Problem: You have array of n numbers a_{1}, a_{2}, …, a_{n}. 

Rearrange these numbers to satisfy |a_{1} - a_{2}| ≤ |a_{2} - a_{3}| ≤ … ≤ |a_{n-1} - a_{n}|, where |x| denotes absolute value of x. It's always possible to find such rearrangement.

Note that all numbers in a are not necessarily different. In other words, some numbers of a may be same.

You have to answer independent t test cases.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^{4}) — the number of test cases.

The first line of each test case contains single integer n (3 ≤ n ≤ 10^{5}) — the length of array a. It is guaranteed that the sum of values of n over all test cases in the input does not exceed 10^{5}.

The second line of each test case contains n integers a_{1}, a_{2}, …, a_{n} (-10^{9} ≤ a_{i} ≤ 10^{9}).

Output

For each test case, print the rearranged version of array a which satisfies given condition. If there are multiple valid rearrangements, print any of them.

Example

Input


2
6
5 -2 4 8 6 5
4
8 1 4 2


Output


5 5 4 6 8 -2
1 2 4 8

Note

In the first test case, after given rearrangement, |a_{1} - a_{2}| = 0 ≤ |a_{2} - a_{3}| = 1 ≤ |a_{3} - a_{4}| = 2 ≤ |a_{4} - a_{5}| = 2 ≤ |a_{5} - a_{6}| = 10. There are other possible answers like "5 4 5 6 -2 8".

In the second test case, after given rearrangement, |a_{1} - a_{2}| = 1 ≤ |a_{2} - a_{3}| = 2 ≤ |a_{3} - a_{4}| = 4. There are other possible answers like "2 4 8 1".

Solution (in JAVA):

Solution:
import java.io.*;
 
import java.math.*;
import java.text.*;
import java.util.*;
import java.util.regex.*;
 
public class Main{
	public static void pn(Object o)
	{
		System.out.println(o);
	}
	public static void p(Object o)
	{
		System.out.print(o+" ");
	}
	public static ArrayList<Integer>[] al=new ArrayList[1100010] ;
	public static boolean prime[]=new boolean[99999999];
	public static void seive()
	{
		int n=99999999;
		for(int i=0;i<n;i++)
		{
			prime[i]=true;
		}
		for(int i=2;i*i<n;i++)
		{
			if(prime[i]) {
			for(int j=i*i;j<n;j+=i)
			{
				prime[j]=false;
			}
			}
		}
		prime[1]=false;
		prime[0]=false;
		
	}
	
   public static void main(String args[])
   {
	   
	  Scanner s=new Scanner(System.in);
	  int t=s.nextInt();
	  while(t-->0)
	  {
		int n=s.nextInt();
		int arr[]=new int[n];
		for(int i=0;i<n;i++)
			arr[i]=s.nextInt();
		Arrays.sort(arr);
		ArrayList<Integer> al=new ArrayList<Integer>();
		for(int i=0,j=n-1;i<=j;i++,j--)
		{
			if(i!=j)
			{al.add(arr[j]);
			al.add(arr[i]);}
			else
				al.add(arr[i]);
		}
		
		Collections.reverse(al);
		for(int x:al)
			p(x);
		
		
		pn("");
	  }
	 // 
	  
   }
   
}