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 B {
	public static int primes(int i) {
		int[] primes = new int[] {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
		return primes[i];
	}
	public static void main(String[] args) throws IOException,CloneNotSupportedException{
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int q = sc.nextInt();
		
		while(q-->0) {
			PriorityQueue<Integer> p = new PriorityQueue<Integer>();
			int n = sc.nextInt();
			int[] arr =new int[n];
			for(int i=0;i<n;i++) {
				p.add(sc.nextInt());
			}
			for(int i=0;i<arr.length;i++)
				arr[i] = p.poll();
			int[] res = new int[n];
			int k = 0;
			for(int i=0,j = n-1;i<=j;i++,j--) {
				if(i!=j) {
				res[k++] = arr[j];
				res[k++] = arr[i];
				}else {
					res[k++] = arr[i];
				}
			}
			for(int i=n-1;i>=0;i--)
				pw.print(res[i] + " ");
			pw.println();
		}
		pw.flush();
		pw.close();
	}
}