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 DemoB{
   
	public static void main(String[] args) throws Exception {
	Scanner sc=new Scanner(System.in);
	     int t=sc.nextInt();
	     while(t-->0){
	        int n=sc.nextInt();
            int[] ar=new int[n+1];
            int[] vis=new int[n+1];
            ArrayList<Integer> al=new ArrayList<>();
             
            for(int i=1;i<=n;i++){
                 ar[i]=sc.nextInt();
            }
            int ans=0;
            for(int i=2;i<=n;i++){
                ans+=Math.abs(ar[i]-ar[i-1]);
            }
            
            for(int i=2;i<=n-1;i++){
                if(Math.abs(ar[i]-ar[i-1])+Math.abs(ar[i]-ar[i+1])<=Math.abs(ar[i-1]-ar[i+1])){
                    vis[i]=1;
                }
            }
            
            for(int i=1;i<=n;i++){
               if( vis[i]==0){
                    al.add(ar[i]);
                }
            }
            StringBuilder sb=new StringBuilder();
            sb.append(al.size());
            sb.append(System.getProperty("line.separator"));
              for(int a:al){
                  sb.append(a);
                  sb.append(" ");
              }
              System.out.println(sb);
    }
  }
}