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 SortedDifferencess {

    static int T, N;
    static long[] vals;

    public static void main(String[] args) throws IOException
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        T = Integer.parseInt(st.nextToken());
        while (T > 0)
        {
            T--;
            st = new StringTokenizer(br.readLine());
            N = Integer.parseInt(st.nextToken());
            vals = new long[N];
            st = new StringTokenizer(br.readLine());
            for (int i = 0; i < N; i++)
                vals[i] = Long.parseLong(st.nextToken());
            Arrays.sort(vals);
            int index = N / 2;
            if (N % 2 == 0)
                index--;
            boolean upPrev = false;
            int mod = 1;
            int count = 0;
            while (count < N)
            {
                count++;
                System.out.print(vals[index] + " ");
                if (upPrev)
                {
                    index -= mod;
                    upPrev = false;
                    mod++;
                }
                else
                {
                    index += mod;
                    upPrev = true;
                    mod++;
                }
            }
            System.out.println();
        }
    }
}