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:
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class test
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner in=new Scanner (System.in);
		int t=in.nextInt();
		while (--t>=0)
		{
		    int n=in.nextInt();
		    int arr[]=new int [n];
		    for(int i=0;i<n;i++)
		    arr[i]=in.nextInt();
		    
		    Arrays.sort(arr);
		    
		    int st = 0;
		    int en = n-1;
		    
		    int ans [] =new int [n];
		    int c =n-1;
		    for(int i=n-1;i>=0;i+=0)
		    {
		        ans[i]=arr[st];
				i--;
				if (i<0)
				break;
		        ans[i]=arr[en];
		        st++;
		        en--;
		        i--;
		    }
		    for(int i=0;i<n;i++)
		    System.out.print(ans[i]+" ");
		    System.out.println();
		}
		
	}
}