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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.BufferedOutputStream;

public class SortedAdjacentDiffernces{

    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 PrintWriter out;
    public static void printArr(int[] arr){
        for(int i = 0;i<arr.length;i++){
            out.print(arr[i] + " ");
        }
        out.println();
    }
    public static void main(String[] args){
        FastReader s = new FastReader();
        out=new PrintWriter (new BufferedOutputStream(System.out));
        int t = s.nextInt();
        for(int u = 0;u<t;u++){
            int n = s.nextInt();
            ArrayList<Integer> arr = new ArrayList<>();
            for(int i = 0;i<n;i++){
                arr.add(s.nextInt());
            }
            Collections.sort(arr);
            int l = 0;
            int r = n-1;
            ArrayList<Integer> ans = new ArrayList<>();
            // for(int i = 0;i<n;i++){
            //     System.out.print(arr.get(i) + " ");
            // }
            if(n%2==0){
                while(l<=r){
                    ans.add(arr.get(r));
                    ans.add(arr.get(l));
                    l++;
                    r--;
                }
            }else{
                while(l<=r){
                    ans.add(arr.get(r));
                    if(l!=r){
                        ans.add(arr.get(l));
                    }
                    r--;
                    l++;
                }
            }
            Collections.reverse(ans);
            for(int i = 0;i<n;i++){
                System.out.print(ans.get(i) + " ");
            }
            System.out.println();
        }
        out.close();
    }

}