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 PYTHON3):

Solution:
def main():
	for _ in range(int(input())):
		n = int(input())
		a = sorted(list(map(int, input().split())))
		first, last = 0, n - 1
		result = list()
		while first < last:
			result += [a[last]]
			result += [a[first]]
			first += 1
			last -= 1
		if first == last:
			result += [a[first]]
		print(*result[::-1])
		"""
		less = [i for i in a if i < 0]
		greater = [i for i in a if i >= 0]
		new_array = greater[:2]
		greater = greater[2:] + less
		num = abs(max(greater)) + abs(min(greater))
		for element in range(len(greater)):
			d = abs(new_array[-1] - new_array[-2])
			last = new_array[-1]
			best = max(greater)
			for i in greater:
				# print(abs(last - i), abs(best - last))
				if d <= abs(last - i) <= abs(best - last):
					best = i
			greater.remove(best)
			new_array += [best]
		print(*new_array)
		"""


if __name__ == '__main__':
	main()