A. Circular Local MiniMax
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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.

Example
Input
4
3
1 1 2
4
1 9 8 4
4
2 0 2 2
6
1 1 1 11 111 1111
Output
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.