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())
result_total = []

while t:
    n = int(input())
    array1 = list(map(int, input().split()))
    array = sorted(array1)

    length = len(array)

    if not length % 2:
        result = []

        start_point = int(length / 2 - 1)
        end_point = int(length / 2)

        result.append(array[start_point])
        for k in range(end_point + 1):
            if k and k != end_point:
                result.append(array[start_point + k])
                result.append(array[start_point - k])
            elif k == end_point:
                result.append(array[start_point + k])

    else:
        result = []

        start_point = int(length // 2)

        result.append(array[start_point])
        for k in range(start_point + 1):
            if k:
                result.append(array[start_point + k])
                result.append(array[start_point - k])
                
    result_total.append(result)
    t -= 1
    
for mas in result_total:
    print(str(mas).replace('[', '').replace(']', '').replace(',', ''))