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.util.*;
import java.io.*;
import java.math.*;

public class Main {

    private static FastReader fr = new FastReader();
    private static Helper hp = new Helper();
    private static StringBuilder result = new StringBuilder();

    public static void main(String[] args) {
        Task solver = new Task();
        solver.solve();
    }

    static class Task {

        public void solve() {
            int nt = fr.ni();
            outer:
            while(nt-- > 0){
                int n = fr.ni();
                char[] s1 = fr.next().toCharArray();
                char[] s2 = fr.next().toCharArray();
                int i = n-1;
                int start = 0;
                int op = 0;
                StringBuilder ans = new StringBuilder();
                while(i>=0){
                    if(s1[i] == s2[i]){
                        i--;
                        continue;
                    }
                    if(s1[start] != s2[i]){
                        op++;
                        // Inverse bits
                        for(int k=0; k<=i; k++){
                            if(s1[k] == '0') s1[k] = '1';
                            else s1[k] = '0';
                        }
                        // Reverse bits
                        int len = i+1;
                        int end = len/2;
                        for(int k=0; k<end; k++){
                            char temp = s1[k];
                            s1[k] = s1[len-1-k];
                            s1[len-1-k] = temp;
                        }
                        ans.append(len).append(" ");
                    }
                    else{
                        int bitIndex = -1;
                        for(int k=i; k>=0; k--){
                            if(s1[k] == s2[i]){
                                bitIndex = k;
                                break;
                            }
                        }
                        // Inverse bits
                        for(int k=0; k<=bitIndex; k++){
                            if(s1[k] == '0') s1[k] = '1';
                            else s1[k] = '0';
                        }
                        // Reverse bits
                        int len = bitIndex+1;
                        int end = len/2;
                        for(int k=0; k<end; k++){
                            char temp = s1[k];
                            s1[k] = s1[len-1-k];
                            s1[len-1-k] = temp;
                        }
                        ans.append(len).append(" ");

                        // Inverse bits
                        for(int k=0; k<=i; k++){
                            if(s1[k] == '0') s1[k] = '1';
                            else s1[k] = '0';
                        }
                        // Reverse bits
                        len = i+1;
                        end = len/2;
                        for(int k=0; k<end; k++){
                            char temp = s1[k];
                            s1[k] = s1[len-1-k];
                            s1[len-1-k] = temp;
                        }
                        ans.append(len).append(" ");
                        op += 2;
                    }
                }
                result.append(op).append(" ").append(ans).append("\n");
            }
            System.out.println(result.toString().trim());
        }
    }

    static class Helper {
        public int[] ipArrInt(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = fr.ni();
            return arr;
        }

        public long[] ipArrLong(int n, int si) {
            long[] arr = new long[n];
            for (int i = si; i < n; i++)
                arr[i] = fr.nl();
            return arr;
        }
    }

    static class FastReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        private static PrintWriter pw;

        public FastReader() {
            reader = new BufferedReader(new InputStreamReader(System.in));
            pw = new PrintWriter(System.out);
            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 ni() {
            return Integer.parseInt(next());
        }

        public long nl() {
            return Long.parseLong(next());
        }

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

        public String rl() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return null;
        }

        public void print(String str) {
            pw.print(str);
            pw.flush();
        }
    }
}