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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;

/**
 * Template by Arpan Mishra (arpan_)
 */
public class ProblemB {
    public static void main(String[] args) {
        final InputStream inputStream = System.in;
        final OutputStream outputStream = System.out;
        final InputReader in = new InputReader(inputStream);
        final PrintWriter out = new PrintWriter(outputStream);
        final Solver solver = new Solver();

        solver.solve(in, out);

        out.close();
    }

    static class Solver {
        public void solve(final InputReader in, final PrintWriter out) {
            int t = in.nextInt();
            while(t-->0) {
                execute(in, out);
            }
        }

        // Contains all core logic for each test case
        public void execute(final InputReader in, final PrintWriter out) {
            int n = in.nextInt();
            long a[] = new long[n];
            int i;
            for(i=0;i<n;i++) {
                a[i] = in.nextInt();
            }

            Arrays.sort(a);

            long result[] = new long[n];
            int index = n-1;
            int low = 0;
            int high = n-1;
            for(i=0;i<n;i++) {
                long ele;
                if(i%2==0) {
                    ele = a[high--];
                } else {
                    ele = a[low++];
                }
                result[index--] = ele;
            }

            for(i=0;i<n;i++) {
                out.print(result[i]);
                if(i!=n-1) {
                    out.print(" ");
                }
            }
            out.println();

        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public Double nextDouble() {
            return Double.parseDouble(next());
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
    }
}