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.util.*;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;
import java.math.*;
import java.util.stream.Collectors;
public class JavaApplication1 {
 
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {

BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
    int t=Integer.parseInt(bf.readLine());
     StringBuilder mout=new StringBuilder();
        while (t-- > 0) {
            int n = Integer.parseInt(bf.readLine());
            String[] in = bf.readLine().split(" ");
           StringBuilder out=new StringBuilder();
            ArrayList al=new ArrayList();
            
        for(int i=0;i<n;i++){
          
        al.add(Integer.parseInt(in[i]));
        }
        Collections.sort(al);
        int l=(n/2)-1;
        int h=(n/2);
        if(n%2==1){out.append(al.get((n/2))+" ");h++;}
            while (true) {
                out.append(al.get(l)+" "+al.get(h)+" ");
                  l--;
                h++;
             
             if(h==n||l==-1){break;}   
            }
            
            mout.append(out+"\n");
        }
        System.out.print(mout);
    }

   
}

//:


/*
4
3
2 -1 -1
4
-1 0 0 1
2
-1 2
3
0 -2 1

*/