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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int T = Integer.parseInt(br.readLine());
		
		for(int t = 0; t < T; t++) {
		    int n = Integer.parseInt(br.readLine());
		    String s[] = br.readLine().split(" ");
		    int prev = Integer.parseInt(s[0]);
		    int curr = Integer.parseInt(s[1]);
		    boolean inc = curr > prev ? true : false;
		    ArrayList ans = new ArrayList();
		    ans.add(prev);
		    
		    for(int i = 2; i < n; i++) {
		        int x = Integer.parseInt(s[i]);
		        
		        if((x > curr && inc) || (x < curr && !inc)){
		        curr = x;
		        continue;}
		        //System.out.println(" -> " + x + " " + curr);
		        ans.add(curr);
		        prev = curr;
		        curr = x;
		        inc = !inc;
		    }
		    
		    ans.add(curr);
		    
		    System.out.println(ans.size());
		    
		    for(int i = 0; i < ans.size(); i++) {
		        System.out.print((int)ans.get(i) + " ");
		    }
		    
		    System.out.println();
		    ans.clear();
		    
		    
		}
	}
}