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.util.*;
import java.io.*;

public class Main {
    // For fast input output
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            try {
                br = new BufferedReader(new FileReader("input.txt"));
                PrintStream out = new PrintStream(new FileOutputStream("output.txt"));
                System.setOut(out);
            } catch (Exception e) {
                br = new BufferedReader(new InputStreamReader(System.in));
            }
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    private static int comparevals (int a, int b)
    {
        if(a>b)
            return -1;
        else if(a==b)
            return 0;
        else
            return 1; 
    }
    // end of fast i/o code
    public static void main(String[] args) {
        FastReader reader = new FastReader();
        StringBuilder str = new StringBuilder("");
        // check where monotonicity breaks
        int t = reader.nextInt();
        while(t-->0)
        {
            int n = reader.nextInt();
            int[] arr = new int[n];
            for(int i = 0; i < n; i++)
                arr[i] = reader.nextInt();
            int curr = 0;
            if(arr[0]<=arr[1])
                curr = 1;
            else    
                curr = -1;
            ArrayList<Integer> list = new ArrayList<>();
            list.add(arr[0]);
            for(int i = 1; i < n-1; i++)
            {
                int val = comparevals(arr[i],arr[i+1]);
                if(val==0 || val==curr)
                    continue;
                else
                {
                    //System.out.println("changed at: "+i);
                    curr = -curr;
                    list.add(arr[i]);
                    //str.append(arr[i]+" ");
                }
            }
            list.add(arr[n-1]);
            str.append(list.size());
            str.append(System.getProperty("line.separator"));
            list.forEach((i) -> str.append(i+" "));
            str.append(System.getProperty("line.separator"));
        }
        System.out.println(str.toString());
    }

}