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;
        FastI in = new FastI(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C2PrefixFlipHardVersion solver = new C2PrefixFlipHardVersion();
        solver.solve(1, in, out);
        out.close();
    }

    static class C2PrefixFlipHardVersion {
        public void solve(int testNumber, FastI sc, PrintWriter out) {
            int t = sc.nextInt();
            while (t > 0) {
                t--;
                int n = sc.nextInt();
                StringBuilder a = new StringBuilder(sc.nextLine());
                String b = sc.nextLine();
                ArrayList<Integer> ans = new ArrayList<>();
                ArrayList<Integer> pos = new ArrayList<>();
                int l = 1;
                int r = n;
                while (l <= r) {
                    pos.add(l);
                    l++;
                    if (l <= r) {
                        pos.add(r);
                        r--;
                    }
                }
                boolean flip = false;
                for (int i = n - 1, u = 0; i >= 0; i--, u++) {
                    if (u % 2 == 1) {
                        flip = true;
                    } else {
                        flip = false;
                    }
                    if (!flip) {
                        if (a.charAt(pos.get(u) - 1) != b.charAt(i)) {
                            ans.add(i + 1);
                        } else {
                            ans.add(1);
                            ans.add(i + 1);
                        }
                    } else {
                        if (a.charAt(pos.get(u) - 1) == b.charAt(i)) {
                            ans.add(i + 1);
                        } else {
                            ans.add(1);
                            ans.add(i + 1);
                        }
                    }
                }
                out.print(ans.size());
                for (int i : ans) {
                    out.print(" " + i);
                }
                out.println();
            }
        }

    }

    static class FastI {
        BufferedReader br;
        StringTokenizer st;

        public FastI(InputStream inputStream) {
            br = new BufferedReader(new
                    InputStreamReader(inputStream));

        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
}