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:
#Sorted Adjacent Differences

import sys

def solve(arr):
	# print("start")
	sol = []
	if len(arr) % 2 == 1:
		i = len(arr)//2
		j = len(arr)//2
	else:
		i = len(arr)//2 - 1
		j = len(arr)//2
	while (i!= -1 and j!= len(arr)):
		# print('i is ' + str(i))
		# print('j is ' + str(j))
		# print(arr[i])
		# print(arr[j])
		if (i == j):
			sol.append(arr[i])
		else:
			sol.append(arr[i])
			sol.append(arr[j])
		i-=1
		j+=1
	return (sol)

def main():
	q = []
	for line in sys.stdin.readlines():
		q.append(line)

	for i in range(len(q)):
		q[i] = q[i].rstrip().split(' ')
		q[i] = [int(x) for x in q[i]]
	
	for i in range(2, len(q), 2):
		q[i].sort()
		# print(q[i])
		sol = solve(q[i])
		# print(sol)
		print(' '.join(map(str, sol)))

if __name__ == '__main__':
	main()