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.lang.reflect.Array;
import java.util.*;
import java.io.*;
import java.math.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader infile=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer(infile.readLine());
        int cas=Integer.parseInt(st.nextToken());
        StringBuilder res=new StringBuilder();
        while(cas-->0){
            st=new StringTokenizer(infile.readLine());
            int n=Integer.parseInt(st.nextToken());
            st=new StringTokenizer(infile.readLine());
            int[] arr=new int[n],ans=new int[n];
            for(int i=0;i<n;i++){
                arr[i]=Integer.parseInt(st.nextToken());
            }
            Arrays.sort(arr);
            int ss=0,l=0,r=n-1;
            while(l<=r){
                if(ss%2==0)ans[ss++]=arr[l++];
                else ans[ss++]=arr[r--];
            }
            for(int i=n-1;i>=0;i--)res.append(ans[i]+" ");
            res.append('\n');
        }
        System.out.println(res);
    }
}