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:
/**
 * @author egaeus
 * @mail sebegaeusprogram@gmail.com
 * @veredict Not sended
 * @url <https://codeforces.com/problemset/problem/CF1364B>
 * @category ?
 * @date 13/06/2020
 **/

import java.io.*;
import java.util.*;
import java.util.stream.Collectors;

import static java.lang.Integer.*;
import static java.lang.Math.*;

public class CF1364B {
    public static void main(String args[]) throws Throwable {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int T = parseInt(in.readLine());
        for (int t = 0; t < T; t++) {
            int N = parseInt(in.readLine());
            int[] arr = new int[N];
            StringTokenizer st = new StringTokenizer(in.readLine());
            int s = 0;
            for (int i = 0; i < N; i++)
                arr[i] = parseInt(st.nextToken());
            ArrayList<Integer> list = new ArrayList<>();
            int last = arr[0];
            list.add(last);
            for (int i = 1; i < N - 1; i++) {
                if (arr[i] < arr[i - 1] && arr[i] < arr[i + 1])
                    list.add(arr[i]);
                else if (arr[i] > arr[i - 1] && arr[i] > arr[i + 1])
                    list.add(arr[i]);
            }
            list.add(arr[N - 1]);
            System.out.println(list.size());
            System.out.println(list.stream().map(a -> a + "").collect(Collectors.joining(" ")));
        }
    }
}