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

testcases = int(sys.stdin.readline())

for i in range(testcases):
    n = int(sys.stdin.readline())

    nums = sys.stdin.readline().split()

    for i in range(len(nums)):
        nums[i] = int(nums[i])

    new_list = []

    nums.sort()

    flag = False

    for index in range(int(n / 2)):
        if flag:
            flag = True
            new_list.append(int(nums[n - index - 1]))
            new_list.append(int(nums[index]))
        else:
            flag = False
            new_list.append(int(nums[index]))
            new_list.append(int(nums[n - index - 1]))

    if n % 2 == 1:
        new_list.append(int(nums[int(n / 2)]))

    new_list.reverse()

    for i in range(len(new_list)):
        new_list[i] = str(new_list[i])

    print(' '.join(new_list))