H. Longest Saw
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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: $$$b_1 \gt b_2 \lt b_3 \gt b_4 \lt \dots$$$ or $$$b_1 \lt b_2 \gt b_3 \lt b_4 \gt \dots$$$.

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.

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.

Example
Input
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