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 Main{
	static final int MAXN = 131072;
	static int[] a = new int[MAXN];
	static int[] ansl = new int[MAXN];
	public static void main( String[] args ){
		Scanner scanner = new Scanner(new BufferedInputStream(System.in));
		int t = scanner.nextInt();
		for( int ti = 1 ; ti <= t ; ++ti ){
			int n = scanner.nextInt();
			for( int i = 1 ; i <= n ; ++i ) a[i] = scanner.nextInt();
			Arrays.sort(a,1,n+1);
			int l = 1, r = n;
			boolean moveR = true;
			for( int i = n ; i >= 1 ; --i ){
				if(moveR){
					ansl[i] = a[r];
					--r;
				}else{
					ansl[i] = a[l];
					++l;
				}
				moveR ^= true;
			}
			for( int i = 1 ; i <= n ; ++i ){
				System.out.print(ansl[i]);
				System.out.print(' ');
			}
			System.out.println();
		}
	}
}