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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

public class B {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder("");
        int t = Integer.parseInt(br.readLine());
        while(t-->0) {
            String[] in = br.readLine().split(" ");
            int n = Integer.parseInt(in[0]);
            in = br.readLine().split(" ");
            int arr[]= new int[n];
            Set<Integer> s = new HashSet<>();
            for(int i=0;i<n;i++){
                arr[i]=Integer.parseInt(in[i]);
                s.add(arr[i]);
            }

            if(s.size()==1) {
                sb.append(0 + "\n");
            } else {
                StringBuilder k = new StringBuilder();
                boolean isSmall = false;
                boolean isGreater = false;
                k.append(arr[0]+" ");
                int count = 1;
                for(int i=1;i<n;i++){
                    if(isSmall){
                        if(arr[i]>arr[i-1]){
                            isSmall = false;
                            isGreater = true;
                            k.append(arr[i-1]);
                            count++;
                            k.append(" ");
                        }
                    } else if(isGreater){
                        if(arr[i]<arr[i-1]){
                            isSmall = true;
                            isGreater = false;
                            k.append(arr[i-1]);
                            count++;
                            k.append(" ");
                        }
                    }else {
                        if(arr[i]>arr[i-1]){
                            isGreater = true;
                        } else if(arr[i]<arr[i-1]){
                            isSmall = true;
                        }
                    }
                    if(i==n-1){
                        count++;
                        k.append(arr[i]+"\n");
                    }
                }
                sb.append(count+"\n");
                sb.append(k);
            }

        }

        out.print(sb);
        out.flush();
        br.close();
    }
}