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.Scanner;

public class TP {
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0) 
		{
			int n=sc.nextInt();
			int a[]=new int[n];
			for(int i=0;i<n;i++)
			{
				a[i]=sc.nextInt();
			}
			Arrays.sort(a);
			int l=0,r=a.length-1,i=0;
			int b[]=new int[n];
			while(l<=r)
			{
				b[i]=a[l];
				i++;
				if(l!=r)
				{
				b[i]=a[r];
				i++;
				}
//				if(l==r)
//				{
//					System.out.print(a[l]+" ");
//				}
//				else
//					System.out.print(a[l]+" "+a[r]+" ");
				l++;
				r--;
			}
			for(i=n-1;i>=0;i--)
			{
				System.out.print(b[i]+" ");
			}
			System.out.println();
		}
		sc.close();
	}
}