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:
t = int(input())
td = t
temp_output_case = []

while t>0:
    input_case = []
    a = int(input())
    str_in = input()
    input_case = list(map(int, str_in.strip().split()))
    temp_case = sorted(input_case)

    new_case = []

    a1_number =(a//2)
    a1 = temp_case[a1_number]
    new_case.append(a1)

    tt = 1
    if a%2 ==1:
        while a1_number-tt >=0:
            p = int(a1_number-tt)
            q = temp_case[p]
            new_case.append(q)

            c = int(a1_number+tt)
            d = temp_case[c]
            new_case.append(d)

            tt += 1
    else:
        while a1_number-tt >0:
            p = int(a1_number-tt)
            q = temp_case[p]
            new_case.append(q)

            c = int(a1_number+tt)
            d = temp_case[c]
            new_case.append(d)

            tt += 1
        e = temp_case[0]
        new_case.append(e)
    for case in new_case:
        print(case, end= " ")
    print("\t")

    t -= 1