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 {
	Reader source;
	BufferedReader br;
	StringTokenizer in;
	PrintWriter out;

	public String nextToken() throws Exception {
		while (in == null || !in.hasMoreTokens()) {
			in = new StringTokenizer(br.readLine());
		}
		return in.nextToken();
	}
	public int nextInt() throws Exception {
		return Integer.parseInt(nextToken());
	}
	public long nextLong() throws Exception {
		return Long.parseLong(nextToken());
	}
	public double nextDouble() throws Exception {
		return Double.parseDouble(nextToken());
	}

	public void solve() throws Exception {
		int t = nextInt();
		for (int i = 0; i < t; i++) {
			int n = nextInt();
			Integer a[] = new Integer [n];
			for (int j = 0; j < n; j++)
				a[j] = nextInt();
			Arrays.sort(a);
			ArrayList<Integer> v = new ArrayList<Integer>();
			int l = 0, r = n - 1;
			while (l + 1 < r) {
				v.add(a[l]);
				v.add(a[r]);
				l++;
				r--;
			}
			v.add(a[l]);
			if (l < r) v.add(a[r]);	
			Collections.reverse(v);
			for (int j : v) out.print(j + " ");
			out.println();
		}
	}

	public void run() throws Exception {
		source = OJ ? new InputStreamReader(System.in) : new FileReader("B.in");
		br = new BufferedReader(source);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}
	public static void main(String[] args) throws Exception {
		new B().run();
	}
	private boolean OJ = System.getProperty("ONLINE_JUDGE") != null;
}