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:
from time import time
from random import randint

def getList(string):
    return list(map(int, string.split()))

def makeArray(array):
    array.sort()
    jump = 1
    target = len(array)//2 #- (len(arr)%2 == 0)
    diff_array = [array[target]]
    go_right = False
    while (target != (0, len(array)-1)[len(array)%2]):
        target += jump if go_right else -jump
        diff_array.append(array[target])
        go_right = not go_right
        jump += 1
    return diff_array

def submit():
    for case in range(int(input())):
        input()
        array = getList(input())
        print(*makeArray(array))


def tryOut():
    start_time = time()
    # -------------------------------------------------------------------------------------------------------------------
    array = getList("5 -2 4 8 6")
    print(makeArray(array))
    # -------------------------------------------------------------------------------------------------------------------
    print(f"\nExecution time: {time() - start_time}s")


submit()
#tryOut()