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 
# try:
# 	sys.stdin = open('input.txt', 'r') 
# 	sys.stdout = open('output.txt', 'w')
# except:
# 	pass

testcases = int(sys.stdin.readline()) #/!\TESTCASES
for iteration in range(testcases):
	n = int(sys.stdin.readline())
	# a,b = map(int,sys.stdin.readline().split())
	arr = list(map(int,sys.stdin.readline().split()))
	arr.sort()
	mid = (n+1)//2 - 1
	r = mid+1
	l = mid-1
	sys.stdout.write(str(arr[mid])+" ")
	flag = 0
	# print(l,r,mid)
	while r<n and l>=0:
		if flag%2==0:
			sys.stdout.write(str(arr[r])+" ")
			r+=1
		else:
			sys.stdout.write(str(arr[l])+" ")
			l-=1
		flag += 1
	while r<n:
		sys.stdout.write(str(arr[r])+" ")
		r+=1
	while l>=0:
		sys.stdout.write(str(arr[l])+" ")
		l-=1
	sys.stdout.write("\n")