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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;

public class Main {

	public static Stack<Integer> func1(int[] arr) {
		Stack<Integer> stack = new Stack<Integer>();
		stack.push(arr[0]);
		for(int i = 1; i < arr.length; i++) {
			if(stack.size() % 2 == 0) {
				if(arr[i] < stack.peek()) {
					stack.pop();
					stack.push(arr[i]);
				} else {
					stack.push(arr[i]);
				}
			} else {
				if(arr[i] > stack.peek()) {
					stack.pop();
					stack.push(arr[i]);
				} else {
					stack.push(arr[i]);
				}
			}
		}
		return stack;
	}
	
	public static Stack<Integer> func2(int[] arr) {
		Stack<Integer> stack = new Stack<Integer>();
		stack.push(arr[0]);
		for(int i = 1; i < arr.length; i++) {
			if(stack.size() % 2 == 0) {
				if(arr[i] > stack.peek()) {
					stack.pop();
					stack.push(arr[i]);
				} else {
					stack.push(arr[i]);
				}
			} else {
				if(arr[i] < stack.peek()) {
					stack.pop();
					stack.push(arr[i]);
				} else {
					stack.push(arr[i]);
				}
			}
		}
		return stack;
	}
	
    public static void main(String args[] ) throws Exception {
    	Scanner s = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		String[] input;
		int t = Integer.parseInt(reader.readLine());
		while(t-->0) {
			int n = Integer.parseInt(reader.readLine());
			input = reader.readLine().split(" ");
			int[] arr = new int[n];
			for(int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(input[i]);
			}
			Stack<Integer> stack1 = func1(arr), stack2 = func2(arr);
			int[] arr1 = new int[stack1.size()];
			int[] arr2 = new int[stack2.size()];
			int idx1 = arr1.length - 1, idx2 = arr2.length - 1;
			while(stack1.size() > 0) {
				arr1[idx1--] = stack1.pop();
			}
			while(stack2.size() > 0) {
				arr2[idx2--] = stack2.pop();
			}
			int sum1 = 0, sum2 = 0;
			for(int i = 1; i < arr1.length; i++) {
				sum1 += Math.abs(arr1[i] - arr1[i - 1]);
			}
			for(int i = 1; i < arr2.length; i++) {
				sum2 += Math.abs(arr2[i] - arr2[i - 1]);
			}
			int[] ans;
			if(sum1 < sum2) {
				ans = arr2;
			} else if(sum1 > sum2) {
				ans = arr1;
			} else {
				if(arr1.length > arr2.length) {
					ans = arr1;
				} else {
					ans = arr2;
				}
			}
			out.println(ans.length);
			for(int i = 0; i < ans.length; i++) {
				out.print(ans[i] + " ");
			}
			out.println();
		}
		out.flush();

    }
	

}