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.*;import java.math.*;import java.lang.*;


public class second
{

    
    
         

    public static void process()throws IOException
    {
         int n = ni();
         int p[] = new int[n];
         for(int i=0;i<n;i++)
         {
              p[i] = ni();
         }

         int length = 1;
         ArrayList<Integer> list = new ArrayList<>();
         list.add(p[0]);
         for(int i=1;i<n-1;i++)
         {
             if((p[i]>p[i-1] && p[i]>p[i+1])||(p[i]<p[i-1] && p[i]<p[i+1]) )
             {
                  list.add(p[i]);
                  length++;
             }
         }
         list.add(p[n-1]);
         length++;
         pn(length);
         for(Integer i : list)
         {
             p(i+" ");
         }
         pn("");
         
    }  
    



    static AnotherReader sc;
    static PrintWriter out;
    public static void main(String[]args)throws IOException
    {
        out = new PrintWriter(System.out);
        sc=new AnotherReader();
        boolean oj = true;

        oj = System.getProperty("ONLINE_JUDGE") != null;
        if(!oj) sc=new AnotherReader(100);

       long s = System.currentTimeMillis();
         int t=ni();//test cases
         while(t-->0)
            process();
        out.flush();
        if(!oj)
          System.out.println(System.currentTimeMillis()-s+"ms");
        System.out.close();  
    }

    static void pn(Object o){out.println(o);}
    static void p(Object o){out.print(o);}
    static void pni(Object o){out.println(o);System.out.flush();}
    static int ni()throws IOException{return sc.nextInt();}
    static long nl()throws IOException{return sc.nextLong();}
    static double nd()throws IOException{return sc.nextDouble();}
    static String nln()throws IOException{return sc.nextLine();}
    static long gcd(long a, long b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int gcd(int a, int b)throws IOException{return (b==0)?a:gcd(b,a%b);}
    static int bit(long n)throws IOException{return (n==0)?0:(1+bit(n&(n-1)));}
    static boolean multipleTC=false;



/////////////////////////////////////////////////////////////////////////////////////////////////////////

    static class AnotherReader
    {
        BufferedReader br; StringTokenizer st;
        AnotherReader()throws FileNotFoundException
        {
              br=new BufferedReader(new InputStreamReader(System.in));
        }
        AnotherReader(int a)throws FileNotFoundException
        {
              br = new BufferedReader(new FileReader("input.txt"));
        }
        String next()throws IOException
        {
              while (st == null || !st.hasMoreElements()) 
                {
                    try
                     {
                               st = new StringTokenizer(br.readLine());
                     }
                    catch (IOException  e)
                    {
                               e.printStackTrace(); 
                     }
                }
                return st.nextToken(); 
        }
        int nextInt() throws IOException
        {
                return Integer.parseInt(next());
        }
        long nextLong() throws IOException
        {  
                return Long.parseLong(next());
        }
        double nextDouble()throws IOException 
        { 
               return Double.parseDouble(next()); 
        }
        String nextLine() throws IOException
        { 
               String str = ""; 
               try
               {
                     str = br.readLine();
               }
               catch (IOException e)
               {
                          e.printStackTrace();
               } return str;
        }
    }
    
/////////////////////////////////////////////////////////////////////////////////////////////////////////////
}