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.util.ArrayList;
import java.math.BigInteger; 
 
public class Main{   
     static class Pair{
     int x;
     int y;
       Pair(){
       
       }
       Pair(int x,int y){
       this.x=x;
       this.y=y;
       }
     }
    
 
    public static void main(String[] args)
    {
    Scanner param = new Scanner(System.in);
    
    int end=param.nextInt();
    c:while(end-->0)
    {
         int n=param.nextInt();
         int arr[]=new int[n];
         for(int i=0;i<n;i++)
         {
             arr[i]=param.nextInt();
             
         }
         ArrayList<Integer>l1=new ArrayList<>();
         long sum=0;
         int ele=arr[0];
         l1.add(ele);
         ele=arr[1];
         l1.add(ele);
         boolean b=true;
         
         if(l1.get(0)>l1.get(1))
         {
             b=false;
         }
         else
         {
             b=true;
         }
         int el=l1.get(1);
         for(int i=2;i<n;i++)
         {
            if(arr[i]>el&&b)
            {
                l1.remove(l1.size()-1);
                l1.add(arr[i]);
                el=arr[i];
                continue;
            }
            if(arr[i]<el&&b==false)
            {
               // System.out.println("123");
                l1.remove(l1.size()-1);
                l1.add(arr[i]);
                el=arr[i];
                continue;
            }
            if(arr[i]<el&&b==true)
            {
                b=false;
                l1.add(arr[i]);
                el=arr[i];
                continue;
                
            }
            if(arr[i]>el&&b==false)
            {
                b=true;
                l1.add(arr[i]);
                el=arr[i];
                continue;
            }
         }
         System.out.println(l1.size());
         for(int i=0;i<l1.size();i++)
         {
             System.out.print(l1.get(i)+" ");
         }
         System.out.println();
         
         
        
         
    }
   
   
    
    
}
}