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:
def run_on_input():
    num_test_cases = int(input())
    for i in range(num_test_cases):
        arr_len = int(input())
        arr = list(map(int, input().split()))
        sorted_adjacent_diff(arr)


def print_after_return(func):
    def wrapper(*args, **kwargs):
        returned = func(*args, **kwargs)
        if isinstance(returned, list) or isinstance(returned, tuple):
            string = " ".join(map(str, returned))
            print(string)
        else:
            print(returned)
    
    return wrapper


@print_after_return
def sorted_adjacent_diff(arr):
    arr.sort()
    medians = ping_pong_array(arr)
    out = [median for median in medians]
    return out


def ping_pong_array(arr):
    median = len(arr) // 2
    jump = -1
    while median >= 0 and median < len(arr):
        yield arr[median]
        median += jump
        # Increase jump by 1 (negatively or postively)
        jump = (abs(jump) + 1) * (jump // abs(jump))
        # Flip jump
        jump *= -1


if __name__ == '__main__':
    run_on_input()