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.*;
public class Main {
  public static void main(String[] args) {
    Scanner console = new Scanner(System.in);
    int t = console.nextInt();
    // -2, 4, 5, 5, 6, 8
    // 5, 5, 4, 6, -2, 8
    // 10, 20 , 50 , 70, 80
    // 50 20 70 10 80
    // 20, 50, 10, 70
    // move the innermost pairs to the front all the way to the outer pairs
    while (t-- > 0) {
      int n = console.nextInt();
      int[] array = new int[n];
      for (int i = 0; i < n; i++) {
        array[i] = console.nextInt();
      }
      Arrays.sort(array);
      boolean cond = true;
      for (int i = 0; i < n/2; i++) {
          if (cond && n % 2 == 1) {
            System.out.print(array[(n/2)] + " ");
            cond = false;
        }
        System.out.print(array[(n/2)-i-1] + " " + array[(n+1)/2+i] + " ");
      }
    }
  }
}