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 B{
	long rem = 998244353L;
	
	public void solve(int test, Scanner sc){
		int n = sc.nextInt();
		int[] a = new int[n];
		
		for(int i=0; i<n; i++){
			a[i] = sc.nextInt();
		}
		
		Arrays.sort(a);
		int[] res = new int[n];
		
		int end = n-1;
		int start = 0;
		boolean s = true;
		int index = n-1;
		while(end >= start){
			if(s){
				res[index--] = a[start++];
			}
			else{
				res[index--] = a[end--];
			}
			s = !s;
		}
		
		for(int i=0; i<(n-1); i++){
			System.out.print(res[i] + " ");
		}
		System.out.println(res[n-1]);
	}
	
	public B(){
		Scanner sc = new Scanner(System.in);
		int tests = sc.nextInt();
        
        for(int t=1; t<=tests; t++){
			solve(t, sc);
        }
	}
	
	public static void main(String[] args){
		new B();
	}
}