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.util.*;
public class Main {
    static int[][] canExit;
    static int[][] vis;

    static class Pair{
        int ind, val;
        Pair(int i, int v){
            ind=i;
            val=v;
        }
    }


    static void solve() throws Exception {
		int n = sc.nextInt();
		int[] p = sc.intArr(n);
		List<Integer> l = new ArrayList<>();
		l.add(p[0]);
		for (int i=1;i<n-1;i++){
			if (p[i]>p[i-1] && p[i]>p[i+1]){
				l.add(p[i]);
			}
			else if (p[i]<p[i-1] && p[i]<p[i+1]){
				l.add(p[i]);
			}
		}
		l.add(p[n-1]);
		pw.println(l.size());
		for (int i=0;i<l.size();i++){
			pw.print(l.get(i) + " ");
		}
		pw.println();
    }



    static PrintWriter pw;
    static MScanner sc;

    public static void main(String[] args) throws Exception {

        pw = new PrintWriter(System.out);
        sc = new MScanner(System.in);

        int tests =sc.nextInt();
        //int tests = 1;
        while (tests-- > 0){
            solve();
            pw.flush();
        }

    }

    static class MScanner {
        StringTokenizer st;
        BufferedReader br;

        public MScanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        public MScanner(String file) throws Exception {
            br = new BufferedReader(new FileReader(file));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int[] intArr(int n) throws IOException {
            int[] in = new int[n];
            for (int i = 0; i < n; i++)
                in[i] = nextInt();
            return in;
        }

        public long[] longArr(int n) throws IOException {
            long[] in = new long[n];
            for (int i = 0; i < n; i++)
                in[i] = nextLong();
            return in;
        }

        public int[] intSortedArr(int n) throws IOException {
            int[] in = new int[n];
            for (int i = 0; i < n; i++)
                in[i] = nextInt();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }

        public long[] longSortedArr(int n) throws IOException {
            long[] in = new long[n];
            for (int i = 0; i < n; i++)
                in[i] = nextLong();
            shuffle(in);
            Arrays.sort(in);
            return in;
        }

        public Integer[] IntegerArr(int n) throws IOException {
            Integer[] in = new Integer[n];
            for (int i = 0; i < n; i++)
                in[i] = nextInt();
            return in;
        }

        public Long[] LongArr(int n) throws IOException {
            Long[] in = new Long[n];
            for (int i = 0; i < n; i++)
                in[i] = nextLong();
            return in;
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public void waitForInput() throws InterruptedException {
            Thread.sleep(3000);
        }
    }

    static void shuffle(int[] in) {
        for (int i = 0; i < in.length; i++) {
            int idx = (int) (Math.random() * in.length);
            int tmp = in[i];
            in[i] = in[idx];
            in[idx] = tmp;
        }
    }

    static void shuffle(long[] in) {
        for (int i = 0; i < in.length; i++) {
            int idx = (int) (Math.random() * in.length);
            long tmp = in[i];
            in[i] = in[idx];
            in[idx] = tmp;
        }
    }
}