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

 
 public class Main	{
   static class Pair implements Comparable<Pair>{
   int a;
   int b;
   public Pair(int x,int y){a=Math.min(x, y);b=Math.max(x, y);}
   public Pair(){}
   public int compareTo(Pair p){
	 return p.a - a;
   }
@Override
public int hashCode() {
	final int prime = 31;
	int result = 1;
	result = prime * result + a;
	result = prime * result + b;
//	out.println("hashcode = "+result);
	return result;
}
@Override
public boolean equals(Object obj) {
	Pair cur = (Pair)obj;
	if((a==cur.a && b==cur.b) || (a==cur.b && b==cur.a))return true;
	return false;
}
 }
   static class cell implements Comparable<cell>{
	   int a,b;
	   long dis;
	   public cell(int x,int y,long z) {a=x;b=y;dis=z;}
	   public int compareTo(cell c) {
		   return Long.compare(dis,c.dis);
	   }
   }
static class TrieNode{
	TrieNode left;
	TrieNode right;
	int op;
	int data;
	public TrieNode() {}
}
  public static int gcd(int a,int b)
  {
    if(a<b)

      return gcd(b,a);
    if(b==0)
      return a;
    return gcd(b,a%b);
    
  }
  static long lcm(int a,int b) {
	  return  a*b / gcd(a,b);
  }
  //static long ans = 0;
  static long mod = 998244353;//(long)(1e9+7);//
   
    public static void main(String[] args) throws Exception {
       new Thread(null, null, "Anshum Gupta", 99999999) {
            public void run() {
                try {
                    solve();
                } catch(Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

static long pow(long x,long y){
    if(y == 0)return 1;
    if(y==1)return x;
    long a = pow(x,y/2);
    a = (a*a)%mod;
    if(y%2==0){
        return a;
    }
    return (a*x)%mod;
}

static long mxx;
static int mxN = (int)(1e7);
static long[]fact,inv_fact;
static long my_inv(long a) {
	return pow(a,mod-2);
}
static long bin(int a,int b) {
	if(a < b || a<0 || b<0)return 0;
    return ((fact[a]*inv_fact[a-b])%mod * inv_fact[b])%mod;
}
//static ArrayList<ArrayList<Integer>>adj;
//static boolean[]vis;
static void make_facts() {
  fact=new long[mxN];
  inv_fact = new long[mxN];
  fact[0]=inv_fact[0]=1L;
  for(int i=1;i<mxN;i++) {
	   fact[i] = (i*fact[i-1])%mod;
	   inv_fact[i] = my_inv(fact[i]);
  }
}
//static int[]bfs(int a){
//	Queue<Integer> q = new  LinkedList<Integer>();
//	
//	vis = new boolean[n+1];
//	int[]dis = new int[n+1];
//	q.add(a);
//	dis[a] = 0;
//	vis[a] = true;
//	while(!q.isEmpty()) {
//		int cur = q.poll();
//	//	vis[cur] = true;
//	//	if(cur == b)break;
//		for(int x : adj.get(cur)) {
//			if(vis[x])continue;
//			q.add(x);
//			dis[x] = dis[cur]+1;
//			vis[x] = true;
//		}
//	}
//	return dis;
//}

 public static void solve() throws Exception {
   // solve the problem here
   MyScanner s = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out), true);
        int tc = s.nextInt();
        mxx = (long)(1e18+5);
//        make_facts();  
        while(tc-->0){
        	int n = s.nextInt();
        	int[]p = new int[n];
        	ArrayList<Integer> ans = new ArrayList<Integer>();
        	for(int i=0;i<n;i++) {
        		p[i] = s.nextInt();
        	}
        	ans.add(p[0]);
        	for(int i=1;i<n-1;i++) {
        		if(p[i] > p[i-1] && p[i] > p[i+1])ans.add(p[i]);
        		if(p[i] < p[i-1] && p[i] < p[i+1])ans.add(p[i]);
        	}
        	ans.add(p[n-1]);
        	out.println(ans.size());
        	for(Integer x : ans) {
        		out.print(x + " ");
        	}
        	out.println();
        }
        	
           
        out.flush();
}
 
     
 
 
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
 
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            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;
        }
    }
    //--------------------------------------------------------
}