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 Solution{
	public static void main (String[] args) throws IOException{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out=new PrintWriter(System.out);
		String[] temp=br.readLine().trim().split(" ");
		
		int numTestCases=Integer.parseInt(temp[0]);
		while(numTestCases-->0) {
			temp=br.readLine().trim().split(" ");
			int n=Integer.parseInt(temp[0]);
			
			ArrayList<Integer> arr=new ArrayList<Integer>();
			temp=br.readLine().trim().split(" ");
			for(int i=0;i<n;i++) {
				arr.add(Integer.parseInt(temp[i]));
			}
			ArrayList<Integer> ans=modifyArray(arr);
			for(int i=0;i<n;i++) {
				out.print(ans.get(i)+" ");
			}
			out.println();
		}
		
		out.flush();
		out.close();
	}
	public static ArrayList<Integer> modifyArray(ArrayList<Integer> arr)
	{
		ArrayList<Integer> ans=new ArrayList<Integer>();
		int n=arr.size();
		Collections.sort(arr);
		int mid=arr.size()/2;
		if(n%2==0) {
			mid--;
		}
		int start=mid;
		int end=mid+1;
		while(start>=0 && end<n) {
			ans.add(arr.get(start));
			ans.add(arr.get(end));
			start--;
			end++;
		}
		if(n%2!=0) {
			ans.add(arr.get(start));
		}
		return ans;
	}
}