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.*;

public class cfpract {
   
    static class pair{
        char ch;  int fr;
        pair(char ch,int fr){this.ch=ch;  this.fr=fr;  }
    }


    public static void solve() throws Exception{
        InputStreamReader ip=new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(ip);
        int t = Integer.parseInt(br.readLine());
        StringBuilder asb=new StringBuilder();

       while(t-->0){
        int n =Integer.parseInt(br.readLine());
        String[] strs=(br.readLine()).trim().split(" ");
        // int n=Integer.parseInt(strs[0]),l=Integer.parseInt(strs[1]),r=Integer.parseInt(strs[2]),s=Integer.parseInt(strs[3]);
        //  String str=(br.readLine()).trim();
        int[] arr=new int[n];

        for(int i=0;i<n;i++){
            arr[i]=Integer.parseInt(strs[i]);
        }

        Arrays.sort(arr);

        int r=n/2;
        int l=r-1;

        while(l>=0 || r<n){
            if(r<n){asb.append(arr[r++]);  asb.append(" "); }
            if(l>=0){asb.append(arr[l--]); asb.append(" "); }
        }

        asb.append("\n");
       }

       System.out.println(asb);
    }
   
//******************************************************************************************************************** */
    public static void main(String[] args) throws Exception{
        solve();
     }

     public static void solve2() throws Exception{
        InputStreamReader ip=new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(ip);
        int t = Integer.parseInt(br.readLine());
        StringBuilder asb=new StringBuilder();

       while(t-->0){
        // int n =Integer.parseInt(br.readLine());
        // String[] strs=(br.readLine()).trim().split(" ");
        // int n=Integer.parseInt(strs[0]),l=Integer.parseInt(strs[1]),r=Integer.parseInt(strs[2]),s=Integer.parseInt(strs[3]);
        //  String str=(br.readLine()).trim();
        
       }
    }
    //sort
     public static void sort(long[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			long temp = arr[i];  arr[i] = arr[idx];  arr[idx] = temp;  //swap
		}
		Arrays.sort(arr);
	}
 
	public static void sort(int[] arr) {
		int n = arr.length;
		for (int i = 0; i < n; i++) {
			int idx = (int) Math.random() * n;
			int temp = arr[i];  arr[i] = arr[idx]; arr[idx] = temp;  //swap
		}
		Arrays.sort(arr);
	}
    //1d print
    public static void print(int[] dp) {
		for (int val : dp) {
			System.out.print(val + " ");
		}
		System.out.println();
	}
 
	public static void print(long[] dp) {
		for (long val : dp) {
			System.out.print(val + " ");
		}
		System.out.println();
	}  
    //2d print
	public static void print(long[][] dp) {
		for (long[] a : dp) {
			for (long val : a) {
				System.out.print(val + " ");
			}
			System.out.println();
		}
	}
 
	public static void print(int[][] dp) {
		for (int[] a : dp) {
			for (int val : a) {
				System.out.print(val + " ");
			}
			System.out.println();
		}
	}
 
	
}