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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.Arrays;
import java.math.BigInteger;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
     public static void main (String[] args) throws java.lang.Exception
     {
     	Scanner in =new Scanner(System.in);
		int l,n,k,r,j,t=1,i,m,p,h;
		String s="",st="";
		int x,y,z;
		t=in.nextInt();
	     for(i=0;i<t;i++)
		{
		     p=0;h=100001;x=0;y=0;
		     n=in.nextInt();
		     int a[]=new int[n];
		     int b[]=new int[n];
		     for(j=0;j<n;j++)
		          a[j]=in.nextInt();
		     b[0]=a[0];
		     for(j=0,x=1;j<n;)
		     {
		          if(j!=n-1 && a[j]<a[j+1])
		          {
		               for(++j;j<n;j++)
		               {
		                    if(j!=n-1 && a[j]<a[j+1])
		                    continue;
          		          else
          		          {
          		               b[x]=a[j];x++;
          		               break;
          		          }
		               }
		          }
		          else if(j!=n-1 && a[j]>a[j+1])
		          {
		               for(++j;j<n;j++)
		               {
		                    if(j!=n-1 && a[j]>a[j+1])
		                    continue;
          		          else
          		          {
          		               b[x]=a[j];x++;
          		               break;
          		          }
		               }
		          }
		          else j++;
		     }
		     System.out.println(x);
		     for(j=0;j<x;j++)
		          System.out.print(b[j]+" ");
		     System.out.println();
		}
     }
}