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:
# -*- coding: utf-8 -*-
"""
Spyder Editor

This is a temporary script file.
"""
#print(f'Hello World SRINI1112')
total_sets=int(input())
#print(f'No. of input sets {total_sets}')

def  diff_order(set):
#    print(f'SRINI:input set is {set}')
    ordered_set=[]
#    same_set=[5,5]
#    positive_set=[1,2,4]
#    negative_set=[-2,-3]
    set.sort()
#    print(set)
    odd=len(set)%2
    nel=len(set)
    half=len(set)//2
    if odd:
        half += 1
#    print(f'Half of length is {half}')
    for j in range(0,half):
        if j == half-1 and odd:
                ordered_set.append(set[j])
        else:
            ordered_set.append(set[nel-1-j])
            ordered_set.append(set[j])


#    print(f'SRINI:ordered_Set{ordered_set}')
    ordered_set.reverse()
    print(*ordered_set, sep=" ")
#    ordered_set = ordered_set + same_set
#    ordered_set = ordered_set + positive_set
#    ordered_set = ordered_set + negative_set
    return ordered_set
nset=[]
set=[]
for i in range(total_sets):
    nelements=int(input())
    nset.append(nelements)
#    print(f'no. of elements {nset[i]}')
    elements=input()
    el_list=[]
    for el in elements.split():
        el_list.append(int(el))
    set.append(el_list)
#    print(f'elements in set {i} is {set[i]}')

#print(f'Total elements {nset}')
#print (f'Entire set is {set}')

for i in range(len(set)):
    diff_order(set[i])