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 adjDif {

	static String sortDifs(int[] a) {
		Arrays.sort(a);
		int l = 0;
		int r = a.length - 1;
		int[] res = new int[a.length];

		for (int i = 0; l < r; i += 2) {
			res[i] = a[l++];
			res[i+1] = a[r--];
		}
		if (l == r) {
			res[a.length-1] = a[l];
		}

		StringBuilder sb = new StringBuilder();

		for (int i = a.length - 1; i >= 0; i--) {
			sb.append(res[i]);
			if (i != 0) {
				sb.append(' ');
			}
		}

		return sb.toString();
	}

	static void swap(int[] a, int i, int j) {
		a[i] ^= a[j];
		a[j] ^= a[i];
		a[i] ^= a[j];
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

		int t = sc.nextInt();
		StringBuilder sb = new StringBuilder();

		for (int i = 0; i < t; i++) {
			int n = sc.nextInt();
			int[] a = new int[n];
			for (int j = 0; j < n; j++) {
				a[j] = sc.nextInt();
			}
			sb.append(sortDifs(a));
			if (i != t - 1) {
				sb.append('\n');
			}
		}

		System.out.println(sb.toString());

		sc.close();
	}
}