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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class Two {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        int t;
        t = in.nextInt();
        //t = 1;
        while (t > 0) {
            solver.call(in,out);
            t--;
        }
        out.close();
    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            int n;
            n = in.nextInt();

            String a, b;

            a = in.next();
            b = in.next();

            char[] arr = new char[n];
            char[] array = new char[n];

            ArrayList<Integer> arrayList = new ArrayList<>();

            for (int i = 0; i < n; i++) {
                arr[i] = a.charAt(i);
            }

            for (int i = n-1; i >=0 ; i--) {
                if(arr[i]==b.charAt(i))
                    continue;

                if(i==0){
                    if(arr[i]!=b.charAt(i)){
                        arrayList.add(1);
                    }
                }
                else {

                    if (arr[0] == b.charAt(i)) {
                        arrayList.add(1);
                        if(arr[0]=='0')
                            arr[0] = '1';
                        else
                            arr[0] = '0';
                    }
                    arrayList.add(i+1);

                    for (int j = 0; j <= i; j++) {
                        array[j] =arr[i-j];
                    }
                    for (int j = 0; j <= i; j++) {
                        if(array[j]=='0')
                            arr[j] = '1';
                        else
                            arr[j]='0';
                    }

                }

            }

            out.print(arrayList.size()+" ");
            for (int i = 0; i < arrayList.size(); i++) {
                out.print(arrayList.get(i)+" ");
            }
            out.println();

        }
    }

    static class answer implements Comparable<answer>{
        int a, b;

        public answer(int a, int b) {
            this.a = a;
            this.b = b;
        }


        @Override
        public int compareTo(answer o) {
            return this.a - o.a;
        }
    }


    static long lcm(long a , long b){
        return (a/gcd(a,b)) *b;
    }

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


    static final Random random=new Random();
    static void shuffleSort(int[] arr) {
        int n = arr.length;
        for (int i=0; i<n; i++) {

            int a=random.nextInt(n), temp=arr[a];
            arr[a]=arr[i];
            arr[i]=temp;

        }

        Arrays.sort(arr);

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }

    }
}