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 sun.nio.cs.KOI8_U;

import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;

public class AA implements Runnable {


    public void run() {
        InputReader sc = new InputReader();
        PrintWriter out = new PrintWriter(System.out);
        int i=0,j=0,k=0;
        int t=0;
        t=sc.nextInt();
        for(int testcase = 0;testcase < t; testcase++)
        {
            int n=sc.nextInt();
            int inparr[]=new int[n];
            int subtractionout[]=new int[n];
            List<Integer> li=new ArrayList<>();
            for (i=0;i<n;i++)
            {
                inparr[i]=sc.nextInt();
                if (i!=0)
                {
                    subtractionout[i-1]=inparr[i-1]-inparr[i];
                }
            }
            subtractionout[n-1]=n+1;
            int len=subtractionout.length;
            li.add(inparr[0]);
            i=0;
            while (i<n-1)
            {
                boolean abc=subtractionout[i]<0;
                if (abc)
                {
                    while (i<n-1&&subtractionout[i]<0)
                        i++;
                }
                else
                {
                    while (i<n-1&&subtractionout[i]>0)
                        i++;
                }
                if (i<n)
                    li.add(inparr[i]);
            }
            out.println(li.size());
            for (int te:li)
                out.print(te+" ");
            out.println();
        }

//================================================================================================================================
        out.flush();
        out.close();
    }


//================================================================================================================================
public static int[] sa(int n,InputReader sc)
{
    int inparr[]=new int[n];
    for (int i=0;i<n;i++)
        inparr[i]=sc.nextInt();
    return inparr;
}

    public static long gcd(long a,long b){
        return (a%b==0l)?b:gcd(b,a%b);
    }
    private static long lcm(long a, long b)
    {
        return a * (b / gcd(a, b));
    }
    public int egcd(int a, int b) {
        if (a == 0)
            return b;

        while (b != 0) {
            if (a > b)
                a = a - b;
            else
                b = b - a;
        }

        return a;
    }



    public int countChar(String str, char c)
    {
        int count = 0;
        for(int i=0; i < str.length(); i++)
        {    if(str.charAt(i) == c)
            count++;
        }
        return count;
    }
    static int binSearch(Integer[] inparr, int number){
        int left=0,right=inparr.length-1,mid=(left+right)/2,ind=0;
        while(left<=right){
            if(inparr[mid]<=number){
                ind=mid+1;
                left=mid+1;
            }
            else
                right=mid-1;
            mid=(left+right)/2;
        }
        return ind;
    }
    static int binSearch(int[] inparr, int number){
        int left=0,right=inparr.length-1,mid=(left+right)/2,ind=0;
        while(left<=right){
            if(inparr[mid]<=number){
                ind=mid+1;
                left=mid+1;
            }
            else
                right=mid-1;
            mid=(left+right)/2;
        }
        return ind;
    }
    static class Pair
    {
        int a,b;
        Pair(int aa,int bb)
        {
            a=aa;
            b=bb;
        }
        String get()
        {
            return a+" "+b;
        }
        String getrev()
        {
            return b+" "+a;
        }
    }

    static boolean isPrime(long n) {
        if(n < 2) return false;
        if(n == 2 || n == 3) return true;
        if(n%2 == 0 || n%3 == 0) return false;
        long sqrtN = (long)Math.sqrt(n)+1;
        for(long i = 6L; i <= sqrtN; i += 6) {
            if(n%(i-1) == 0 || n%(i+1) == 0) return false;
        }
        return true;
    }
    static long factorial(long n)
    {
        if (n == 0)
            return 1;
        return n*factorial(n-1);
    }
//================================================================================================================================

    static class InputReader
    {
        BufferedReader br;
        StringTokenizer st;

        public InputReader()
        {
            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;
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new AA(),"Main",1<<27).start();
    }
}