A14350. Mean Inequality

You are given an array $a$ of $2n$ distinct integers. You want to arrange the elements of the array in a circle such that no element is equal to the the arithmetic mean of its $2$ neighbours.

More formally, find an array $b$ , such that:

- $b$ is a permutation of $a$ .
- For every $i$ from $1$ to $2n$ , $b_i \neq \frac{b_{i-1}+b_{i+1}}{2}$ , where $b_0 = b_{2n}$ and $b_{2n+1} = b_1$ .

It can be proved that under the constraints of this problem, such array $b$ always exists.

The first line of input contains a single integer $t$ $(1 \leq t \leq 1000)$ — the number of testcases. The description of testcases follows.

The first line of each testcase contains a single integer $n$ $(1 \leq n \leq 25)$ .

The second line of each testcase contains $2n$ integers $a_1, a_2, \ldots, a_{2n}$ $(1 \leq a_i \leq 10^9)$ — elements of the array.

Note that there is no limit to the sum of $n$ over all testcases.

For each testcase, you should output $2n$ integers, $b_1, b_2, \ldots b_{2n}$ , for which the conditions from the statement are satisfied.

In the first testcase, array $[3, 1, 4, 2, 5, 6]$ works, as it's a permutation of $[1, 2, 3, 4, 5, 6]$ , and $\frac{3+4}{2}\neq 1$ , $\frac{1+2}{2}\neq 4$ , $\frac{4+5}{2}\neq 2$ , $\frac{2+6}{2}\neq 5$ , $\frac{5+3}{2}\neq 6$ , $\frac{6+1}{2}\neq 3$ .