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:
/******************************************************************************

                            Online Java Compiler.
                Code, Compile, Run and Debug java program online.
Write your code in this editor and press "Run" button to execute it.

*******************************************************************************/
import java.io.*;
import java.util.*;
public class Main
{
    private static String process(int[] nums) {
        int ans = 0;
        int prev = nums[0];
        boolean up = nums[1]>nums[0];
        List<Integer> list = new ArrayList<Integer>();
        list.add(nums[0]);
        for(int i = 2; i < nums.length; i++) {
            if (up && nums[i]<nums[i-1]) {
                list.add(nums[i-1]);
                up = false;
            } else if (!up && nums[i]>nums[i-1]) {
                list.add(nums[i-1]);
                up = true;
            }
        }
        if (nums[nums.length-1] != list.get(list.size()-1)) list.add(nums[nums.length-1]);
        StringBuilder sb = new StringBuilder();
        sb.append(list.size()+"\n");
        sb.append(list.get(0));
        for(int i = 1; i < list.size(); i++) {
            sb.append(" "+list.get(i));
        }
        return sb.toString();
    }
	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(br.readLine());
		while(t-->0) {
		    StringTokenizer tok = new StringTokenizer(br.readLine());
		    int n = Integer.parseInt(tok.nextToken());
		    int[] nums = new int[n];
		    tok = new StringTokenizer(br.readLine());
		    for(int i = 0; i<n; i++) nums[i]=Integer.parseInt(tok.nextToken());
		    System.out.println(process(nums));
		}
		br.close();
	}
}