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.awt.Point;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.IOException;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Optional;
import java.util.Queue;
import java.util.Set;
import java.util.TreeMap;
import java.util.TreeSet;

public class Codeforces {

    public static void main(String[] args) throws java.lang.Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while(t-- > 0){
          int n = Integer.parseInt(br.readLine());
          int[] arr = new int[n];
          String[] s = br.readLine().trim().split(" ");
          
          for(int i = 0; i < n; i++){
              arr[i] = Integer.parseInt(s[i]);
          }
          Arrays.sort(arr);
          List<Integer> list = new ArrayList<>();
          int size = list.size();
          int index = n / 2;
          list.add(arr[index]);
          int first = index - 1;
          int last = index + 1;
          while(size != n){
              if(first >=0)list.add(arr[first]);
              if(last < n) list.add(arr[last]);
              first--;
              last++;
              size = list.size();
          }
          
          
          
          for(int i : list){
              System.out.print(i +" ");
          }
          System.out.println();
          

    }
}}