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.Arrays;
import java.util.PriorityQueue;
import java.util.Scanner;
 
 
public class Solution  {		
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = Integer.parseInt(scan.nextLine());
		while(n > 0) {
			int size = Integer.parseInt(scan.nextLine());
			int[] arr = new int[size];
			String[] arrS = scan.nextLine().split(" ");
			for(int i=0;i<size;i++) {
				arr[i] = Integer.parseInt(arrS[i]);
			}
			Arrays.sort(arr);
			int i,j;
			if( size%2 == 0) {
				i = size/2 -1;
				j = size/2;
			}else {
				i = size/2;
				j = size/2+1;
			}
			while(i >=0 && j <size) {
				System.out.print(arr[i] + " "+ arr[j] + " ");
				i--;
				j++;
			}
			if(size%2 == 1) {
				System.out.print(arr[i]+ " ");
			}
			n--;
		}
		scan.close();
	}
}