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.util.*;
public class Main{
    public static void main(String args[])throws IOException{
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int test=Integer.parseInt(br.readLine().trim());
        while(test-->0){
            int n=Integer.parseInt(br.readLine().trim());
            String inp[]=br.readLine().trim().split(" ");
            int arr[]=new int[n];
            for(int i=0;i<n;i++){
                int num=Integer.parseInt(inp[i]);
               arr[i]=num;
            }
            Arrays.sort(arr);
            if(n%2 == 0){
                int i=n/2-1;
                System.out.print(arr[i]+" "+arr[i+1]+" ");
                i--;
                while(i>=0){
                    System.out.print(arr[i]+" "+arr[n-i-1]+" ");
                    i--;
                }
            }
            else{
                int i=n/2;
                System.out.print(arr[i]+" ");
                i--;
                while(i>=0){
                  System.out.print(arr[n-i-1]+" "+arr[i]+" ");
                  i--;
                }
            }
            System.out.println();
        }
    }
}