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:
# link: https://codeforces.com/problemset/problem/1339/B
if __name__ == "__main__":
    for _ in range(int(input())):
        n = int(input())
        a = list(map(int, input().split()))                                       
        a.sort()
        i = n//2 - 1
        j = i + 1
        while i>-1 or j<n:
            if j<n:
                print(a[j], end = " ")
                j += 1
            if i>-1:
                print(a[i], end = " ")
                i -= 1
"""32767 16383 65535 8191 131071 4095 262143 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911

32767 16383 65535 8191 131071 4095 262143 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1"""