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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;



public class A
{
	static class Pair
	{
	    int a;
	    int b;
	    Pair(int a,int b)
	    {
	        this.a = a;
	        this.b = b;
	    }
	    public int hashCode(){
	        //System.out.println("In hashcode");
	        int hashcode = 0;
	        hashcode = a*20;
	        hashcode += b*20;
	        return hashcode;
	    }
	     
	    public boolean equals(Object obj){
	        //System.out.println("In equals");
	        if (obj instanceof Pair) {
	            Pair pp = (Pair) obj;
	            return (pp.a == this.a && pp.b == this.b);
	        } else {
	            return false;
	        }
	    
	}
	}
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }

    static int gcd(int a,int b)
	{
		if(a == 0) return b;
		if(b == 0) return a;
		
		return gcd(b,a%b);
	}
    
    
    
    public static void main(String[] args)
    {
        OutputStream outputStream = System.out;
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(outputStream);
        
        int t = sc.nextInt();
        while(t-- > 0)
        {
        	int n = sc.nextInt();
        	Integer ar[] = new Integer[n];
        	
        	for(int i = 0; i < n; i++)
        	{
        		ar[i] = sc.nextInt();
        	}
        	
        	Arrays.sort(ar);
        	
        	ArrayList<Integer> a = new ArrayList<>();
        	if(n%2 != 0)
        	{
        		a.add(ar[n/2]);
        		
        		int l = n/2-1;
        		int r = n/2+1;
        		
        		while(l >= 0)
        		{
        			a.add(ar[l]);
        			a.add(ar[r]);
        			l--;
        			r++;
        		}
        	}
        	
        	else
        	{
        		int l = n/2-1;
        		int r = n/2;
        		
        		while(l >= 0)
        		{
        			a.add(ar[l]);
        			a.add(ar[r]);
        			l--;
        			r++;
        		}
        	}
        	
        	for(int i:a)
        	{
        		out.print(i+" ");
        	}
        	
        	out.println();
        }
        
        out.close();
    }

}