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

# решена
def task_1343_c():
    b = int(input())
    array = [int(num) for num in input().split()]

    maxPositive = 0
    minNegative = -10000000000
    res = 0

    for i in range(b):
        if array[i] < 0:
            if i != 0 and array[i - 1] >= 0:
                res += maxPositive
                maxPositive = 0
            minNegative = max(minNegative, array[i])
        else:
            if i != 0 and array[i - 1] < 0:
                res += minNegative
                minNegative = -10000000000
        maxPositive = max(maxPositive, array[i])
    
    if minNegative == -10000000000:
        res += maxPositive
    else:
        res += maxPositive + minNegative

    print(res)

# не работает от слова совсем
def task_1341_b():
    doorSize, heightLen = map(int, input().split())
    heights = [int(num) for num in input().split()]

    perf = [0 for i in range(heightLen)]
    a = 0
    for i in range(heightLen - 1):
        if i == 0:
            perf[i] = 0
        else:
            if heights[i - 1] < heights[i] and heights[i] > heights[i + 1]:
                a += 1
            perf[i] = a

    maxl = [0 for i in range(2)]
    local = [0 for i in range(2)]
    for i in range(heightLen - doorSize):
        local[0] = perf[i + doorSize]
        local[1] = i
        if maxl[0] < local[0]:
            maxl[0] = local[0]
            maxl[1] = local[1]
    
    print(maxl[0], maxl[1])

#
def task_1340_a():
    print()

#
def task_1339_b():
    n = int(input())
    array = [int(num) for num in input().split()]

    array.sort()
    output = [0 for i in range(0, n)]
    i = 0
    h = 0
    j = n - 1
    while i <= j:
        output[h] = array[i]
        h += 1
        i += 1

        if h < n:
            output[h] = array[j]
            h += 1
            j -= 1
    
    for val in reversed(output):
        print(val, end=' ')


# решена
def task_1338_a():
    n = int(input())
    inputArr = [int(num) for num in input().split()]

    max_sec = 0
    for i in range(1, n):
        local_sec = 0

        a = inputArr[i - 1] - inputArr[i]
        if a <= 0:
            continue
        else:
            b = math.floor(math.log2(a))
            local_sec = b + 1

            for j in range(b, -1, -1):
                if a < pow(2, j):
                    continue

                inputArr[i] += pow(2, j)
                a -= pow(2, j)

            if local_sec > max_sec:
                max_sec = local_sec

    print(max_sec)


a = int(input())
for i in range(a):
    task_1339_b()