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:
t = int(input())
for _ in range(t):
    n = int(input())
    arr = list(map(int, input().rstrip().split(" ")))
    arr = sorted(arr)
    mid = n // 2 + 1
    left = True
    res = []
    offset = 1
    for i in range(n):
        res.append(str(arr[mid - 1]))
        if left:
            mid = mid - offset
            left = False
        else:
            mid = mid + offset
            left = True
        offset += 1
    print(' '.join(res))

'''
    -2  4   5   5   6   8
-2  i   6   7   7   8   10
4   6   i   1   1   2   4
5   7   1   i   0   1   3
5   7   1   0   i   1   3
6   8   2   1   1   i   2
8   10  4   3   3   2   i

-2 4 5 5 6 8

5 5 4 6 -2 8

    1   2   4   8
1   i   1   3   7
2   1   i   2   6
4   3   2   i   4
8   7   6   4   i
'''