D. Longest Max Min Subsequencetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an integer sequence $$$a_1, a_2, \ldots, a_n$$$. Let $$$S$$$ be the set of all possible non-empty subsequences of $$$a$$$ without duplicate elements. Your goal is to find the longest sequence in $$$S$$$. If there are multiple of them, find the one that minimizes lexicographical order after multiplying terms at odd positions by $$$-1$$$.For example, given $$$a = [3, 2, 3, 1]$$$, $$$S = \{[1], [2], [3], [2, 1], [2, 3], [3, 1], [3, 2], [2, 3, 1], [3, 2, 1]\}$$$. Then $$$[2, 3, 1]$$$ and $$$[3, 2, 1]$$$ would be the longest, and $$$[3, 2, 1]$$$ would be the answer since $$$[-3, 2, -1]$$$ is lexicographically smaller than $$$[-2, 3, -1]$$$.A sequence $$$c$$$ is a subsequence of a sequence $$$d$$$ if $$$c$$$ can be obtained from $$$d$$$ by the deletion of several (possibly, zero or all) elements.A sequence $$$c$$$ is lexicographically smaller than a sequence $$$d$$$ if and only if one of the following holds: $$$c$$$ is a prefix of $$$d$$$, but $$$c \ne d$$$; in the first position where $$$c$$$ and $$$d$$$ differ, the sequence $$$c$$$ has a smaller element than the corresponding element in $$$d$$$.InputEach test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 5 \cdot 10^4$$$). The description of the test cases follows.The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 3 \cdot 10^5$$$) — the length of $$$a$$$.The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the sequence $$$a$$$.It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.OutputFor each test case, output the answer in the following format:Output an integer $$$m$$$ in the first line — the length of $$$b$$$.Then output $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ in the second line — the sequence $$$b$$$.ExamplesInput443 2 1 341 1 1 193 2 1 3 2 1 3 2 111Output3
3 2 1
1
1
3
3 1 2
1
1
Input1021 2105 2 1 7 9 7 2 5 5 221 2102 2 8 7 7 9 8 1 9 699 1 7 5 8 5 6 4 133 3 361 6 4 4 6 563 4 4 5 3 3104 1 4 5 4 5 10 1 5 171 2 1 3 2 4 6Output2
1 2
5
5 1 9 7 2
2
1 2
6
2 7 9 8 1 6
7
9 1 7 5 8 6 4
1
3
4
1 4 6 5
3
4 5 3
4
5 4 10 1
5
2 1 3 4 6
NoteIn the first example, $$$S = \{[1], [2], [3], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2], [2, 1, 3], [3, 2, 1]\}$$$. Among them, $$$[2, 1, 3]$$$ and $$$[3, 2, 1]$$$ are the longest and $$$[-3, 2, -1]$$$ is lexicographical smaller than $$$[-2, 1, -3]$$$, so $$$[3, 2, 1]$$$ is the answer.In the second example, $$$S = \{[1]\}$$$, so $$$[1]$$$ is the answer.