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 SortedAdjacentDifferences {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static PrintWriter pw = new PrintWriter(System.out);
	
	public static void main(String[] args) throws IOException {
		int T = readInt();
		
		for (int t = 0; t < T; t ++) {
			int n = readInt();
			int[] a = new int[n];
			for (int i = 0; i < n; i ++) a[i] = readInt();
			Arrays.parallelSort(a);
			int low, high;
			if (n % 2 == 0) { low = n / 2 - 1; high = n / 2; }
			else { low = n / 2; high = n / 2 + 1; }
			
			pw.print(a[low] + " ");
			pw.print(a[high] + " ");
			low --; high ++;

			boolean flag = false;
			while (true) {
				if (!flag) { 
					if (low == -1) break;
					pw.print(a[low] + " ");
					low --;
					flag = true;
				} else {
					if (high == n) break;
					pw.print(a[high] + " ");
					high ++;
					flag = false;
				}
			}
			pw.println();
		}
		pw.close();
	}

	static String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) 
			st = new StringTokenizer(br.readLine().trim());
		return st.nextToken();
	}
	static long readLong() throws IOException {
		return Long.parseLong(next());
	}
	static int readInt() throws IOException {
		return Integer.parseInt(next());
	}
	static double readDouble() throws IOException {
		return Double.parseDouble(next());
	}
	static char readCharacter() throws IOException {
		return next().charAt(0);
	}
	static String readLine() throws IOException {
		return br.readLine().trim();
	}
}