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.FileReader;
import java.io.InputStreamReader;
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;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        C1PrefixFlipEasyVersion solver = new C1PrefixFlipEasyVersion();
        solver.solve(1, in, out);
        out.close();
    }

    static class C1PrefixFlipEasyVersion {
        char[] a;
        char[] b;
        int n;

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int t = sc.nextInt();
            while (t-- > 0) {
                n = sc.nextInt();
                a = sc.nextLine().toCharArray();
                b = sc.nextLine().toCharArray();
                int ans = 0;
                int r = n - 1;
                int l = 0;
                StringBuilder sb = new StringBuilder();
                while (r >= 0) {
//                pw.println(Arrays.toString(a));
//                pw.println(Arrays.toString(b));
                    if (a[0] == b[r]) {
                        ans++;
                        sb.append(1 + " ");
                        change(0);
                    }
                    change(r);
                    ans++;
                    sb.append(r + 1 + " ");
                    r--;
                }
                pw.println(ans + " " + sb.toString());
            }
        }

        void change(int n1) {
            for (int i = 0; i <= n1; i++) {
                a[i] = a[i] == '0' ? '1' : '0';
            }
            char[] tmp = new char[n1 + 1];
            int x = n1;
            for (int i = 0; x >= 0; i++) {
                tmp[x--] = a[i];
            }
            for (int i = 0; i <= n1; i++) {
                a[i] = tmp[i];
            }
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

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

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

        public String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

    }
}