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.*;

/**
 * User :- sudhakar
 * Date :- 01/06/20
 * Time :- 7:41 PM
 */

public class SortedAdjacentDifferences {
    private static final Reader r = new Reader();
    static final int MOD = 1000000007;
    static final int MAX_VALUE = Integer.MAX_VALUE;
    static final int MIN_VALUE = Integer.MIN_VALUE;

    /*Inner class for fast input*/
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public String nextString() throws IOException {
            byte c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            StringBuilder builder = new StringBuilder();
            builder.append((char) c);
            c = read();
            while (!Character.isWhitespace(c)) {
                builder.append((char) c);
                c = read();
            }
            return builder.toString();
        }

        public char nextChar() throws IOException {
            byte c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            return (char) c;
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        public int[] nextIntArray(Reader r, int size) throws IOException {
            int[] arr = new int[size + 1];
            for (int i = 1; i <= size; i++)
                arr[i] = r.nextInt();
            return arr;
        }

        public long[] nextLongArray(Reader r, int size) throws IOException {
            long[] arr = new long[size + 1];
            for (int i = 1; i <= size; i++)
                arr[i] = r.nextLong();
            return arr;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    private static int ni() throws IOException {
        return r.nextInt();
    }

    private static long nl() throws IOException {
        return r.nextLong();
    }

    private static char nc() throws IOException {
        return r.nextChar();
    }

    private static double nd() throws IOException {
        return r.nextDouble();
    }

    private static String ns() throws IOException {
        return r.nextString();
    }

    private static int[] nextIntArr(int size) throws IOException {
        return r.nextIntArray(r, size);
    }

    private static long[] nextLongArr(int size) throws IOException {
        return r.nextLongArray(r, size);
    }

    private static double min(double a, double b) {
        return Math.min(a, b);
    }

    private static double max(double a, double b) {
        return Math.max(a, b);
    }


    // CODE STARTS HERE
    public static void main(String[] args) throws IOException {
        int T = ni();


        while (T-- > 0) {
            int n = ni();
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            Arrays.sort(a);
            int l = 0, r = 0;
            if ((n - 1) % 2 == 0) {
                l = r = (n - 1) / 2;
            } else {
                l = (n - 1) / 2;
                r = l + 1;
            }
            while (l >= 0 && r <= n - 1) {
                if (l == r)
                    System.out.print(a[l] + " ");
                else
                    System.out.print(a[l] + " " + a[r] + " ");
                l--;
                r++;
            }
            System.out.println();
        }
    }
}