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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String args[]) {
        int num;
        Scanner s = new Scanner(System.in);

        num = s.nextInt();

        for(int i = 0;i < num; i++) {
            int size;

            size = s.nextInt();

            int[] arr = new int[size];

            for(int j = 0;j < size; j++) {
                arr[j] = s.nextInt();
            }

            printResult(size, arr);
        }
    }

    public static void printResult(int size, int[] arr){
        Arrays.sort(arr);
        ArrayList<Integer> result = new ArrayList<>(size);

        for(int i = 0;i < size; i++) {
            result.add(0);
        }

        int temp = size-1;

        //if number of elements is even
        if(size%2 == 0) {
            for(int i = 0;i <= size/2 - 1; i++) {
                int first = arr[i];
                int second = arr[size-i-1];

                result.set(temp-1, first);
                result.set(temp, second);
                temp -= 2;
            }
        }
        else {
            for(int i = 0;i <= size/2; i++) {
                int first = arr[i];
                int second = arr[size-i-1];

                //the last number is added
                if(i == size-i-1) {
                    result.set(0, first);
                }
                else {
                    result.set(temp-1, first);
                    result.set(temp, second);
                    temp -= 2;
                }
            }
        }

        for(int i = 0;i < size; i++) {
            System.out.print(result.get(i)+" ");
        }
    }
}