Problem: This is the easy version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved.

There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix.

For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001.

Your task is to transform the string a into b in at most 3n operations. It can be proved that it is always possible.

Input

The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 3t lines contain descriptions of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 1000) — the length of the binary strings.

The next two lines contain two binary strings a and b of length n.

It is guaranteed that the sum of n across all test cases does not exceed 1000.

Output

For each test case, output an integer k (0≤ k≤ 3n), followed by k integers p_1,…,p_k (1≤ p_i≤ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation.

Example

Input


5
2
01
10
5
01011
11100
2
01
01
10
0110011011
1000110100
1
0
1


Output


3 1 2 1
6 5 2 5 3 1 2
0
9 4 1 2 10 4 1 2 1 5
1 1

Note

In the first test case, we have 01→ 11→ 00→ 10.

In the second test case, we have 01011→ 00101→ 11101→ 01000→ 10100→ 00100→ 11100.

In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged.

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class c
{
    public static void print(String str,int val){
        System.out.println(str+"  "+val);
    }

    public long gcd(long a, long b) {
        if (b==0L) return a;
        return gcd(b,a%b);
    }

    public static void debug(long[][] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(Arrays.toString(arr[i]));
        }
    }
    public static void debug(int[][] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(Arrays.toString(arr[i]));
        }
    }
    public static void debug(String[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.println(arr[i]);
        }
    }

    public static void print(int[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }
    public static void print(String[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }
    public static void print(long[] arr){
        int len = arr.length;
        for(int i=0;i<len;i++){
            System.out.print(arr[i]+" ");
        }
        System.out.print('\n');
    }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }
        public FastReader(String path) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(path));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException  e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }


    public static void main(String[] args) throws IOException {
        FastReader s=new FastReader();
        int t = s.nextInt();
        for(int tt=0;tt<t;tt++){
            int n = s.nextInt();
            String a = s.nextLine();
            String b = s.nextLine();
            solve(n,a,b);
        }

    }

    static void solve(int n,String a,String b) throws IOException {
        char[] arr_a = a.toCharArray();
        char[] arr_b = b.toCharArray();
        ArrayList<Integer> sizes = new ArrayList<>();
        int idx = 0;
        boolean flip = false;
        for(int i=n-1;i>=0;i--){
            if(flip){
                if(arr_a[idx]!=arr_b[i]){
                    sizes.add(1);
                }
            }
            else {
                if(arr_a[idx]==arr_b[i]){
                    sizes.add(1);
                }
            }
            sizes.add(i+1);
            if(flip){
                idx-=i;
            }
            else {
                idx+=i;
            }
            flip = !flip;
        }

//        System.out.println(sizes.size());
        OutputStream out = new BufferedOutputStream( System.out );
        out.write((sizes.size()+" ").getBytes());
        for(int i:sizes){
            out.write((i+" ").getBytes());
        }
        out.write('\n');
        out.flush();
    }




//    OutputStream out = new BufferedOutputStream( System.out );
//        for(int i=1;i<n;i++){
//              out.write((arr[i]+" ").getBytes());
//         }
//        out.flush();
//  long start_time = System.currentTimeMillis();
//  long end_time = System.currentTimeMillis();
//  System.out.println((end_time - start_time) + "ms");



}