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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.InputMismatchException;

public class B {
	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		InputReader s = new InputReader(System.in);
		PrintWriter p = new PrintWriter(System.out);
		int t = s.nextInt();
		while (t-- > 0) {
			int n = s.nextInt();
			ArrayList<Long> list = new ArrayList<>();
			for (int i = 0; i < n; i++) {
				list.add(s.nextLong());
			}
			Collections.sort(list);
			long[] ans = new long[n];
			int i = 0, j = n - 1;
			int k = n - 1;
			while (i <= j) {
				if (i == j) {
					ans[k] = list.get(j);
					break;
				}
				ans[k] = list.get(j);
				k--;
				ans[k] = list.get(i);
				k--;
				j--;
				i++;
			}
			for (i = 0; i < n; i++) {
				p.print(ans[i] + " ");
			}
			p.println();
		}
		p.flush();
		p.close();
	}

	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static long LCM(long a, long b) {
		return (a * b) / GCD(a, b);
	}

	static class pair implements Comparable<pair> {
		Integer x, y;

		pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(pair o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);

			return result;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				return p.x - x == 0 && p.y - y == 0;
			}
			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}
	}

	static class InputReader {

		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}

	static class CodeX {
		public static void sort(long arr[]) {
			merge_sort(arr, 0, arr.length - 1);
		}

		private static void merge_sort(long A[], long start, long end) {
			if (start < end) {
				long mid = (start + end) / 2;
				merge_sort(A, start, mid);
				merge_sort(A, mid + 1, end);
				merge(A, start, mid, end);
			}

		}

		private static void merge(long A[], long start, long mid, long end) {
			long p = start, q = mid + 1;
			long Arr[] = new long[(int) (end - start + 1)];
			long k = 0;

			for (int i = (int) start; i <= end; i++) {
				if (p > mid)
					Arr[(int) k++] = A[(int) q++];

				else if (q > end)
					Arr[(int) k++] = A[(int) p++];

				else if (A[(int) p] < A[(int) q])
					Arr[(int) k++] = A[(int) p++];

				else
					Arr[(int) k++] = A[(int) q++];
			}
			for (int i = 0; i < k; i++) {
				A[(int) start++] = Arr[i];
			}

		}

	}

}