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.Scanner;
import java.util.Arrays;

public class secProg {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int T = sc.nextInt();
		StringBuilder finalAns = new StringBuilder();
		while (--T >= 0) {
			int n = sc.nextInt(), a[] = new int[n], finalA[] = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = sc.nextInt();
			Arrays.sort(a);
			int count = n - 1;
			for (int i = 0; i < n / 2; i++) {
				finalA[count--] = a[i];
				if (count >= 0)
					finalA[count--] = a[n - 1 - i];
			}
			if (n % 2 == 1)
				finalA[0] = a[(n / 2)];
			for (int i = 0; i < n; i++)
				finalAns.append(finalA[i] + " ");
			finalAns.append("\n");
		}
		sc.close();
		System.out.print(finalAns);
	}
}