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 javafx.util.Pair;

import java.util.*;
import java.io.*;
//Captain on duty!



public class Main {

    static void compare(Main.pair a[] , int n) {

        Arrays.sort(a, new Comparator<Main.pair>() {
            @Override
            public int compare(Main.pair p1, Main.pair p2) {
                return p1.f - p2.f;
            }
        });
    }
    public static boolean checkPalindrome(String s)
    {
        // reverse the given String
        String reverse = new StringBuffer(s).reverse().toString();

        // check whether the string is palindrome or not
        if (s.equals(reverse))
            return true;

        else
            return false;
    }

    static class pair implements Comparable
    {
        int f;
        int s;
        pair(int fi, int se)
        {
            f=fi;
            s=se;
        }
        public int compareTo(Object o)//desc order
        {
            pair pr=(pair)o;
            if(s>pr.s)
                return -1;
            if(s==pr.s)
            {
                if(f>pr.f)
                    return 1;
                else
                    return -1;
            }
            else
                return 1;
        }
        public boolean equals(Object o)
        {
            pair ob=(pair)o;
            if(o!=null)
            {
                if((ob.f==this.f)&&(ob.s==this.s))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s).hashCode();
        }


    }

    public static boolean palin(int l, int r, char[] c) {
        while (l <= r) {
            if (c[l] != c[r]) return false;
            l++;
            r--;
        }
        return true;
    }


    public static long gcd(long a, long b)
    {
        if(b==0)
            return a;

        return gcd(b, a%b);
    }

    public static long hcf(long a, long b)
    {
        long t;
        while(b != 0)
        {
            t = b;
            b = a%b;
            a = t;
        }
        return a;
    }

    public static boolean isPrime(long n)
    {
        if (n <= 1)
            return false;

        // Check from 2 to n-1
        for (int i = 2; i <=Math.sqrt(n)+1; i++)
            if (n % i == 0)
                return false;

        return true;
    }

    public static String reverse(String str)
    {
        String str1="";
        for(int i=0;i<str.length();i++)
        {
            str1 = str1 + str.charAt(str.length()-i-1);
        }
        return str1;
    }

    public static long fact(long a)
    {
        if(a==1)
            return 1;
        else
            return a*fact(a-1);
    }
    public static boolean isPerfectSquare(long x)
    {

        // Find floating point value of
        // square root of x.
        long sr = (long) Math.sqrt(x);

        // If square root is an integer
        return ((sr - Math.floor(sr)) == 0);
    }



    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

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

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }


    }


    public static void main(String[] args) {
        FastReader s = new FastReader();

        long t=s.nextLong();
        while(t-->0)
        {
            int n=s.nextInt();
            int[] a=new int[n];
            for(int i=0;i<n;i++)
                a[i]=s.nextInt();
            Arrays.sort(a);
            int[] ans=new int[n];
            int c=0;

            for(int i=0;i<n/2;i++)
            {
                ans[c]=a[n-i-1];
                c++;
                ans[c]=a[i];
                c++;
            }
            int[] ans1=new int[n];
            if(n%2==1)
                ans[n-1]=a[n/2];
            for(int i=0;i<n;i++)
            {
                ans1[i]=ans[n-i-1];
                System.out.print(ans1[i]+" ");
            }
            System.out.println();


        }




    }

}