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.*;
import java.io.*;
public class sortedadjacentdiff {
    public static void main(String[]args){
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t = sc.nextInt();

        for(int i = 0; i < t; i++){
            ArrayList<Integer>sortedList = new ArrayList<>();
            int n = sc.nextInt();
            for(int j = 0; j < n; j++){
                sortedList.add(sc.nextInt());
            }
            Collections.sort(sortedList);
            int start = 0;
            int end = sortedList.size()-1;
            int ind = sortedList.size()-1;
            int[]order = new int[sortedList.size()];
            while(start<=end && ind>=0){
                if(start == end){
                    order[ind] = sortedList.get(start);
                    ind--;
                }
                else{
                    order[ind] = sortedList.get(start);
                    start++;
                    ind--;
                    order[ind] = sortedList.get(end);
                    end--;
                    ind--;
                }
            }
            for(int j = 0; j < n; j++){
                out.print(order[j] + " ");
            }
            out.println();
        }
        out.close();
    }
}