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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Rearrange {
    public static void main(String[] args) throws Exception {
        new Rearrange().read();
    }

    public void read() throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int T = Integer.valueOf(br.readLine());

        for (int t = 1; t <= T; t++) {
            testCase(t, br);
        }
        br.close();
    }

    public void testCase(int testNumber, BufferedReader br) throws Exception{

        int N=Integer.valueOf(br.readLine());
        int[] arr=new int[N];
        String temp[]=br.readLine().split(" ");
        for(int i=0;i<N;i++)
            arr[i]=Integer.valueOf(temp[i]);

        Arrays.sort(arr);
        int m=arr.length/2;
        if(arr.length%2==0) m--;
        int elemCount=0;
        StringBuilder sb=new StringBuilder();
        int i=1;
        sb.append(arr[m]);
        sb.append(" ");
        sb.append(arr[m+1]);
        while(elemCount<arr.length){
            if(m-i>-1) {
                sb.append(" ");
                sb.append(arr[m - i]);
            }

            if(m+i+1<arr.length) {
                sb.append(" ");
                sb.append(arr[m + 1 + i]);
            }
            elemCount+=2;
            i++;
        }

        System.out.println(sb.toString());


    }


    public void print() {
        System.out.format("Case #%d: %d %d %d\n");
    }
}