1685A · Circular Local MiniMax

Problem: 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 $b_{n+1}=b_1$.

Input Format: 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 $2\cdot 10^5$.

Output Format: 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.

Note: It can be shown that there are no valid arrangements for the first and the third test cases.

In the second test case, the arrangement $[1, 8, 4, 9]$ works. In this arrangement, $1$ and $4$ are both smaller than their neighbors, and $8, 9$ are larger.

In the fourth test case, the arrangement $[1, 11, 1, 111, 1, 1111]$ works. In this arrangement, the three elements equal to $1$ are smaller than their neighbors, while all other elements are larger than their neighbors.