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.*;
import java.text.*;
import java.util.*;
import java.math.*;
public class B {
  public static void main(String[] args) throws Exception {
    new B().run();
  }
  public void run() throws Exception {
    FastScanner f = new FastScanner();
    PrintWriter out = new PrintWriter(System.out);
    int t = f.nextInt();
    while(t-- > 0){
      int n = f.nextInt();
      int [] arr = new int [n];
      for(int i = 0; i < n; i++){
        arr[i] = f.nextInt();
      }
      Arrays.sort(arr);
      int start = 0;
      int change = 1;
      int flip = 1;
      if(n%2 == 0){
        start = n/2 -1;
      }
      else{ 
        start = n/2;
        flip = -1;
      }
      for(int i = 0; i < n-1; i++){
        out.print(arr[start] + " ");
        start += change *flip;
        change++;
        flip = -flip;
      }
      out.print(arr[arr.length-1]);
//      if(n%2 == 0){
//        out.print(arr[arr.length-1]);
//      }
//      else{
//        out.print(arr[0]);
//      }
      out.println();
    }
    out.flush();
  }
  static class FastScanner {
    public BufferedReader reader;
        public StringTokenizer tokenizer;
        public FastScanner() {
          reader = new BufferedReader(new InputStreamReader(System.in), 32768);
          tokenizer = null;
        }
        public String next() {
          while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                  tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                  throw new RuntimeException(e);
                }
          }
          return tokenizer.nextToken();
        }
        public int nextInt() {
          return Integer.parseInt(next());
        }
        public long nextLong() {
          return Long.parseLong(next());
        }
        public double nextDouble() {
          return Double.parseDouble(next());
        }
        public String nextLine() {
          try {
            return reader.readLine();
          } catch(IOException e) {
            throw new RuntimeException(e);
          }
        }
  }
}