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.lang.*;
import java.math.*;

public class Sorted_Adjacent_Differences {
	
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		
		for(int i=0; i<t; i++){
			  int n = sc.nextInt();
			  int[] arr = new int[n];
			  int[] ans = new int[n];
			  for(int j=0; j<n; j++){
				   arr[j] = sc.nextInt();
			  }
			  
			  Arrays.sort(arr);
			  
			  int k=n-1, w=0;
			  for(int j=n-1;j>0; j-=2){
				  ans[j]=arr[k--];
				  ans[j-1] = arr[w++];
			  }
			  
			  if(n%2==1) ans[0] = arr[w];
			  for(int j=0; j<n; j++){
				  System.out.print(ans[j]);
				  if(j!=n-1) System.out.print(" ");
			  }
			   System.out.println();
				  
		}
	}
}