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.math.*;
public class SortedDifferences
{
	public static void main(String[] args)
		{
			Scanner sc = new Scanner(System.in);
			int runs = sc.nextInt();
			while(runs-->0)
			{
				int size = sc.nextInt();
				long[] arr = new long[size];
				for(int i = 0;i<size;i++)
				{
					arr[i] = sc.nextLong();
				}
				Arrays.sort(arr);
				int p1 = 0;
				int p2 = size-1;
				if(size%2==0)
				{
					p1 = size/2 - 1;
					p2 = p1 + 1;
				}
				else
					p1 = p2 = size/2;
					
				while(true)
				{
					if(p1<0||p2>=size)
						break;
					if(p1==p2)
					{
						System.out.print(arr[p1]+" ");
					}
					else
						System.out.print(arr[p1]+" "+arr[p2]+" ");
					p1--;
					p2++;
					
				}
				System.out.println();
			}
		}
		
}