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:



#start the code from here

t=int(input())
for i in range(t):
	n=int(input())
	l=list(map(int,input().split()))
	flag=False
	a=[]
	for w in range(1,n):
		if len(a)>0:
			h=a[-1]
			if h<=abs(l[w]-l[w-1]):
				flag=False
			else:
				flag=True
				break
		a.append(abs(l[w]-l[w-1]))
	if flag==False:
		print(*l)
	else:
		l.sort()
		# print(l,"aas")
		ans=[]
		for w in range(len(l)):
			if w==(len(l)//2):
				# print(w,"hh")
				break
			ans.append(l[-1-w])
			ans.append(l[w])
			# print(l[-1-w],l[w],end=" ")
			
		if len(l)%2==1:
			ans.append(l[n//2])
		# print(ans)
		ans.reverse()
		print(*ans)