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.Arrays;
import java.util.StringTokenizer;

public class adjacent_differences
{
   static int n, testcases;

   public static void main(String[] args) throws Exception
   {
      BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
      PrintWriter outf = new PrintWriter(new OutputStreamWriter(System.out));
      StringTokenizer st = new StringTokenizer(f.readLine());
      testcases = Integer.parseInt(st.nextToken());

      for (int t = 0; t < testcases; t++)
      {
         st = new StringTokenizer(f.readLine());
         n = Integer.parseInt(st.nextToken());

         int[] in = new int[n];
         st = new StringTokenizer(f.readLine());
         for (int i = 0; i < n; i++)
         {
            in[i] = Integer.parseInt(st.nextToken());
         }

         Arrays.sort(in);

         int[] reverseIn = new int[n];

         int r = n; // index for reversing

         for (int k = 0; k < n; k++)
         {
            reverseIn[r - 1] = in[k];
            r--;
         }

         int[] arr = new int[n];
         int a = 0;
         int i = 0;
         r = 0;
         boolean toggle = true;

         while (a < n)
         {
            if (toggle)
            {
               arr[a] = in[i];
               i++;
            }
            else
            {
               arr[a] = reverseIn[r];
               r++;
            }
            a++;
            toggle = !toggle;
         }

//         System.out.println(Arrays.toString(arr));

         for (int j = n - 1; j >= 1; j--)
         {
            System.out.print(arr[j] +  " ");
         }
         System.out.print(arr[0]);
         System.out.println();


      }


      f.close();
      outf.close();
   }
}