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:
# import sys 
# sys.stdin = open('input.txt', 'r') 
# sys.stdout = open('output.txt', 'w')
# import re 
# def negmod(a, m): 
#     return (a%m + m) % m 
# for C in range(int(input())):
# rawstr = ''.join([int(x) * '(' + x + ')' * int(x) for x in str(input())])
# for _ in range(9):
# rawstr = rawstr.replace(')(', '')
# print("Case #{}: {}".format(C+1, rawstr))
# def f(n):
# 	if(n<=1):
# 		return 1
# 	elif(n==2):
# 		return 2
# 	else:
# 		return((f(n-1)*2)-1)
t=int(input())
while(t):
	t-=1
	n=int(input())
	# print(f(2*(n-1)))
	# ans=0
	l=list(map(int,input().split()))
	l.sort()
	# print(l)
	if(n%2==0):
		i=n//2
		j=i-1
		while(j>=0 and i<n):
			print(l[j],end=" ")
			print(l[i],end=" ")
			j-=1
			i+=1
	else:
		i=(n//2)+1
		j=i-1
		while(j>=1 and i<n):
			print(l[j],end=" ")
			print(l[i],end=" ")
			i+=1
			j-=1
		print(l[0],end=" ")
	print()
	# if(n<=1):
	# 	print(1)
	# elif(n==2):
	# 	print(2)
	# else:
	# 	ans=2
	# 	for i in range (1,n-1):
	# 		ans=(ans*2)-1
	# 	print(ans)

# 	l=[]
# 	regrex=""
# 	for i in range(0,n):
# 		l.append(str(input()))
# 		regrex+=l[i]
# 	# print(l,regrex,end=" ")
# 	for i in range(0,len(l)):
# 		match = re.match(regrex,l[i])
# 		print(match)
# def get(now,distance):
# 	if(now==distance):
# 		return (now+distance)
# 	elif(now - distance>0):
# 		return (now- distance)
# 	else:
# 		return(now+ distance)
# n,k,s=map(int,input().split())
# if((n-1)*k < s or k>s):
# 	print("NO")
# else:
# 	print("YES")
# 	l=[]
# 	l.append(1)
# 	td=0
# 	dif=(s-td)
# 	while(k>0):
# 		walk=min(n-1,dif-k+1)
# 		p=get(l[-1],walk)
# 		# print(l[-1],p)
# 		l.append(p)
# 		k-=1
# 		dif-=walk
# 	for i in range (1,len(l)):
# 		print(l[i],end=" ")
# # l=[1,2,3,4,5]
# # print(l[1:-1])