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.*;

public class B 
{    
    public static void main(String [] args) throws IOException
    {
        Foster sc = new Foster();
        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();
            }
            ArrayList<Integer> ans = new ArrayList<>();
            ans.add(a[0]);
            for(int i = 1; i < n-1; i++)
            {
                if(a[i] > a[i-1] && a[i] > a[i+1])
                    ans.add(a[i]);
                if(a[i] < a[i-1] && a[i] < a[i+1])
                    ans.add(a[i]);
            }
            ans.add(a[n-1]);
            System.out.println(ans.size());
            for(int i = 0; i < ans.size(); i++)
            {
                System.out.print(ans.get(i)+" ");
            }
            System.out.println();
        }
    }

static class Foster { 
    /* Java fast IO : Source - https://www.codechef.com/viewsolution/24906792 */
        final private int BUFFER_KA_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
        public Foster() { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_KA_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
        public Foster(String file_name) throws IOException { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_KA_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_KA_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(); 
        } 
    }
}