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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA2 solver = new TaskA2();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskA2 {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int T = in.nextInt();
            while (T-- > 0) {
                int N = in.nextInt();
                char[] a = in.next().toCharArray();
                char[] b = in.next().toCharArray();
                ArrayList<Integer> p = new ArrayList<>();
                int l = 0;
                int r = N - 1;
                boolean flag = false;
                for (int i = N - 1; i >= 0; i--) {
                    if (!flag) {
                        if (flip(a[r], false) != b[i]) {
                            if (a[l] == a[r]) {
                                p.add(i + 1);
                            } else {
                                p.add(1);
                                p.add(i + 1);
                            }
                            flag = true;
                            l++;
                        } else {
                            r--;
                        }
                    } else {
                        if (flip(a[l], true) != b[i]) {
                            if (a[l] == a[r]) {
                                p.add(i + 1);
                            } else {
                                p.add(1);
                                p.add(i + 1);
                            }
                            flag = false;
                            r--;
                        } else {
                            l++;
                        }
                    }
                }
                out.println(p.size());
                for (int j : p) {
                    out.print(j + " ");
                }
                out.println();
            }
        }

        char flip(char i, boolean flag) {
            if (!flag) {
                return i;
            }
            if (i == '0') {
                return '1';
            }
            return '0';
        }

    }

    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());
        }

    }
}