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:
# Python program to rearrange an array in minimum 
# maximum form 

# Prints max at first position, min at second position 
# second max at third position, second min at fourth 
# position and so on. 
def rearrange(arr, n): 
	# Auxiliary array to hold modified array 
	temp = n*[None] 

	# Indexes of smallest and largest elements 
	# from remaining array. 
	small,large =0,n-1

	# To indicate whether we need to copy rmaining 
	# largest or remaining smallest at next position 
	flag = True

	# Store result in temp[] 
	for i in range(n): 
		if flag is True: 
			temp[i] = arr[large] 
			large -= 1
		else: 
			temp[i] = arr[small] 
			small += 1

		flag = bool(1-flag) 

	# Copy temp[] to arr[] 
	for i in range(n): 
		arr[i] = temp[i] 
	return arr 

# Driver program to test above function 
for _ in range(int(input())):
    n=int(input())
    arr=list(map(int,input().split()))
    arr.sort()
    rearrange(arr, n)
    print(*arr[::-1])

# This code is contributed by Pratik Chhajer