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.*;
 
public class Main {
static        List<Integer>[] gp;
static int cnt1=0;
static int cnt2=0;
    public static void main(String[] args)  {
  
      try{
       PrintWriter out = new PrintWriter(System.out);
       int t=in.nextInt();
       while(t-->0){
        int n=in.nextInt();
    //long res=0;
      //  int m=in.nextInt();
        int[] a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=in.nextInt();
            //a[i][1]=in.nextInt();
        }
        List<Integer> res=new ArrayList();
        
        for(int i=0;i<n;i++){
          if(i==n-1||i==0||(a[i]>a[i-1])!=(a[i+1]>a[i]))res.add(a[i]);
        }
        out.println(res.size());
        for(int i:res)out.print(i+" ");
        out.println();
        out.flush();
           
       }
           // System.ot.println();
           
      }catch(Exception e){
          e.printStackTrace();
      }  
	}
	
	static void dfs(int i,int c,HashSet<Integer> hs){
	    if(c==1){
	        cnt1++;
	    }else{
	        cnt2++;
	    }
	    hs.add(i);
	    for(int j:gp[i]){
	        if(!hs.contains(j))dfs(j,-c,hs);
	    }
	}
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            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;
        }
    }
 
    static FastReader in = new FastReader();
	
}