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.util.*;

// 8663601
// VGoma
public class B {

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);

        int numCases = scan.nextInt();
        for (int c = 0; c < numCases; c++) {
            int length = scan.nextInt();
            ArrayList<Integer> nums = new ArrayList<>();

            for (int i = 0; i < length; i++) {
                nums.add(scan.nextInt());
            }

            Collections.sort(nums);
            ArrayList<Integer> newNums = new ArrayList<>();
            int index = (length - 1) / 2;

            if (length % 2 == 0) {
                while (index >= 0) {
                    newNums.add(nums.get(index));
                    newNums.add(nums.get(length - 1 - index--));
                }
            } else {
                newNums.add(nums.get(index--));
                while (index >= 0) {
                    newNums.add(nums.get(index));
                    newNums.add(nums.get(length - 1 - index--));
                }
            }

            for (int i = 0; i < newNums.size(); i++) {
                System.out.print(newNums.get(i) + " ");
            }
            System.out.println();
        }
    }

    public static int findMinDiff(ArrayList<Integer> nums, ArrayList<Integer> newNums) {
        int lastNum = newNums.get(newNums.size() - 1);
        int minDiff = Integer.MAX_VALUE;
        int minIndex = -1;
        for (int i = 0; i < nums.size(); i++) {
            int n = nums.get(i);
            if (Math.abs(n - lastNum) < minDiff) {
                minDiff = Math.abs(n - lastNum);
                minIndex = i;
            }
        }

        return minIndex;
    }
}