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.cf;

import java.util.Arrays;
import java.util.Scanner;

/**
 * Created on 2020/4/13
 *
 * @author WuYi
 */
public class SortedAdjacent {

    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        int n = scanner.nextInt();
        for (int i = 0; i < n; i++) {
            int len = scanner.nextInt();
            int data[]=new int[len];
            for (int j = 0; j < len; j++) {
                data[j]=scanner.nextInt();
            }
            int[] cal = cal(data);
            for (int j = 0; j < cal.length-1; j++) {
                System.out.print(cal[j]+" ");
            }
            System.out.println(cal[cal.length-1]);
        }
    }

    public static int[] cal(int[] data) {
        int len = data.length;
        if (len <= 1) {
            return data;
        }
        int[] res = new int[data.length];
        Arrays.sort(data);

        int count = 0;
        for (int i = len - 1; i >= 0; i = i - 2, count++) {
            res[i] = data[count];
        }


        count = len - 1;
        for (int i = len - 2; i >= 0; i = i - 2, count--) {
            res[i] = data[count];
        }
        return res;

    }

}