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 adjacent {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int test = sc.nextInt();
		for(int i = 0; i < test; i++)  {
			int number = sc.nextInt();
			int[] numbers = new int[number];
			for(int j = 0; j < number; j++)  {
				numbers[j] = sc.nextInt();
			}
			Arrays.sort(numbers);
			if(number%2 == 0)  {
				int small = number/2-1;
				int great = number/2;
				while(small >=0 && great < number)  {
					System.out.print(numbers[small]+" "+numbers[great]+" ");
					small--;
					great++;
				}
			}
			else  {
				int small = number/2-1;
				int great = number/2+1;
				System.out.print(numbers[number/2]+" ");
				while(small >= 0 && great < number)  {
					System.out.print(numbers[small]+" "+numbers[great]+" ");
					small--;
					great++;
				}
			}
			System.out.println();
		}
		sc.close();
		

	}

}