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.*;
public class asd
{
         public static void main(String args[])
         {
                  Scanner s=new Scanner(System.in);
                  int t=s.nextInt();
                  while(t-->0)
                  {
                           int n=s.nextInt();
                           int arr[]=new int[n];
                           for(int i=0;i<n;i++)
                           {
                                    arr[i]=s.nextInt();
                                    
                           }
                           Arrays.sort(arr);
                          int q=01;
                          int r=(n/2);
                          if(n%2==1)
                          {
                                   System.out.print(arr[r]+" ");
                                   while(q<=n/2)
                                   {
                                            System.out.print(arr[r+q]+" "+arr[r-q]+" ");q++;
                                   }
                          }
                          else
                          {
                                   q=n/2;
                                   r=q-1;
                                   while(r>=0&&q<n)
                                   {
                                            System.out.print(arr[q]+" "+arr[r]+" ");
                                            q++;
                                            r--;
                                            
                                   }
                          }
                          System.out.println();
                  }
         }
}