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 Round_649;

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

public class Socially_Dist_Subsequence {  
    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        
        int numTrials = in.nextInt();
        while(numTrials --> 0) {
            int len = in.nextInt();
            int[] nums = new int[len];
            for(int i = 0; i < len; i++) {
                nums[i] = in.nextInt();
            }
            
            int last = nums[0];
            ArrayDeque<Integer> arr = new ArrayDeque<Integer>();
            int increasing = 0; // -1 is dec 0 is ? 1 is inc
            
            if(nums[1] > nums[0]) {
                increasing = 1;
            }
            else if(nums[1] < nums[0]) {
                increasing = -1;
            }
            
            arr.add(last);
            
            for(int i = 1; i < nums.length; i++) {
                int curr = nums[i];
                
                if(curr > last) {
                    if(increasing == -1) {
                        increasing = 1;
                        arr.add(last);
                    }
                }
                else if(curr < last) {
                    if(increasing == 1) {
                        increasing = -1;
                        arr.add(last);
                    }
                }
                
                last = curr;
            }
            
            arr.add(nums[nums.length - 1]);
            
            out.println(arr.size());
            StringBuilder s = new StringBuilder();
            while(!arr.isEmpty()) {
                s.append(arr.poll() + " ");
            }
            
            out.println(s.toString().trim());
        }
        
        out.flush();
    }
    
    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; 
        } 
    } 
}