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.*;
import java.io.*;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		
		int cases = in.nextInt();
		for (int i=0; i<cases; i++) {
			int size = in.nextInt();
			long[] a = new long[size];
			
			for (int j=0; j<size; j++) {
				a[j] = in.nextInt();
				
			}
			
			//start problem
			//start problem
			Arrays.sort(a);
			long[] answer = thing(a);
			
			for (int k=0; k<size; k++) {
				if (k==size-1) System.out.print(answer[k]);
				else System.out.print(answer[k] + " ");
			}
			System.out.print("\n");
		}
	}
	
	public static long[] thing(long[] array) {
		long[] answer = new long[array.length];
		int middle = (array.length-1)/2;
		int index=0;
		
		answer[0] = array[middle];
		for (int i=1; i<=middle; i++) {
			answer[2*i-1] = array[middle+i];
			answer[2*i] = array[middle-i];
		}
		
		if (array.length%2==0) {
			answer[array.length-1] = array[array.length-1]; 
		}

		return answer;
	}

}