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.util.*;
import java.util.stream.*;
import java.io.*;
import java.math.*;

public class Main { 
    
    static boolean FROM_FILE = false;
    
    static boolean LOCAL = System.getProperty("ONLINE_JUDGE") == null;

    static class FastReader { 
        BufferedReader br; 
        StringTokenizer st; 
        public FastReader() { 
            if (FROM_FILE) {
                try {
                    br = new BufferedReader(new FileReader("input.txt")); 
                } catch (IOException error) {
                }   
            } else {
                br = new BufferedReader(new InputStreamReader(System.in));    
            }
        }
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine()); 
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        }
        int nextInt() { 
            return Integer.parseInt(next()); 
        }
        long nextLong() { 
            return Long.parseLong(next()); 
        }
  
        double nextDouble() { 
            return Double.parseDouble(next()); 
        } 
        String nextLine() { 
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
    static int max(int... nums) {
        int res = Integer.MIN_VALUE;
        for (int num: nums) res = Math.max(res, num);
        return res;
    }
    static int min(int... nums) {
        int res = Integer.MAX_VALUE;
        for (int num: nums) res = Math.min(res, num);
        return res;
    }
    static long max(long... nums) {
        long res = Long.MIN_VALUE;
        for (long num: nums) res = Math.max(res, num);
        return res;
    }
    static long min(long... nums) {
        long res = Long.MAX_VALUE;
        for (long num: nums) res = Math.min(res, num);
        return res;
    }
    
    static FastReader fr = new FastReader();
    static PrintWriter out;
    
    public static void main(String[] args) { 
        if (FROM_FILE) {
            try {
                out = new PrintWriter(new FileWriter("output.txt"));
            } catch (IOException error) {
                
            }
        } else {
            out = new PrintWriter(new OutputStreamWriter(System.out));
        }
        new Main().run();
        out.flush();
        out.close();
    } 
    
    void reverse(char[] s, int a, int b) {
        while (a < b) {
            char tmp = s[a];
            s[a] = s[b];
            s[b] = tmp;
            s[a] = s[a] == '1' ? '0' : '1';
            s[b] = s[b] == '1' ? '0' : '1';
            a += 1; b -= 1;
        }
        if (a == b) s[a] = s[a] == '1' ? '0' : '1';
    }
    
    void run() {
        int t = fr.nextInt();
        while (t-- > 0) {
            int n = fr.nextInt();
            char[] a = fr.nextLine().toCharArray(), b = fr.nextLine().toCharArray();
            char[] c = Arrays.copyOf(a, n);
            List<Integer> res = new ArrayList<>();
            for (int i = n - 1; i > 0; i -= 1) {
                if (b[i] == a[i]) continue;
                if (b[i] != a[0]) {
                    res.add(i + 1);
                    reverse(a, 0, i);
                } else {
                    res.add(1);
                    a[0] = a[0] == '1' ? '0' : '1';
                    res.add(i + 1);
                    reverse(a, 0, i);
                }
            }
            if (a[0] != b[0]) res.add(1);
            for (int num : res) {
                reverse(c, 0, num - 1);
                // out.println(num + " " + String.valueOf(c));
            }
            // out.println(res);
            // out.println(String.valueOf(b));
            out.println(res.size() + " " + res.stream().map(e -> "" + e).collect(Collectors.joining(" ")));
        }
    }
}