Most socially-distanced subsequence

Description:

Input:

The first line contains an integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — the length of the permutation $$$p$$$.

The second line of each test case contains $$$n$$$ integers $$$p_1$$$, $$$p_2$$$, $$$\ldots$$$, $$$p_{n}$$$ ($$$1 \le p_i \le n$$$, $$$p_i$$$ are distinct) — the elements of the permutation $$$p$$$.

The sum of $$$n$$$ across the test cases doesn't exceed $$$10^5$$$.

Output:

For each test case, the first line should contain the length of the found subsequence, $$$k$$$. The second line should contain $$$s_1$$$, $$$s_2$$$, $$$\ldots$$$, $$$s_k$$$ — its elements.

If multiple subsequences satisfy these conditions, you are allowed to find any of them.

Sample Input:

2
3
3 2 1
4
1 3 4 2

Sample Output:

2
3 1 
3
1 4 2 

Note:

In the first test case, there are $$$4$$$ subsequences of length at least $$$2$$$:

• $$$[3,2]$$$ which gives us $$$|3-2|=1$$$.
• $$$[3,1]$$$ which gives us $$$|3-1|=2$$$.
• $$$[2,1]$$$ which gives us $$$|2-1|=1$$$.
• $$$[3,2,1]$$$ which gives us $$$|3-2|+|2-1|=2$$$.

So the answer is either $$$[3,1]$$$ or $$$[3,2,1]$$$. Since we want the subsequence to be as short as possible, the answer is $$$[3,1]$$$.