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:
/*
-------------------------------------------------------------------
* @Name:           1382C1 Prefix Flip (Easy Version)
* @Author:         Yanan
* @Create Time:    2020/7/22 23:40:20  (UTC+08:00)
* @Url:            https://codeforces.com/contest/1382/problem/C1
* @Description:    
-------------------------------------------------------------------
*/

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

public class CF_1382C1_PrefixFlipEasyVersion
{
    public static void main(String[] args) throws IOException
    {
        // if (System.getProperty("ONLinE_JUDGE") == null)
        // {
        // // redirect stdin/stdout to local file
        // System.setIn(new FileInputStream(new
        // File("CF_1382C1_PrefixFlipEasyVersion.in")));
        // System.setOut(new PrintStream(new
        // File("CF_1382C1_PrefixFlipEasyVersion.out")));
        // }

        Scanner in = new Scanner(System.in);
        PrintStream out = System.out;

        new CF_1382C1_PrefixFlipEasyVersion_Solution().Solve(in, out);

        in.close();
        out.close();
    }
}

class CF_1382C1_PrefixFlipEasyVersion_Solution
{
    public void Solve(Scanner in, PrintStream out)
    {
        /*
         * int n = in.nextint(); // read input as integer long k = in.nextLong(); //
         * read input as long double d = in.nextDouble(); // read input as double String
         * str = in.next(); // read input as String String s = in.nextLine(); // read
         * whole line as String
         */
        // out.println("OK");
        int t = in.nextInt();
        for (int i = 0; i < t; ++i)
        {
            int n = in.nextInt();
            String a = in.next(), b = in.next();
            var fans = new ArrayList<Integer>();
            if (n == 1)
            {
                if (a.equals(b) == false)
                {
                    out.println("1 1");
                    // cout<<1<<' '<<1<<'\n';
                } else
                {
                    out.println(0);
                }
                continue;
            }
            for (int j = 1, ss = a.length(); j < ss; ++j)
            {
                if (a.charAt(j) != a.charAt(j - 1))
                {
                    fans.add(j);
                }
                if (j == ss - 1)
                {
                    if (a.charAt(j) == '1')
                    {
                        fans.add(j + 1);
                    }
                }
            }
            var sans = new ArrayList<Integer>();
            for (int j = 1, ss = b.length(); j < ss; ++j)
            {
                if (b.charAt(j) != b.charAt(j - 1))
                {
                    sans.add(j);
                }
                if (j == ss - 1)
                {
                    if (b.charAt(j) == '1')
                    {
                        sans.add(j + 1);
                    }
                }
            }
            Collections.reverse(sans);
            out.print(fans.size() + sans.size());
            for (int j = 0; j < fans.size(); ++j)
            {
                out.print(' ');
                out.print(fans.get(j));
            }
            for (int j = 0; j < sans.size(); ++j)
            {
                out.print(' ');
                out.print(sans.get(j));
            }
            out.println();
        }
    }
}