#P1364B. Most socially-distanced subsequence
Most socially-distanced subsequence
Description
Given a permutation $p$ of length $n$, find its subsequence $s_1$, $s_2$, $\ldots$, $s_k$ of length at least $2$ such that:
- $|s_1-s_2|+|s_2-s_3|+\ldots+|s_{k-1}-s_k|$ is as big as possible over all subsequences of $p$ with length at least $2$.
- Among all such subsequences, choose the one whose length, $k$, is as small as possible.
If multiple subsequences satisfy these conditions, you are allowed to find any of them.
A sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deleting some (possibly, zero or all) elements.
A permutation of length $n$ is an array of length $n$ in which every element from $1$ to $n$ occurs exactly once.
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 $10^5$.
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.
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.
Samples
2
3
3 2 1
4
1 3 4 2
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 $[3,1]$.