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:
from sys import stdin,stdout
Pi = lambda x: stdout.write(str(x) + '\n')
Ps = lambda x: stdout.write(str(x))
S = lambda x: x*(x+1) // 2
I = lambda x: 1+(2*x)
R = lambda:stdin.readline()
Ri = lambda x:map(int,x.split())
Rs = lambda x:map(str,x.split())
Rf = lambda x:map(float,x.split())
MaxN = int(1e5) + 10

def main():
	for x in stdin:
		t = int(x)
		for test in range(t):
			n = int(R())
			A = list(Ri(R()))
			B = []
			i = n//2 - 1
			if n%2:i+=1
			j = i + 1
			sw = 1
			A.sort()
			while i>=0 or j<n:
				if sw and i>=0:					
					B.append(str(A[i]))
					i -= 1
				elif j<n:					
					B.append(str(A[j]))
					j += 1
				sw = (sw + 1)%2
			if i>=0:
				B.append(str(A[0]))
			if j<n:
				B.append(str(A[j]))
			print(' '.join(B))


 
if __name__=='__main__':
    main()
# Esta mal el Problema?????

# 1 2 3 2 1 3 
# 1 1 1 4 4 4 10 10 10
# 1 4 10 4 1