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.IOException;
    import java.io.InputStreamReader;
    import java.util.StringTokenizer;
    import java.io.PrintWriter;
    import java.util.ArrayList;
    import java.util.List;
    import java.util.HashMap;
    import java.util.TreeMap;
    import java.util.Map;
    import java.util.Arrays;
    import java.util.Set;
    import java.util.HashSet;
    import java.util.Iterator;
    import java.util.Collections;
    import java.util.LinkedList;
    import java.util.Stack;
    
    /*
     *
     *  @author Riddle
     *
     */

    public final class Sort
    {
        final static long MOD = (long)1e9+7;

        static class Pair
        {
            int first;
            int second;
            public Pair(int first, int second)
            {
                this.first = first;
                this.second = second;
            }

            @Override
            public boolean equals(Object obj)
            {
                Pair p = (Pair)obj;
                return p.first==first && p.second==second;
            }
        }
        
        static class FastReader
        {
            BufferedReader br;
            StringTokenizer st;
     
            public FastReader()
            {
                br = new BufferedReader(new
                         InputStreamReader(System.in));
            }
     
            String next()
            {
                while (st == null || !st.hasMoreElements())
                {
                    try
                    {
                        st = new StringTokenizer(br.readLine());
                    }
                    catch (IOException  e)
                    {
                        e.printStackTrace();
                    }
                }
                return st.nextToken();
            }
     
            int nextInt()
            {
                return Integer.parseInt(next());
            }
     
            long nextLong()
            {
                return Long.parseLong(next());
            }
     
            double nextDouble()
            {
                return Double.parseDouble(next());
            }
     
            String nextLine()
            {
                String str = "";
                try
                {
                    str = br.readLine();
                }
                catch (IOException e)
                { 
                    e.printStackTrace();
                }
                return str;
            }

            int[] readArray(int arr[], int n)
            {
                for(int i=0;i<n;i++)
                {
                    arr[i] = nextInt();
                }

                return arr;
            }   
        }

        public static void main(String args[])
        {
            FastReader reader = new FastReader();
            PrintWriter out = new PrintWriter(System.out);
            int test = reader.nextInt();
            for(int t =0;t<test;t++)
            {
                int n = reader.nextInt();
                long arr[] = new long[n];
                for(int i=0;i<n;i++)
                {
                    arr[i] = reader.nextLong();
                }

                Arrays.sort(arr);
                int front = 0;
                int end = n-1;
                long result[] = new long[n];
                int i = n-1;
                while(front<end)
                {
                    result[i] = arr[end];
                    i--;
                    result[i] = arr[front];
                    front++;
                    end--;
                    i--;
                }

                if(front==end)
                {
                    result[i] = arr[end];
                }
                for(long s : result)
                {
                    out.print(s+" ");
                }
                out.println();
            }
            out.flush();        
            out.close();
        }

    }