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.*;

import static java.lang.Math.*;

public class Main {
    static void run() throws IOException {
        file("", "");
        int t = nextInt();
        while (t-- > 0)
            solution();
        end();
    }


    static void solution() throws IOException {
        int n = nextInt();
        List<Integer> arr = new ArrayList<>();
        for (int i = 0; i < n; i++)
            arr.add(nextInt());
        int l = 1;
        int r = n - 2;
        boolean right = true;
        int[] ans = new int[n];
        Collections.sort(arr);
        if (abs(arr.get(0) - arr.get(n - 2)) >= abs(arr.get(n - 1) - arr.get(1))) {
            ans[n - 1] = arr.get(n - 1);
            ans[n - 2] = arr.get(0);
            ans[n - 3] = arr.get(n - 2);
            r--;
            right = false;
        } else {
            ans[n - 1] = arr.get(0);
            ans[n - 2] = arr.get(n - 1);
            ans[n - 3] = arr.get(1);
            l++;
        }
        int point = n - 4;
        while (point >= 0) {
            if (right) {
                ans[point] = arr.get(r);
                r--;
            } else {
                ans[point] = arr.get(l);
                l++;
            }
            point--;
            right = !right;
        }
        for (int i = 0; i < n; i++) {
            out.print(ans[i] + " ");
        }
        out.println();
    }


    static mem create_mem() {
        mem y = new mem();

        return y;
    }

    static class mem {

    }

    static long pow(long a, long b) {
        long h = 1;
        while (b > 0) {
            if (b % 2 != 0) {
                h *= a;
                b--;
            }
            b /= 2;
            a *= a;
        }
        return h;
    }

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

    static long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    static void end() {
        out.flush();
        out.close();
    }

    static BufferedReader br;
    static PrintWriter out;

    static void file(String input, String output) {
        if (input.equals("")) {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            try {
                br = new BufferedReader(new FileReader(input));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            try {
                out = new PrintWriter(output);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
    }

    static StringTokenizer in = new StringTokenizer("");

    public static String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            String s = br.readLine();
            if (s == null) return null;
            in = new StringTokenizer(s);
        }
        return in.nextToken();
    }


    public static int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public static void main(String[] args) throws IOException {
        run();

    }

}