Longest Saw
Description
You are given the sequence $a_1, a_2, \dots, a_n$. You can choose any subset of elements and then reorder them to create a "saw".
The sequence $b_1, b_2, \dots, b_m$ is called a "saw" if the elements satisfy one of the following series of inequalities: $b_1>b_2<b_3>b_4<\dots$ or $b_1<b_2>b_3<b_4>\dots$.
Find the longest saw which can be obtained from a given array.
Note that both the given sequence $a$ and the required saw $b$ can contain duplicated (non-unique) values.
The first line contains an integer $t$ ($1 \le t \le 10^5$) — the number of test cases in the input. Then the descriptions of the $t$ test cases follow. Each test case begins with a line containing integer $n$ ($1 \le n \le 2\cdot10^5$). Then a line containing $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) follows.
It's guaranteed that $\sum{n}$ doesn't exceed $2 \cdot 10^5$.
For each test case, print two lines: print the length of the longest saw in the first line, and the saw itself in the second line. If there are several solutions, print any of them.
Input
The first line contains an integer $t$ ($1 \le t \le 10^5$) — the number of test cases in the input. Then the descriptions of the $t$ test cases follow. Each test case begins with a line containing integer $n$ ($1 \le n \le 2\cdot10^5$). Then a line containing $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) follows.
It's guaranteed that $\sum{n}$ doesn't exceed $2 \cdot 10^5$.
Output
For each test case, print two lines: print the length of the longest saw in the first line, and the saw itself in the second line. If there are several solutions, print any of them.
Samples
3
10
10 9 8 7 6 5 4 3 2 1
7
1 2 2 2 3 2 2
3
100 100 100
10
1 6 2 7 3 8 4 9 5 10
4
2 1 3 2
1
100