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.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
	public static void shuffle(int[] A) {
		for (int i = 0; i < A.length; i++) {
			int idx = (int) (i * Math.random());
			int tmp = A[i];
			A[i] = A[idx];
			A[idx] = tmp;
		}
	}

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder out = new StringBuilder();

		int T = Integer.parseInt(br.readLine());
		while (T-- > 0) {
			int N = Integer.parseInt(br.readLine());
			int[] A = new int[N];
			StringTokenizer st = new StringTokenizer(br.readLine());
			for (int i = 0; i < N; i++) {
				A[i] = Integer.parseInt(st.nextToken());
			}
			shuffle(A);
			Arrays.sort(A);
			if (N % 2 == 1) {
				out.append(A[N / 2]).append(' ');
				for (int i = 1; i <= N / 2; i++) {
					out.append(A[N / 2 - i]).append(' ');
					out.append(A[N / 2 + i]).append(' ');
				}
			} else {
				for (int i = 1; i <= N / 2; i++) {
					out.append(A[N / 2 - i]).append(' ');
					out.append(A[N / 2 + i - 1]).append(' ');
				}
			}
			out.setCharAt(out.length() - 1, '\n');
		}

		System.out.print(out);

		br.close();
	}
}