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 javax.swing.*;
import java.io.*;
import java.util.*;
import java.math.*;

import static java.util.Comparator.*;


public class Main {
    public static void main(String[] args) throws IOException {
        FastReader s = new FastReader();
        int t=s.nextInt();
        StringBuilder ans=new StringBuilder();
        while(t-->0) {
            int n=s.nextInt();
            long[] arr=new long[n];
            for(int i=0;i<n;i++)
            {
                arr[i]=s.nextLong();
            }
            Arrays.sort(arr);
//            List<Node > list=new ArrayList<>();
//            System.out.println(Integer.MAX_VALUE);
//            long min=Long.MAX_VALUE;
//            int ind=-1;
//            for(int i=1;i<n;i++)
//            {
//                if(Math.abs(arr[i]-arr[i-1])<min)
//                {
//                    min=Math.abs(arr[i]-arr[i-1]);
//                    ind=i;
//                }
//
//
//            }
//            for(int i: arr)
//            {
//                System.out.print(i+" ");
//            }
//            System.out.println();
            int ind=n/2;
            ans.append(arr[ind]).append(" ");

            int l=ind-1,r=ind+1;
            while(l>=0 || r<n)
            {

//                System.out.println(l+" "+r);
                if(l>=0)
                {
                    ans.append(arr[l--]).append(" ");
                }
                if(r<=n-1)
                {
                    ans.append(arr[r++]).append(" ");
                }

            }
            ans.append("\n");
            System.out.println(ans.toString());
            ans=new StringBuilder();

        }
//        System.out.println(ans.toString());
    }

}

class Node
{
    int val,ind;

    public Node(int val, int ind) {
        this.val = val;
        this.ind = ind;
    }
}

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;
    }
}
//3
//2 1 3
//3 3 6
//99995 9998900021 999890031
//import javax.swing.*;
//import java.io.*;
//import java.util.*;
//import java.math.*;
//
//import static java.util.Comparator.*;
//
//
//public class Main {
//    static int gcd(int a, int b)
//    {
//        if (a == 0)
//            return b;
//        return gcd(b % a, a);
//    }
//    public static void main(String[] args) throws IOException {
//        FastReader s = new FastReader();
////        int t=s.nextInt();
//////        StringBuilder ans=new StringBuilder();
////        while(t-->0) {
//            int n=s.nextInt();
//            String str=s.next();
//            StringBuilder ans=new StringBuilder();
//            long count=0;
//            for(int i=0;i<n;i++)
//            {
//                char c=str.charAt(i);
//                for(int j=i+1;j<n;j++)
//                {
//                    if(str.charAt(j)==c)
//                    {
//                        continue;
//                    }
//                    for(int k=j+1;k<n;k++)
//                    {
//                        if(str.charAt(k)==str.charAt(j) || str.charAt(k)==c)
//                        {
//                            continue;
//                        }else if(Math.abs(j-i)==Math.abs(k-j))
//                        {
//                            continue;
//                        }
//                        else
//                        {
//                            count++;
//                        }
//                    }
//                }
//            }
//            System.out.println(count);
//
////        }
//    }
//
//}
//
//
//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;
//    }
//}
////3
////2 1 3
////3 3 6
////99995 9998900021 999890031