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.*;

public class Main {
    private static String reverse(String s, boolean flag, int x){
        StringBuilder sb = new StringBuilder("");
        int i = 0;
        if(flag) {
            sb.append(s.charAt(0));
           i = 1;
        }
        for(; i<=x; i++){

                if (s.charAt(i) == '1') sb.append(0);
                else sb.append(1);
        }
        sb.reverse();
        for(;i<s.length(); i++){
            sb.append(s.charAt(i));
        }
     //   System.out.println(sb);
        return sb.toString();
    }
    private static void solver(InputReader sc, PrintWriter out) throws Exception {
        int test = sc.nextInt();
        for (int ii = 0; ii < test; ii++) {
                int n = sc.nextInt();
                String s  = sc.next();
                String t = sc.next();
                List<Integer> al = new ArrayList<>();
                for(int i=n-1; i>=0; i--){
                    if(i==0){
                        if(s.charAt(0)==t.charAt(i)) break;
                        else al.add(1);
                        break;
                    }
                    if(s.charAt(0) == t.charAt(i)){
                        al.add(1);
                        s = reverse(s, true, i);
                    }else
                        s = reverse(s,false, i);
                    al.add(i+1);

                }
                out.print(al.size()+" ");
                for(int xx : al) out.print((xx)+" ");
                out.println();
        }
    }

    private static int lcm(int a, int b) {

        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {

        if (b == 0)
            return a;

        return gcd(b, a % b);
    }

    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solver(in, out);
        out.close();
    }

    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());
        }

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

class Pair {
    int x, y;

    Pair(int x, int y) {
        this.x = x;
        this.y = y;
    }
}

class Tuple implements Comparable<Tuple> {
    int x, y, z;

    public Tuple(int x, int y, int z) {
        this.x = x;
        this.y = y;
        this.z = z;
    }

    public int compareTo(Tuple t) {
        if (this.z == t.z) {
            if (this.y == t.y) {
                return t.x - this.x;
            } else return t.y - this.y;
        } else
            return this.z - t.z;
    }


}