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 {

	public static void solve() throws IOException {
		int n= Integer.parseInt(read.readLine());
		String[] s=read.readLine().split(" ");
		int arr[]=new int[n];
		for (int i=0;i<n;i++) {
			arr[i]=Integer.parseInt(s[i]);
		}
		Arrays.sort(arr);
		int left=n/2-1;
		int right=n/2;
		for(int i=0;i<n/2;i++){
			System.out.print(arr[right]+" "+arr[left]+" ");
			right++;
			left--;

		}
		if(n%2!=0){
			System.out.print(arr[n-1]);
		}
		System.out.println();
		// System.out.println(Arrays.toString(arr));

	}

	static final Scanner scan=new Scanner(System.in);
	static final BufferedReader read=new BufferedReader(new InputStreamReader(System.in));
	public static void main(String[] args) throws IOException {
		int t=Integer.parseInt(read.readLine());
		for (int i = 0; i < t; i++) {
			solve();
		}
	}
}