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.IOException;
import java.io.InputStreamReader;
import java.io.Reader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class TaskB {
    public static String doMain(Reader reader) throws IOException {
        MyReader in = new MyReader(reader);
        int tests = in.nextInt();
        StringBuilder sb = new StringBuilder();
        for (int t = 0; t < tests; ++t) {
            int n = in.nextInt();
            int[] nums = in.readIntArray(n);
            Arrays.sort(nums);
            int[] ans = new int[n];
            for (int i = 0; i < n / 2; i++) {
                ans[2 * i] = nums[i];
                ans[2 * i + 1] = nums[n - i - 1];
            }
            if (n % 2 == 1) {
                ans[n - 1] = nums[n / 2];
            }
            int[] ans2 = new int[n];
            for (int i = 0; i < n; i++) {
                ans2[i] = ans[n-i-1];
            }
            for (int i = 0; i < n; i++) {
                sb.append(ans2[i]).append(" ");
            }
            sb.append("\n");
        }
        return sb.toString();
    }

    public static void main(String[] args) throws IOException {
        String result = doMain(new InputStreamReader(System.in));
        System.out.println(result);
    }

    static class MyReader {
        BufferedReader bf;

        StringTokenizer st;

        String last;

        MyReader(Reader reader) throws IOException {
            bf = new BufferedReader(reader);
            readNextLine();
        }

        String nextToken() throws IOException {
            while (!st.hasMoreTokens()) {
                readNextLine();
            }
            return st.nextToken();
        }

        void readNextLine() throws IOException {
            last = bf.readLine();
            if (last == null) last = "";
            st = new StringTokenizer(last);
        }

        String nextLine() throws IOException {
            String s = last;
            readNextLine();
            return s;
        }

        long nextLong() throws IOException {
            return Long.parseLong(nextToken());
        }

        int nextInt() throws IOException {
            return Integer.parseInt(nextToken());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(nextToken());
        }

        int[] readIntArray(int n) throws IOException {
            int[] answer = new int[n];
            for (int i = 0; i < n; ++i) {
                answer[i] = nextInt();
            }
            return answer;
        }

        long[] readLongArray(int n) throws IOException {
            long[] answer = new long[n];
            for (int i = 0; i < n; ++i) {
                answer[i] = nextLong();
            }
            return answer;
        }

        double[] readDoubleArray(int n) throws IOException {
            double[] answer = new double[n];
            for (int i = 0; i < n; ++i) {
                answer[i] = nextDouble();
            }
            return answer;
        }
    }
}