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

# use `log(...)` to print data when debugging
def log(*argv): pass
log = print # when debug is over, remove this line to mute log

def read_str(): return input()
def read_int(): return int(input())
def read_str_list(): return input().strip().split(' ')
def read_int_list(): return list(map(int, input().strip().split(' ')))
def read_lines(n, read_func): return [read_func() for _ in range(n)]
def list_to_str(l, sep=' '): return sep.join(map(str, l))

def main():
    T = read_int()
    for case_idx in range(1, T + 1):
        ans = solve_case()
        print("{}".format(ans))

def solve_case():
    N = read_int()
    nums = read_int_list()

    nums.sort()

    ans = []
    for i in range(N):
        if i % 2 == 0:
            ans.append(nums[(N - 1) // 2 - i // 2])
        else:
            ans.append(nums[(N - 1) // 2 + i // 2 + 1])

    return list_to_str(ans)

if __name__ == '__main__':
    sys.setrecursionlimit(1000000)
    main()