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 collections import Counter as C,defaultdict as D,deque as Q
from operator import itemgetter as I
from itertools import product as P
from bisect import bisect_left as BL,bisect_right as BR
from heapq import heappush as HPUSH,heappop as HPOP
from math import floor as MF,ceil as MC, gcd as MG,factorial as F,sqrt as SQRT, inf as INFINITY,log as LOG
from sys import stdin, stdout
INPUT=stdin.readline
PRINT=stdout.write

def player1():
	print("")

def player2():
	print("")

def isPrime(n):

	for i in range(2,MC(SQRT(n))+1):
		if n%i==0:
			return False
	return True

def factors(x):

	ans=[]

	for i in range(1,MC(SQRT(x))+1):
		if x%i==0:
			ans.append(i)
			if x%(x//i)==0:
				ans.append(x//i)
	return ans


def main():

	for _ in range(int(INPUT())):
		n=int(input())
		a=sorted(map(int,INPUT().split( )))

		mid=n//2
		PRINT(str(a[mid])+" ")
		diff=1
		while diff+mid<n and mid-diff>=0:
			PRINT(str(a[mid-diff])+" "+str(a[mid+diff])+" ")
			diff+=1
		if not n&1:
			PRINT(str(a[0])+"\n")
main()