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 codeforces;

import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

public class SortedAdjacentDifferences {

    public class Custom {
        int x;
        int y;
        int diff;

        public Custom(int x, int y, int diff) {
            this.x = x;
            this.y = y;
            this.diff = diff;
        }
    }
    public void print(int arr[]) {

        Arrays.sort(arr);
        int ans[] = new int[arr.length];
        if(arr.length%2 == 0) {
            int k = arr.length - 1;
            for(int i = 0; i < arr.length/2; i++) {
                int x = arr[i];
                int y = arr[arr.length - i - 1];
                ans[k--] = y;
                ans[k--] = x;

            }
        } else {
            int k = arr.length - 1;
            ans[0] = arr[arr.length/2];
            for(int i = 0; i < arr.length/2; i++) {
                int x = arr[i];
                int y = arr[arr.length - i - 1];
                ans[k--] = y;
                ans[k--] = x;

            }
        }
        for(int i = 0; i < arr.length; i++) {
            System.out.print( ans[i]);
            if(i!=arr.length - 1) {
                System.out.print(" ");
            }
        }
        System.out.println();
    }
    public static void main(String []args) {


        SortedAdjacentDifferences l = new SortedAdjacentDifferences();
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        while ( n > 0) {
            int p =sc.nextInt();
            int arr[] = new int[p];
            int i = 0;
            while (i < p) {
                arr[i++] = sc.nextInt();
            }
            l.print(arr);
            n--;
        }
    }
}