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.util.*;
import static java.lang.Math.*;

public class b implements Runnable
{
    boolean multiple = false; // for multiple test cases
    long MOD = 998244353;

    @SuppressWarnings("Duplicates")
    void solve() throws Exception
    {
       int t = sc.nextInt();
       while(t-->0) {
    	   int n = sc.nextInt();
    	   long [] arr = new long[n];
    	   for(int i = 0 ; i <n ;i++) {
    		   arr[i] = sc.nextLong();
    	   }
    	   
    	   Arrays.sort(arr);
    	   int r = arr.length-1;
    	   int l = 0 ; 
    	   long[] ans = new long[n];
    	   int ind = n -1;
    	   while(l <=r) {
    		   ans[ind] = arr[l] ;
    		   ind--;
    		   l++;
    		   if(l<=r)
    		   {
    			   ans[ind] = arr[r] ;
    			   ind--;
    			   r--;
    		   }
    	   }
    	  
    	   for(long val : ans) {
    		   out.print(val+" ");
    	   }
    	   out.println();
       }
       out.flush();
    }

  
    class Node implements Comparable<Node>
    {
        int k, pos, idx;
        Node(int K, int P, int I)
        {
            k = K;
            pos = P;
            idx = I;
        }

        @Override
        public int compareTo(Node o)
        {
            return Integer.compare(k, o.k);
        }
    }


    long powmod(long x, long y){
        if(y==0) return 1L;
        long t=powmod(x,y/2);
        if (y%2==0) return (t*t)%MOD;
        return (((x*t)%MOD)*t)%MOD;
    }
    long inv(long a, long b){return 1<a ? b - inv(b%a,a)*b/a : 1;}
    TreeMap<Integer, TreeSet<Integer>> buildGraph(int n, int m) throws Exception{TreeMap<Integer, TreeSet<Integer>> graph = new TreeMap<>();for (int i = 1; i <= n; i++) graph.put(i, new TreeSet<>());for (int i = 0; i < m; i++) { int u = sc.nextInt();int v = sc.nextInt();graph.get(u).add(v);graph.get(v).add(u); }return graph; }
    TreeMap<Integer, TreeSet<Integer>> buildDirGraph(int n, int m) throws Exception { TreeMap<Integer, TreeSet<Integer>> graph = new TreeMap<>();for (int i = 1; i <= n; i++) graph.put(i, new TreeSet<>());for (int i = 0; i < m; i++) graph.get(sc.nextInt()).add(sc.nextInt());return graph; }
    TreeMap<Integer, TreeSet<Integer>> revGraph(TreeMap<Integer, TreeSet<Integer>> graph) { TreeMap<Integer, TreeSet<Integer>> rev = new TreeMap<>();for (Integer u : graph.keySet()) rev.put(u, new TreeSet<>());for (Integer u : graph.keySet()) for (Integer v : graph.get(u)) rev.get(v).add(u);return rev; }
    TreeMap<Long, Integer> counts(long[] arr) { TreeMap<Long, Integer> counts = new TreeMap<>(); for (long a : arr) { if (!counts.containsKey(a)) counts.put(a, 0); counts.put(a, counts.get(a) + 1);} return counts; }
    String reverse(String s, int i, int j) /*[i, j] closed*/ { return (i > j) ? reverse(s, j, i) : s.substring(0, i) + (new StringBuilder(s.substring(i, j + 1))).reverse() + ((j + 1 <= s.length() - 1) ? s.substring(j + 1) : "");}

    @Override public void run() { try { in = new BufferedReader(new InputStreamReader(System.in));out = new PrintWriter(System.out);sc = new FastScanner(in);if (multiple) { int q = sc.nextInt();for (int i = 0; i < q; i++) solve(); } else solve(); } catch (Throwable uncaught) { b.uncaught = uncaught; } finally { out.close(); }} public static void main(String[] args) throws Throwable{ Thread thread = new Thread(null, new b(), "", (1 << 26));thread.start();thread.join();if (b.uncaught != null) {throw b.uncaught;} } static Throwable uncaught; BufferedReader in; FastScanner sc; PrintWriter out; } class FastScanner { BufferedReader in; StringTokenizer st; public FastScanner(BufferedReader in) {this.in = in;}public String nextToken() throws Exception { while (st == null || !st.hasMoreTokens()) { st = new StringTokenizer(in.readLine()); }return st.nextToken(); }public int nextInt() throws Exception { return Integer.parseInt(nextToken()); }public long nextLong() throws Exception { return Long.parseLong(nextToken()); }public double nextDouble() throws Exception { return Double.parseDouble(nextToken()); }
}