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.*;
import java.math.*;
public class HelloWorld {

     public static void main(String []args){
        Scanner inp=new Scanner(System.in);
        int t=inp.nextInt();
        for(int q=0;q<t;q++){
            int n=inp.nextInt();
            List<Long> a=new ArrayList<Long>();
            for(int i=0;i<n;i++){
                long no=inp.nextLong();
                a.add(no);
            }
            // Collections.sort(a,new MySalaryComp());
            Collections.sort(a);
            Long[] answer = new Long[n];
            int j=0;int i=n-1;
            int pos=i;
            while(pos-1>=0){
                answer[pos]=a.get(i);
                answer[pos-1]=a.get(j);
                i--;
                j++;
                pos--;
                pos--;
            }
            if(n%2==1)
                answer[0]=a.get(i);
            for(i=0;i<n;i++){
                System.out.print(answer[i]+" ");
            }
            System.out.println();
            // System.out.println(a);
        }
     }
}