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:
// package com.company;
import javax.swing.*;
import javax.swing.text.html.HTMLDocument;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.lang.*;
/**
 * @author_jigar_nainuji
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Palindrome solver = new Palindrome();
        int t = in.nextInt();
//        int t=1;
        for(int i=0;i<t;i++) {
            solver.solve(i, in, out);
        }
        out.close();
    }

    static class Palindrome {
        static int mod = 1000000007;
        static long dp[] = new long[10000];

        void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int a[] = new int[n];
            for(int i=0;i<n;i++)
                a[i]=in.nextInt();
            Arrays.sort(a);
            if(n%2==0)
            {
                int i,j;
                for(i=n/2-1,j=n/2;i>=0 && j<n;i--,j++)
                {
                    System.out.print(a[j]+" "+a[i]+" ");
                }
            }
            else
            {
                int i,j;
                if(Math.abs(a[n/2]-a[n/2-1])>Math.abs(-a[n/2]+a[n/2+1])) {
                    System.out.print(a[n / 2] + " " + a[n / 2 - 1] + " " + a[n / 2 + 1] + " ");
                    for(i=n/2-2,j=n/2+2;i>=0 && j<n;i--,j++)
                    {
                        System.out.print(a[i]+" "+a[j]+" ");
                    }
                }
                else {
                    System.out.print(a[n / 2] + " " + a[n / 2 + 1] + " " + a[n / 2 - 1] + " ");
                    for (i = n / 2 - 2, j = n / 2 + 2; i >= 0 && j < n; i--, j++) {
                        System.out.print(a[j] + " " + a[i] + " ");
                    }
                }

            }
            System.out.println();




    }


    }
    static class v{
        int first;
        int second;
    }
    static class pair {
        int r;
        int idx;
        pair(int r,int idx)
        {
            this.r = r;
            this.idx=idx;
        }
    }
    static class Maths{
        static int gcd(int a, int b) {
            if (a == 0)
                return b;
            return gcd(b % a, a);
        }

        public  static int lcm(int a, int b)
        {
            return (a*b)/gcd(a, b);
        }

        public static long factorial(int n){
            long fact = 1;
            for(int i=1;i<=n;i++){
                fact *= i;
            }
            return fact;
        }
    }


    static class Binary {
        public static long numberOfBits(long n){
            long count=0;
            while(n>0){
                count++;
                n >>=1;
            }
            return count;
        }

        public static long numberOfSetBits(long n){
            long count = 0;
            int p = 1;
            while (n>0){
                if((n&p) == 1){
                    count++;
                }
                n >>= 1;
            }
            return count;
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

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

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

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

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