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.*;
import java.lang.*;

public class Difference{
	public static void main(String[] args)throws IOException{
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); 
		int t = Integer.parseInt(in.readLine());
		while(t-->0){
			int n = Integer.parseInt(in.readLine());
			int[] p = new int[n];
			boolean[] deleted = new boolean[n];
			int deleteCount = 0;
			String[] temp = in.readLine().split(" ");
			for (int i = 0; i < n; i++){
				p[i] = Integer.parseInt(temp[i]);
			}

			for(int i = 1; i < (n-1); i++){
				if(Math.abs(p[i]-p[i+1]) + Math.abs(p[i]-p[i-1]) <= Math.abs(p[i+1] - p[i-1])){
					deleteCount++;
					deleted[i] = true;
				}
			}

			System.out.println(n-deleteCount);

			for(int i = 0; i < n; i++)
				if(!deleted[i])
					System.out.print(p[i] + " ");
			System.out.println();
		}
	}
}