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 class node{
        int k,v;
        node(int k,int v){
            this.k = k;
            this.v = v;
        }
        node(){}
    }





     void solve(Scanner in) throws Exception {
        int n = in.nextInt();
        int[] arr = readIntArray(in,n);
        List<Integer> ans = new ArrayList<>();
        ans.add(arr[0]);
        int start = 0,end = 1;
        for(;end<n&&start<n;){
            if(arr[end]<arr[start]){
                while(end!=n-1&&arr[end+1]<arr[end]){
                    end++;
                }
                ans.add(arr[end]);
                start = end;
                end = start+1;
            }
            else{
                while(end!=n-1&&arr[end+1]>arr[end]) end++;
                ans.add(arr[end]);
                start=end;
                end = start+1;
            }
        }
         System.out.println(ans.size());
        for(int i=0;i<ans.size();i++){
            System.out.printf("%d%s",ans.get(i),i==ans.size()-1?'\n':' ');
        }
    }

    public static int[] readIntArray(Scanner in,int tokens) {
        int[] ret = new int[tokens];
        for (int i = 0; i < tokens; i++) {
            ret[i] = in.nextInt();
        }
        return ret;
    }


    public static void main(String[] args) throws Exception{
//                Scanner in = new Scanner(System.in);
//         Scanner in = new Scanner(new File("input.txt"));
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int T = in.nextInt();
        for(int i=1;i<=T;i++){
//            System.out.printf("Case #"+i+": ");
            new Main().solve(in);
        }
//        nums = new int[1000001];
//        Arrays.fill(nums,1);
//        nums[0]=nums[1]=0;
//        for(int i=2;i<1000001;i++){
//            if(nums[i]==1){
//                for(int j=i+i;j<nums.length;j+=i){
//                    nums[j] = 0;
//                }
//            }
//        }
//        int T = in.nextInt();
//        for(int i=1;i<=T;i++){
//            solve4(in);
//        }
    }

}


// class Pair{
//    Integer key, value;
//     Pair(int _key,int _value){
//        key = _key;
//        value = _value;
//    }
//    @Override
//    public int hashCode() {
//        return (key ==null?0: key.hashCode()) ^(value ==null?0: value.hashCode());
//    }
//
//    @Override
//    public boolean equals(Object obj) {
//        if(obj==null) return false;
//        Pair a = (Pair)obj;
//        return this.key.equals(a.key)&&this.value.equals(a.value);
//    }
//}