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.*;
import java.util.*;

public class Main {
    private static void solver(InputReader sc, PrintWriter out) throws Exception {
        int test = sc.nextInt();
        for (int ii = 0; ii < test; ii++) {
            int  n = sc.nextInt();
            Long arr[] = new Long[n];
            for(int i=0; i<n; i++) arr[i] = sc.nextLong();
            Arrays.sort(arr);
            List<Long> al = new ArrayList<>();
            for(int i=0,j=n-1; i<=j; i++,j--){
                if(i==j)
                    al.add(arr[i]);
                else {
                    al.add(arr[i]);
                    al.add(arr[j]);
                }
            }
            int size = al.size();
            for(int i=size-1;i>=0;i--){
                out.print(al.get(i)+" ");
            }
            out.println();

        }
    }
    private static boolean isprime(int x){
        if(x==2)
            return true;
        int sqs = (int)Math.sqrt(x);
        for(int i=2; i<=sqs; i++){
            if(x%i==0)
                return false;
        }
        return true;
    }

    private static int gcd (int a, int b) {
        if (b == 0)
            return a;
        else
            return gcd (b, a % b);
    }
    private static int gcd (int a, int b, int c) {
      int gcd1 = gcd(a,b);
      return gcd(gcd1,c);
    }

    private static long helper(long x){
        long ans = (x * (x-1))/2;
        return ans;
    }
    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solver(in,out);
        out.close();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

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

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

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int[] readIntArray(int n){
            int arr[] = new int[n];
            for(int i=0;i<n;i++) arr[i] = nextInt();
            return arr;
        }
    }
}
class Pair {
    int x;
   char y;

    Pair(int x, char y) {
        this.x = x;
        this.y = y;
    }

    @Override
    public boolean equals(Object o) {
        Pair pair = (Pair) o;
        return this.x < pair.x && this.y == pair.y;
    }

    @Override
    public int hashCode() {
        return Objects.hash(x, y);
    }
}
class Twos{
    int x;
    int y;
    Twos(int x, int y){
        this.x = x;
        this.y = y;
    }
}