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.math.*;
import java.util.*;


// @author : Dinosparton [ SHIVAM BHUVA ]

public class test {
	 
	   static class Pair{ 
		   int x;
		   int y;
		   
		   Pair(int x,int y){ 
			   this.x = x;
			   this.y = y;
			   
		   }
	   }
	  
	   static class Compare { 
		   
		     void compare(Pair arr[], int n) 
		    { 
		        // Comparator to sort the pair according to second element 
		        Arrays.sort(arr, new Comparator<Pair>() { 
		            @Override public int compare(Pair p1, Pair p2) 
		            { 
		                return p1.x - p2.x; 
		            } 
		        }); 
		  
//		        for (int i = 0; i < n; i++) { 
//		            System.out.print(arr[i].x + " " + arr[i].y + " "); 
//		        } 
//		        System.out.println(); 
		    } 
		} 
	  
	   public static void main(String args[]) { 
		
		  Scanner sc = new Scanner(System.in);
		
		  int tc = sc.nextInt();
		   
		   while(tc-->0) { 
			  
			int n = sc.nextInt();
			
			long a[] = new long[n];
			
			for(int i=0;i<n;i++)
				a[i] = sc.nextLong();
			
			Arrays.sort(a);
			
			long b[] = new long[n];
			int p = 0;
			
			for(int i=0;i<n/2;i++) { 
				b[p] = a[i];
				p++;
				b[p] = a[n-i-1];
				p++;
			}
			if(n%2!=0) { 
				b[p] = a[n/2];
			}
			
			for(int i=0;i<n/2;i++) { 
				long temp = b[i];
				b[i] = b[n-i-1];
				b[n-i-1] = temp; 
			}
			
			for(int i=0;i<n;i++)
				System.out.print(b[i]+" ");
			
			System.out.println(); 
		   }
	   }  
}