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.*;

public class CodeForces1339B {

    static BufferedReader f = new BufferedReader(new InputStreamReader(System.in));

    public static void main(String[] args) throws IOException {
        /*
        IDEA:
        first arrange all the the number from the ascending order
        then look at the middle, go in bigger circle
        ex) -2,4,5,5,6,8
        start in 5 in the middle, first go to 5, 4,6,-2,8

        even odd are different
        if even go from length/2-1
        if odd go from length/2
         */


        int numOfTests = Integer.parseInt(f.readLine());
        for (int i = 0; i < numOfTests; i++) {
            int length = Integer.parseInt(f.readLine());
            ArrayList<Integer> allNums = new ArrayList<>();
            StringTokenizer tok = new StringTokenizer(f.readLine());
            for (int j = 0; j < length; j++) {
                allNums.add(Integer.parseInt(tok.nextToken()));
            }
            Collections.sort(allNums);

            //startFrom middle
            int index;
            int leftIndex;
            int rightIndex;
            if (length % 2 == 0) {
                index = (allNums.size() / 2) - 1;
                leftIndex = index;
                rightIndex = index + 1;
            } else {
                index = allNums.size() / 2;
                System.out.println(allNums.get(index));
                leftIndex = index - 1;
                rightIndex = index + 1;
            }

            boolean indexChange = true; //true = ++, false:--

            while (leftIndex >= 0) {
                System.out.print(allNums.get(leftIndex) + " "+allNums.get(rightIndex)+" ");
                leftIndex--;
                rightIndex++;
            }

            System.out.println();


        }


    }


}