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.List;
import java.util.StringTokenizer;

public class Solution {
    private FastScanner in;
    private PrintWriter out;

    public static void main(String[] args) throws Exception {
        (new Solution()).run();
    }

    private void run() throws Exception {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    private void solve() throws Exception {
        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            String a = in.next();
            String b = in.next();
            boolean reversed = false;
            int start = 0;
            int end = n - 1;
            List<Integer> commands = new ArrayList<>();
            int pointer = n - 1;
            while (start != end) {
                int need = b.charAt(pointer) - '0';
                int first = reversed ? ('1' - a.charAt(end)) : (a.charAt(start) - '0');
                if (first == need) {
                    commands.add(1);
                }
                commands.add(end - start + 1);
                if (reversed) {
                    end--;
                } else {
                    start++;
                }
                reversed = !reversed;
                pointer--;
            }
            if ((reversed ? ('1' + '0' - a.charAt(start)) : a.charAt(start)) != b.charAt(0)) {
                commands.add(1);
            }
            out.print(commands.size());
            commands.forEach(val -> out.print(" " + val));
            out.println();
        }
    }

    private static class FastScanner implements Closeable {
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        public FastScanner(InputStream inputStream) {
            this.bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public FastScanner(File file) throws FileNotFoundException {
            this(new FileInputStream(file));
        }

        public String next() throws IOException {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                String line = bufferedReader.readLine();
                if (line == null) {
                    throw new EOFException("End of input stream is reached.");
                }
                stringTokenizer = new StringTokenizer(line);
            }
            return stringTokenizer.nextToken();
        }

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

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

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

        @Override
        public void close() throws IOException {
            bufferedReader.close();
        }
    }
}