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.lang.*; 
import java.io.*; 
public class Anurag
{ 
	public static void main(String args[]) throws IOException
	{
		OutputStream outputStream =System.out;
		PrintWriter out =new PrintWriter(outputStream);
		//Scanner s=new Scanner(System.in);
		Reader s=new Reader();
		int T=s.nextInt();
		while(T-->0)
		{
			int N=s.nextInt();
			int A[]=new int[N];
			for(int i=0;i<N;i++)
			{
				A[i]=s.nextInt();
			}
			if(N==2)
			{
				out.println(2);
				out.println(A[0]+" "+A[1]);
				continue;
			}
			int i=0,j=1,k=2,f=0,c=2;;
		    while(k<=N-1)
		    {
		    	int a=Math.abs(A[i]-A[j])+Math.abs(A[j]-A[k]);
		    	if(a==Math.abs(A[k]-A[i]))
		    	{
		    		A[j]=-1;
		    		j++;
		    		k++;
		    	}else
		    	{
		    		c++;
		    		i=j;
		    		j++;
		    		k++;
		    	}
		    }
		    out.println(c);
		    for(i=0;i<N;i++)
		    {
		    	if(A[i]!=-1)
		    	out.print(A[i]+" ");
		    }
		    out.println();
			
		}
		out.close();
	}
}



class Reader 
{ 
	final private int BUFFER_SIZE = 1 << 16; 
	private DataInputStream din; 
	private byte[] buffer; 
	private int bufferPointer, bytesRead; 

	public Reader() 
	{ 
		din = new DataInputStream(System.in); 
		buffer = new byte[BUFFER_SIZE]; 
		bufferPointer = bytesRead = 0; 
	} 

	public Reader(String file_name) throws IOException 
	{ 
		din = new DataInputStream(new FileInputStream(file_name)); 
		buffer = new byte[BUFFER_SIZE]; 
		bufferPointer = bytesRead = 0; 
	} 

	public String readLine() throws IOException 
	{ 
		byte[] buf = new byte[64]; // line length 
		int cnt = 0, c; 
		while ((c = read()) != -1) 
		{ 
			if (c == '\n') 
				break; 
			buf[cnt++] = (byte) c; 
		} 
		return new String(buf, 0, cnt); 
	} 

	public int nextInt() throws IOException 
	{ 
		int ret = 0; 
		byte c = read(); 
		while (c <= ' ') 
			c = read(); 
		boolean neg = (c == '-'); 
		if (neg) 
			c = read(); 
		do
		{ 
			ret = ret * 10 + c - '0'; 
		}  while ((c = read()) >= '0' && c <= '9'); 

		if (neg) 
			return -ret; 
		return ret; 
	} 

	public long nextLong() throws IOException 
	{ 
		long ret = 0; 
		byte c = read(); 
		while (c <= ' ') 
			c = read(); 
		boolean neg = (c == '-'); 
		if (neg) 
			c = read(); 
		do { 
			ret = ret * 10 + c - '0'; 
		} 
		while ((c = read()) >= '0' && c <= '9'); 
		if (neg) 
			return -ret; 
		return ret; 
	} 

	public double nextDouble() throws IOException 
	{ 
		double ret = 0, div = 1; 
		byte c = read(); 
		while (c <= ' ') 
			c = read(); 
		boolean neg = (c == '-'); 
		if (neg) 
			c = read(); 

		do { 
			ret = ret * 10 + c - '0'; 
		} 
		while ((c = read()) >= '0' && c <= '9'); 

		if (c == '.') 
		{ 
			while ((c = read()) >= '0' && c <= '9') 
			{ 
				ret += (c - '0') / (div *= 10); 
			} 
		} 

		if (neg) 
			return -ret; 
		return ret; 
	} 

	private void fillBuffer() throws IOException 
	{ 
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
		if (bytesRead == -1) 
			buffer[0] = -1; 
	} 

	private byte read() throws IOException 
	{ 
		if (bufferPointer == bytesRead) 
			fillBuffer(); 
		return buffer[bufferPointer++]; 
	} 

	public void close() throws IOException 
	{ 
		if (din == null) 
			return; 
		din.close(); 
	} 
} 


class B
{
	int F;
	int S;
	public B(int F,int S)
	{
		this.F=F;
		this.S=S;			
	}
	public String toString()
	{
		return this.F+" "+this.S;
	}
}

class Sort implements Comparator<B>
{
	public int compare(B a,B b)
	{
		if(a.F==b.F)
		{
			return a.S-b.S;
		}else
		{
			return a.F-b.F;
		}
	}
}