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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeSet;

import javax.swing.event.TreeExpansionEvent;

public class Contest {
	private static PrintWriter out = new PrintWriter(System.out);
	private static int n, m, k, tc, x;
	private static int[] a;
	private static int[][] grid;

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		tc = sc.nextInt();
		while (tc-- > 0) {
			n = sc.nextInt();
			a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = sc.nextInt();
			ruffleSort(a);
			ArrayList<Integer> res = new ArrayList<>();
			for (int i = 0; i < n / 2; i++) {
				
				
					res.add(a[i]);
					res.add(a[n - i - 1]);
				
			}
			if(n%2!=0)
				res.add(a[n/2]);
			for(int i = 0;i < n;i++) {
				if(i != 0)
					out.print(" ");
				out.print(res.get(n - i - 1));
			}
			out.println();
		}
		out.flush();
	}

	private static void sort(int[] a, int n) {
		ArrayList<Integer> b = new ArrayList<Integer>();
		for (int i = 0; i < n; i++)
			b.add(a[i]);
		Collections.sort(b);
		for (int i = 0; i < n; i++)
			a[i] = b.get(i);
	}

	static final Random random = new Random();

	static void ruffleSort(int[] a) {
		int n = a.length;// shuffle, then sort
		for (int i = 0; i < n; i++) {
			int oi = random.nextInt(n), temp = a[oi];
			a[oi] = a[i];
			a[i] = temp;
		}
		java.util.Arrays.sort(a);
	}

	private static class Scanner {
		public BufferedReader reader;
		public StringTokenizer st;

		public Scanner(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			st = null;
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					String line = reader.readLine();
					if (line == null)
						return null;
					st = new StringTokenizer(line);
				} catch (Exception e) {
					throw (new RuntimeException());
				}
			}
			return st.nextToken();
		}

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

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

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

}