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:
import sys


def read_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def solve(values):
    sorted_values = list(sorted(values))
    result = []
    while len(sorted_values) > 0:
        result.append(sorted_values[0])
        del sorted_values[0]
        if len(sorted_values) > 0:
            result.append(sorted_values[-1])
            del sorted_values[-1]
    return list(reversed(result))


def println_list(array):
    for i in range(len(array) - 1):
        sys.stdout.write(str(array[i]) + " ")
    sys.stdout.write(str(array[-1]) + "\n")


if __name__ == "__main__":
    results = []

    cycles = read_int()

    for cycle in range(cycles):
        n = read_int()
        values = read_list()
        results.append(solve(values))

    for r in results:
        println_list(r)