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 math

def is_odd(n):
    return n % 2 == 1

def is_even(n):
    return n % 2 == 0

def sorted_dff(arr):
    _sorted = sorted(arr)
    n = len(arr)
    res = []

    if is_odd(n):
        mid = math.floor(n/2)
        res.append(_sorted[mid])
        left, right = int(mid - 1), int(mid + 1)
    else:
        left, right = int(n/2 - 1),  int(n/2)

    while left >= 0:
        res.extend([_sorted[left], _sorted[right]])
        left -= 1
        right += 1

    print(" ".join(map(str, res)))


if __name__ == '__main__':
    t = int(input())

    while t > 0:
        n = int(input())
        arr = list(map(int, input().split(' ')))
        sorted_dff(arr)
        t -= 1