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:


/* package codechef; // don't place package name! */
//devanshjsr

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

/* Name of the class has to be "Main" only if the class is public. */
public class Solution
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	    StringTokenizer st=new StringTokenizer(br.readLine());
	    
		    int t=Integer.parseInt(st.nextToken());
		    
		    while(t>0)
		    {
		        st=new StringTokenizer(br.readLine());
		        int n=Integer.parseInt(st.nextToken());
		        
		        
		        st=new StringTokenizer(br.readLine());
		        
		        int[] arr=new int[n];
		        int[] tmp=new int[n];
		        
		        for(int i=0;i<n;i++)
		        {
		            arr[i]=Integer.parseInt(st.nextToken());
		        }
		        
		        tmp[0]=0;
		        
		        for(int i=1;i<n;i++)
		        {
		            if(arr[i]>arr[i-1])
		            {
		                tmp[i]=1;
		            }
		            else if(arr[i]==arr[i-1])
		            {
		                tmp[i]=0;
		            }
		            else
		            {
		                tmp[i]=-1;
		            }
		        }
		        
		        int j=1;
		        
		        
		        ArrayList<Integer> al=new ArrayList<Integer>();
		        
		        al.add(0);
		        
		        while(j<n)
		        {
		            if(tmp[j]==1)
		            {
		                while(tmp[j]==1)
		                {
		                    j++;
		                    
		                    if(j==n)
		                    {
		                        break;
		                    }
		                }
		                
		                    al.add(j-1);
		                
		                
		            }
		            else
		            {
		                if(tmp[j]==-1)
		                {
		                     while(tmp[j]==-1)
    		                {
    		                    j++;
    		                    
    		                    if(j==n)
    		                    {
    		                        break;
    		                    }
    		                }
    		                
    		                    al.add(j-1);
    		                
		                }
		                else
		                {
		                      while(tmp[j]==0)
    		                {
    		                    j++;
    		                    
    		                    if(j==n)
    		                    {
    		                        break;
    		                    }
    		                }
    		                
    		                    al.add(j-1);
    		                
		                }
		            }
		        }
		        
		       // System.out.println(al);
		        for(int i=1;i<al.size();i++)
		        {
		            if((arr[al.get(i)]==arr[al.get(i-1)]))
		            {
		                al.remove(i);
		                i--;
		            }
		        }
		        
		        //System.out.println(al);
		        
		        for(int i=1;i<al.size();i++)
		        {
		            if((tmp[al.get(i)]==tmp[al.get(i-1)]))
		            {
		                al.remove(i-1);
		               
		            }
		        }
		        
		        System.out.println(al.size());
		        
		        for(int i=0;i<al.size();i++)
		        {
		            System.out.print(arr[al.get(i)]+" ");
		        }
		        
		        System.out.println();
		        
		        
		        t--;
		    }
	}
}