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:
//Problem: Prefix Flip (Easy Version) (https://codeforces.com/problemset/problem/1381/A1) & Prefix Flip (Hard Version) (https://codeforces.com/problemset/problem/1381/A2)
//Status: Not Accepted

import java.util.*;
import java.io.*;

public class _1381A {
    private static InputReader infile = new InputReader();
    private static PrintWriter outfile = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        int numTestCases = infile.nextInt();
        for(int t = 1; t <= numTestCases; t++) {
            int length = infile.nextInt();
            char[] curr = infile.nextLine().toCharArray();
            char[] target = infile.nextLine().toCharArray();
            ArrayList<Integer> operations = new ArrayList<Integer>(2 * length);

            int index = length - 1;
            while(index >= 0) {
                if(curr[0] != target[index]) {
                    flip(curr, index + 1);
                    operations.add(index + 1);
                    index--;
                }
                else {
                    flip(curr, 1);
                    operations.add(1);
                }
            }

            outfile.print(operations.size());
            for(int operation : operations)
                outfile.print(" " + operation);
            outfile.println();
        }

        infile.close();
        outfile.close();
    }

    private static void flip(char[] curr, int len) {
        char[] temp = new char[len];
        for(int i = 0; i < len; i++) {
            if(curr[i] == '0')
                temp[len - i - 1] = '1';
            else
                temp[len - i - 1] = '0';
        }
        for(int i = 0; i < len; i++)
            curr[i] = temp[i];
    }

    static class InputReader {
        private static BufferedReader infile;
        private static StringTokenizer st;

        public InputReader() {
            infile = new BufferedReader(new InputStreamReader(System.in));
            st = null;
        }

        public String next() throws IOException {
            if(st == null || !st.hasMoreTokens())
                st = new StringTokenizer(infile.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return infile.readLine();
        }

        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());
        }

        public void close() throws IOException {
            infile.close();
        }
    }
}