A15122 | Circular Local MiniMax

You are given $n$ integers $a_1, a_2, \ldots, a_n$ . Is it possible to arrange them on a circle so that each number is strictly greater than both its neighbors or strictly smaller than both its neighbors?

In other words, check if there exists a rearrangement $b_1, b_2, \ldots, b_n$ of the integers $a_1, a_2, \ldots, a_n$ such that for each $i$ from $1$ to $n$ at least one of the following conditions holds:

- $b_{i-1} < b_i > b_{i+1}$
- $b_{i-1} > b_i < b_{i+1}$

To make sense of the previous formulas for $i=1$ and $i=n$ , one shall define $b_0=b_n$ and $b_{n+1}=b_1$ .

The first line of the input contains a single integer $t$ ( $1 \le t \le 3\cdot 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $3 \le n \le 10^5$ ) — the number of integers.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 10^9$ ).

The sum of $n$ over all test cases doesn't exceed $2\cdot 10^5$ .

For each test case, if it is not possible to arrange the numbers on the circle satisfying the conditions from the statement, output $\texttt{NO}$ . You can output each letter in any case.

Otherwise, output $\texttt{YES}$ . In the second line, output $n$ integers $b_1, b_2, \ldots, b_n$ , which are a rearrangement of $a_1, a_2, \ldots, a_n$ and satisfy the conditions from the statement. If there are multiple valid ways to arrange the numbers, you can output any of them.