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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.*;

public class adjdiff {
    public static void main(String[] args) throws Exception {
        InputStreamReader r = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(r);
        PrintWriter pw = new PrintWriter(new BufferedWriter(
            new OutputStreamWriter(System.out)));

        int numCases = Integer.parseInt(br.readLine());

        for (int i = 0; i < numCases; i++) {
        	int length = Integer.parseInt(br.readLine());
        	String[] input = br.readLine().split(" ");
        	Arrays.sort(input, new InpComp());

        	int counter = 1;
        	int sign = -1;
        	int idx = length / 2;
        	while (counter <= length) {
        		pw.print(input[idx] + " ");
        		idx += sign * counter;
        		counter++;
        		sign *= -1;
        	}
        	pw.println();
        }        
    pw.close();
    }
}

class InpComp implements Comparator<String> {
	@Override
	public int compare(String s, String o) {
		int sint = Integer.parseInt(s);
		int oint = Integer.parseInt(o);
		return sint - oint;
	}
}