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.*;
public class B{
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        for(int i = 0; i < t; i++) {
            int n = input.nextInt();
            int[] nums = new int[n];
            for(int k = 0; k < n; k++) {
                nums[k] = input.nextInt();
            }
            ArrayList<Integer> result = new ArrayList<>();
            boolean increasing = false;
            boolean decreasing = false;
            result.add(nums[0]);
            for(int k = 1; k < n; k++) {
                if(nums[k] > nums[k - 1]) {
                    increasing = true;
                    if(decreasing != false) {
                        decreasing = false;
                        result.add(nums[k - 1]);
                    }
                } else if(nums[k] < nums[k - 1]) {
                    decreasing = true;
                    if(increasing != false) {
                        increasing = false;
                        result.add(nums[k - 1]);
                    }
                }
            }
            result.add(nums[n - 1]);
            System.out.println(result.size());
            for(Integer k : result) {
                System.out.print(k + " ");
            }
            System.out.println();
        }
    }
}