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:
    /* package codechef; // don't place package name! */
     
    import java.util.*;
    import java.lang.*;
    import java.io.*;
     
    /* Name of the class has to be "Main" only if the class is public. */
    //System.out.println();
    public class Solution
    { 
    	public static void main (String[] args) throws java.lang.Exception
    	{
    		BufferedReader br = new BufferedReader(new  InputStreamReader(System.in));
    		int t = Integer.parseInt(br.readLine());
    		for(int T = 0; T < t; T++) {
    		    int n = Integer.parseInt(br.readLine());
    		    String s[] = br.readLine().split(" ");
    		    int arr[] = new int[n];
    		    
    		    for(int i = 0; i < n; i++) {
    		        arr[i] = Integer.parseInt(s[i]);
    		    }
    		    
    		    Arrays.sort(arr);
    		    int ans[] = new int[n];
    		    int ind = n - 1;
    		    for(int i = 0; i < n / 2; i++) {
    		        
    		        ans[ind] = arr[n - 1 - i];
    		        ind -= 1;
    		        ans[ind] = arr[i];
    		        ind -= 1;
    		        
    		    }
    		    
    		    if(n % 2 != 0) {
    		        ans[0] = arr[n / 2];
    		    }
    		    
    		    for(int i = 0; i < n; i++) {
    		        System.out.print(ans[i] + " ");
    		    }
    		    System.out.println();
    		}
    	}   
     
    }