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.util.*;
import java.util.Map.Entry;


public class  Sorted_Adjacent_Differences     
{ 
    
    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; 
        } 
    } 
    public static long changeme(long b,int i,int fin,long num)
    {
        return ((b>>i)|(b<<(fin-i)))&num;
    }
    static long power(long x, long y, long m)  
    { 
        if (y == 0) 
            return 1; 
          
        long p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p%m; 
        else
            return (x * p) % m; 
    } 
    static long modInverse(long a,long m) 
    { 
        return power(a, m - 2, m);  
    } 
    static long gcd(long a,long b)  
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 
    static int kFactors(long n,long k) 
    { 
        ArrayList<Long> P = new ArrayList<Long>(); 
      
        // Insert all 2's in list 
        while (n % 2 == 0) 
        { 
            P.add(2l); 
            n /= 2; 
        } 
        for (int i = 3; i * i <= n; i = i + 2) 
        { 
            while (n % i == 0) 
            { 
                n = n / i; 
                P.add((long)i); 
            } 
        } 
        if (n > 2) 
            P.add(n); 
        if (P.size() < k) 
        {  
            return 0; 
        } 
        else
        {
            return 1;
        }
    } 
    public static void main(String[] args) 
    { 
        FastReader sc=new FastReader(); 
        PrintWriter pw=new PrintWriter(System.out);
        
        int t=sc.nextInt();

        m:while(t-->0)
        {
            
            int n=sc.nextInt();

            long arr[]=new long[n];

            for(int i=0;i<n;i++)
                arr[i]=sc.nextLong();

            Arrays.sort(arr);

            int a=(n/2);
            int b=n-a;

            long f[]=new long[a];
            long s[]=new long[b];

            for(int i=a-1,j=0;i>=0;i--,j++)
            {
                f[j]=arr[i];
            }
            for(int i=a,j=0;i<n;i++,j++)
            {
                s[j]=arr[i];
            }

            for(int i=0;i<a;i++)
            {
                pw.print(s[i]+" "+f[i]+" ");
            }

            /*for(long aa:f)
                System.out.print(aa+" ");
            System.out.println();
            for(long aa:s)
                System.out.print(aa+" ");
            System.out.println();*/

            if(n%2==1)
                pw.print(s[b-1]);
            pw.println();
           pw.flush();



            
        }
        

        
    }

}