Problem: Given a permutation p of length n, find its subsequence s_1, s_2, …, s_k of length at least 2 such that:

  * |s_1-s_2|+|s_2-s_3|+…+|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.

Input

The first line contains an integer t (1 ≤ t ≤ 2 ⋅ 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 ≤ n ≤ 10^5) — the length of the permutation p.

The second line of each test case contains n integers p_1, p_2, …, p_{n} (1 ≤ p_i ≤ 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, …, s_k — its elements.

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

Example

Input


2
3
3 2 1
4
1 3 4 2


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].

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	public static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	public static Scanner sc = new Scanner(System.in);
	public static StringTokenizer st;

	public static void main(String[] args) throws NumberFormatException, IOException {

		int iter = Integer.parseInt(br.readLine());

		for (int i = 0; i < iter; i++) {
			solve();
		}
		bw.flush();
	}

	private static void solve() throws NumberFormatException, IOException {
		int n = Integer.parseInt(br.readLine());

		st = new StringTokenizer(br.readLine());

		int before = Integer.parseInt(st.nextToken());

		int ans = 1;

		List<Integer> ansList = new ArrayList<Integer>();
		ansList.add(before);

		int dir = -123;

		int now = -1;
		for (int i = 1; i < n; i++) {
			now = Integer.parseInt(st.nextToken());
			if (before < now) {
				if (dir == -1) {
					ansList.add(before);
				}
				dir = 1;
			} else if (before > now) {
				if (dir == 1) {
					ansList.add(before);
				}
				dir = -1;
			} else {
				continue;
			}
			before = now;
		}
		if (ansList.get(ansList.size() - 1) != now) {
			ansList.add(now);
		}

		bw.write(ansList.size() + "\n");
		for (int i : ansList) {
			bw.write(i + " ");
		}
		bw.write("\n");
	}

}