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 bisect import bisect_left as lower_bound, bisect_right as upper_bound
from sys import stdin, stdout
from collections import defaultdict

def solve(arr, n):
    pass

def main():
    t = int(stdin.readline())

    for _ in range(t):
        n = int(stdin.readline())
        arr = list(map(int, stdin.readline().strip().split()))

        arr.sort()

        if n&1:
            i, j = n//2, n//2+1

        else:
            i, j = n//2-1, n//2

        ret = [-1 for _ in range(n)]

        k = 0

        while i >= 0 or j < n:
            ret[k] = arr[i]
            k += 1

            if j < n: 
                ret[k] = arr[j]
                k += 1

            i -= 1
            j += 1

        stdout.write(" ".join(list(map(str, ret))) + "\n")


if __name__ == "__main__": main()