codeforces#P1685A. Circular Local MiniMax
Circular Local MiniMax
Description
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.
Input
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
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.
Samples
4
3
1 1 2
4
1 9 8 4
4
2 0 2 2
6
1 1 1 11 111 1111
NO
YES
1 8 4 9
NO
YES
1 11 1 111 1 1111
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.