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 Main {
	static final long M = 1000000007;
		static FastReader in = new FastReader();
		static PrintWriter out = new PrintWriter(System.out);
//		static Scanner in = new Scanner(System.in);
//        File file = new File("input.txt");
//        Scanner in = new Scanner(file);
//        PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
    public static void main(String[] args) {
    	
    	int t = in.nextInt();
    	while(t-- > 0) {
    		int n = in.nextInt();
        	ArrayList<Integer> ar = new ArrayList<>(), a = new ArrayList<>();
    		int[] arr = new int[n];
    		for(int i = 0; i<n; i++) arr[i] = in.nextInt();
    		Arrays.sort(arr);
    		for(int i = 0; i<n; i++) a.add(arr[i]);
    		while(a.size()>0) {
    			if(a.size()%2==0 && a.size()!=0) {
    				int mid = a.size()/2;
    				mid--;
    				ar.add(a.get(mid));
    				a.remove(mid);
    			}else {
    				int mid = a.size()/2;
    				ar.add(a.get(mid));
    				a.remove(mid);
    			}
    		}
    		for(int k: ar) out.print(k+" ");
    		out.println();    		
    	}
    	out.close();
    	
    	
    }
  
    
    private static int gcd(int a, int b) {
    	if(b==0) return a;
    	return gcd(b, a%b);
    }

	static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}