if(f==0) { f=1;ans[k]=a[l];l++;k++;}
				else { f=0;ans[k]=a[r];r--;k++;}
			}
			debug(ans);
		}
	}
	
	
	//************************Fast Scanner*****************************//
 
    static BufferedReader reader;
    static StringTokenizer tokenizer;
 
    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }
 
    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(reader.readLine() );
        }
        return tokenizer.nextToken();
    }
 
    static int nextInt() throws IOException {return Integer.parseInt( next() );}
    static long nextLong() throws IOException{ return Long.parseLong( next() ); }
    static double nextDouble() throws IOException {return Double.parseDouble( next() ); }
    static int [] readArray(int n) throws IOException {int a[]=new int[n];for(int i=0;i<n;i++)a[i]=nextInt();return a;}
    static void writeArray(int arr[]) {String ans="";for(int i=0;i<arr.length;i++)ans+=(""+arr[i]+" ");System.out.println(ans);}
    
    //************************Functions*****************************//
    
    static long gcd(long a,long b){if(b==0){return a;}return gcd(b,a%b);}
    static void debug(int arr[]) {String ans="";for(int i=0;i<arr.length;i++)ans+=(""+arr[i]+" ");System.out.println(ans);}
    static void sort(int[] a){ArrayList<Integer>l=new ArrayList<>();for(int i:a)l.add(i);Collections.sort(l);for(int i=0;i<a.length;i++)a[i]=l.get(i);}
}