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.List;
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;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        A2PrefixFlipHardVersion solver = new A2PrefixFlipHardVersion();
        solver.solve(1, in, out);
        out.close();
    }

    static class A2PrefixFlipHardVersion {
        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int t = in.nextInt();
            while (t-- > 0) {
                int len = in.nextInt();
                String s = in.nextLine();
                String e = in.nextLine();
                if (e.equals(s)) {
                    out.println(0);
                    continue;
                }

                int[] a = new int[len];
                int[] b = new int[len];
                for (int i = 0; i < len; i++) {
                    a[i] = s.charAt(i) - '0';
                    b[i] = e.charAt(i) - '0';
                }

                int l = 0;
                int r = len - 1;
                int mod = 0;
                List<Integer> ans = new ArrayList<>();

                for (int i = len - 1; i >= 0; i--) {
                    int p = mod == 0 ? l++ : r--;
                    int val = (a[p] + mod) % 2;
                    mod = (mod + 1) % 2;
                    if (val == b[i]) {
                        ans.add(1);
                    }
                    ans.add(i + 1);
                }

                out.print(ans.size() + " ");
                for (Integer an : ans) {
                    out.print(an + " ");
                }
                out.println();

            }
        }

    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

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

            }
            return st.nextToken();
        }

        public String nextLine() {
            String str = "";

            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return str;
        }

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

    }
}