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:
t = int(input())


while t != 0:

	n = int(input()) 
	arr = [int(x) for x in input().split()] 

	arr.sort()

	negative = []
	positive = []

	for val in arr:

		if val < 0:
			negative.append(val)
		else:
			positive.append(val)

	# negative.reverse() 
	positive.reverse() 

	# print(negative)
	# print(positive)

	output = []
	len_posi = len(positive)
	len_nega = len(negative)
	max_len = max( len_nega,len_posi)

	index_nag = 0
	index_posi = 0
	total_cnt = 0

	while total_cnt <= n:
		# print(index_posi)
		# print(index_nag)
		if index_posi < len_posi and index_nag < len_nega:
			output.append(positive[index_posi])
			output.append(negative[index_nag])
			index_nag+=1
			index_posi+=1
			total_cnt+=2
		elif index_posi < len_posi:
			output.append(positive[index_posi])
			total_cnt+=1
			index_posi+=1
			# print(len_posi)
			# print(index_posi)
			if index_posi <= len_posi-1:
				
				output.append(positive[len_posi-1])
				len_posi-=1
				total_cnt+=1
		elif index_nag < len_nega:
			output.append(negative[len_nega-1])
			len_nega-=1
			total_cnt+=1
			if index_nag <= len_nega-1:
				output.append(negative[index_nag])
				total_cnt+=1
				index_nag+=1
		else:
			total_cnt+=1

	output.reverse()
	print(*output)


	

	t-=1