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:
/**
 * @author egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict Not sended
 * @url <https://codeforces.com/problemset/problem/CFB>
 * @category ?
 * @date 10/06/2020
 **/

import java.io.*;
import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

import static java.lang.Integer.*;
import static java.lang.Math.*;

public class CFB {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int T = parseInt(in.readLine());
        for (int t = 0; t < T; t++) {
            StringBuilder sb = new StringBuilder();
            int N = parseInt(in.readLine());
            long[] arr = new long[N];
            StringTokenizer st = new StringTokenizer(in.readLine());
            for (int i = 0; i < N; i++) {
                arr[i] = parseInt(st.nextToken());
            }
            Arrays.sort(arr);
            long[] solution = new long[N];
            int i = N / 2 - (N % 2 == 0 ? 1 : 0), j = N / 2 + 1 - (N % 2 == 0 ? 1 : 0);
            int k = 0;
            for (; k < N && i >= 0 && j < N; k++)
                if (k % 2 == 0) solution[k] = arr[i--];
                else solution[k] = arr[j++];
            for (; i >= 0; i--)
                solution[k++] = arr[i];
            for (; j < N; j++)
                solution[k++] = arr[j];

            System.out.println(LongStream.of(solution).mapToObj(a -> a + "").collect(Collectors.joining(" ")));
        }
    }

}