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.*;

 
public class Main{
  
	   static long gcd(long a, long b) {
		   
		   if(b == 0)return a;
		   
		   return gcd(b,a%b);
	   }

	public static void main(String args[])throws IOException{
		
	
	     BufferedReader ob = new BufferedReader(new InputStreamReader(System.in));
	     
	      int t = Integer.parseInt(ob.readLine());
	      
	      while(t --> 0) {
	    	  int n = Integer.parseInt(ob.readLine());
	    	  int []ar = new int[n];
	    	  StringTokenizer st = new StringTokenizer(ob.readLine());
	    	  
	    	  for(int i = 0; i < n; i++) {
	    		  ar[i] = Integer.parseInt(st.nextToken());
	    	  }
	    	  Arrays.sort(ar);
	    	  int []ans = new int[n];
	    	  int k = n-1;
	    	  int i = 0; 
	    	  int j = n-1;
	    	  
	    	  while(i <= j && k >= 0) {
	    		  
	    		  ans[k] = ar[j];
	    		  j--;
	    		  k--;
	    		  if(k >= 0) {
	    			  ans[k] = ar[i];
	    			  i++;
	    			  k--;
	    		  }
	    	  }
	    	  
	    	  for(int a : ans) {
	    		  System.out.print(a+" ");
	    	  }
	    	  System.out.println();
	    	  
	      }
	
}
}