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:
/*
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Don't let that studying and grades consume you
Just live life young
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1st on Billboard, what do you think of it
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Higher, higher, even higher, to the point you won’t even be able to see me
https://www.a2oj.com/Ladder16.html
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300IQ as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class B
   {
      public static void main(String omkar[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int T = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         while(T-->0)
         {
            int N = Integer.parseInt(infile.readLine());
            int[] arr = new int[N];
            st = new StringTokenizer(infile.readLine());
            for(int i=0; i < N; i++)
               arr[i] = Integer.parseInt(st.nextToken());
            boolean[] remove = new boolean[N];
            for(int i=1; i < N-1; i++)
               if(arr[i-1] < arr[i] && arr[i] < arr[i+1] || arr[i+1] < arr[i] && arr[i] < arr[i-1])
                  remove[i] = true;
            ArrayList<Integer> ls = new ArrayList<Integer>();
            for(int i=0; i < N; i++)
               if(!remove[i])
                  ls.add(arr[i]);
            sb.append(ls.size()+"\n");
            for(int x: ls)
               sb.append(x+" ");
            sb.append("\n");
         }
         System.out.print(sb);
      }
   }