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.io.*;
import java.awt.*;

public class Main {
    public static void main(String[] args) throws Exception {
        InputReader sc = new InputReader(System.in);
        StringBuilder sb=new StringBuilder();
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt();
            int[] a=new int[n];
            for(int i=0;i<n;i++)a[i]=sc.nextInt();
            int last=a[0];
            LinkedList<Integer> ll=new LinkedList<>();
            ll.add(last);
            for(int i=1;i<n-1;i++){
                if(a[i]>=a[i-1] && a[i]>a[i+1])ll.add(a[i]);
                else if(a[i]<=a[i-1] && a[i]<a[i+1])ll.add(a[i]);
            }
            ll.add(a[n-1]);
            sb.append(ll.size()+"\n");
            for(int i:ll)sb.append(i+" ");
            sb.append("\n");
        }
        System.out.println(sb);
    }
}
/*********************************************************************************
 ----------------------------------SOLUTION END-----------------------------------
 *********************************************************************************/
class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
    public int read() {
        if (numChars==-1) throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try { numChars = stream.read(buf); }
            catch (IOException e) { throw new InputMismatchException(); }

            if(numChars <= 0) return -1;
        }
        return buf[curChar++];
    }
    public String nextLine() {
        String str = "";
        try { str = br.readLine(); }
        catch (IOException e) { e.printStackTrace(); }
        return str;
    }
    public int nextInt() {
        int c = read();
        while(isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if(c<'0'||c>'9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }
    public long nextLong() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        while (!isSpaceChar(c));
        return res * sgn;
    }
    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9') throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E') return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9') throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
    public String readString() {
        int c = read();
        while (isSpaceChar(c)) c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        }
        while (!isSpaceChar(c));
        return res.toString();
    }
    public boolean isSpaceChar(int c) {
        if (filter != null) return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    public String next() { return readString();}
    public interface SpaceCharFilter { public boolean isSpaceChar(int ch);}
}