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

public class Program {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        try {
            int T = scanner.nextInt();
            while(T-- > 0) {
                int n = scanner.nextInt();
                List<Integer> l = new ArrayList<>();
                int first = scanner.nextInt();
                int prev = scanner.nextInt();
                int delta = prev - first;
                l.add(first);
                l.add(prev);
                for (int i=2; i<n; i++) {
                    int x = scanner.nextInt();
                    int delta2 = x - prev;
                    if (delta > 0 && delta2 > 0 || delta < 0 && delta2 < 0) {
                        l.set(l.size()-1, x);
                    } else {
                        l.add(x);
                    }
                    prev = x;
                    delta = delta2;
                }
                String s = String.join(" ", l.stream().map(el -> String.valueOf(el)).collect(Collectors.toList()));
                System.out.println(l.size());
                System.out.println(s);
            }
        } finally {
            scanner.close();
        }
    }   
    
}