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.security.*;
import java.text.*;
import java.lang.*;
import java.util.*;
import java.util.concurrent.*;
public class Result{
    public static void main(String[] args)  {
        Scanner s=new Scanner(System.in);
        int t=s.nextInt();
        while(t-->0){
            int n=s.nextInt();
            long[] arr=new long[n];
            for(int i=0;i<n;i++){
                arr[i]=s.nextLong();
            }
            Arrays.sort(arr);
            int k=n/2;
            long[] res=new long[n];
            int l=0;
            int st=1;
            int count=0;
            while(k>=0&&k<n){
                res[l]=arr[k];
                if(count%2==0){
                    k-=st;
                }
                else{
                    k+=st;
                }
                st++;
                count++;
                l++;
            }
            for(int i=0;i<n;i++){
                System.out.print(res[i]+" ");
            }
            System.out.println(" ");
        }
    }
}