H. Longest Sawtime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor 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.ExampleInput
3
10
10 9 8 7 6 5 4 3 2 1
7
1 2 2 2 3 2 2
3
100 100 100
Output
10
1 6 2 7 3 8 4 9 5 10 
4
2 1 3 2 
1
100 

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  
['*special problem', 'constructive algorithms']