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.*;
import java.util.*;

/**
 * @author Tran Anh Tai
 * @template for CP codes
 */
public class ProbB {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        public void solve(InputReader in, PrintWriter out) {
            int t = in.nextInt();
            for (int i = 0; i < t; i++){
                int n = in.nextInt();
                int[] p = new int[n];
                boolean ok = true;
                for (int j = 0; j < n; j++){
                    p[j] = in.nextInt();
                }
                if (n == 2){
                    out.println(2);
                    out.println(p[0] + " " + p[1]);
                }
                else{
                    int j = 1;
                    ArrayList<Integer> result  = new ArrayList<>();
                    result.add(p[0]);
                    boolean inc = (p[0] < p[1]);
                    while (j < n - 1){
                        if (p[j] < p[j + 1]){
                            if (!inc){
                                result.add(p[j]);
                                inc = true;
                            }
                        }
                        else{
                            if (inc){
                                result.add(p[j]);
                                inc = false;
                            }
                        }
                        j++;
                    }
                    if (result.get(result.size() - 1) != p[n - 1]){
                        result.add(p[n - 1]);
                    }
                    out.println(result.size());
                    for (int num : result){
                        out.print(num + " ");
                    }
                    out.println();
                }
            }
        }
        static class Pair{
            public  int x, y;
            public Pair(int x, int y){
                this.x = x;
                this.y = y;
            }
        }
    }

    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}