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.*;
import java.util.*;
public class Ishu
{
    static Scanner scan = new Scanner(System.in);
    static BufferedWriter output = new BufferedWriter(new OutputStreamWriter(System.out)); 
    static void tc() throws Exception
    {
    int n = scan.nextInt();
    String a = scan.next();
    String b = scan.next();
    int i,j;
    int l,r;
    List<Integer> ans = new ArrayList<Integer>();
    j = n - 1;
    r = n - 1;
    i = 0;
    l = 0;
    int cnt = 0;
    while(true)
        {
        int t = a.charAt(j) - '0';
        t = (t + cnt % 2) % 2;
        if(i < j)
            {
            if(t == b.charAt(r) - '0')
                {
                --j;
                --r;
                }
            else
                {
                if(t == 1 && b.charAt(r) == '0')
                    {
                    int temp = a.charAt(i) - '0';
                    temp = (temp + cnt % 2) % 2;
                    if(temp == 1)
                        {
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i + 1;
                        i = temp;
                        }
                    else
                        {
                        ans.add(1);
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i + 1;
                        i = temp;
                        }
                    }
                else if(t == 0 && b.charAt(r) == '1')
                    {
                    int temp = a.charAt(i) - '0';
                    temp = (temp + cnt % 2) % 2;
                    if(temp == 0)
                        {
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i + 1;
                        i = temp;
                        }
                    else
                        {
                        ans.add(1);
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i + 1;
                        i = temp;
                        }
                    }
                --r;
                }
            }
        else if(j < i)
            {
            if(t == b.charAt(r) - '0')
                {
                ++j;
                --r;
                }
            else
                {
                if(t == 1 && b.charAt(r) == '0')
                    {
                    int temp = a.charAt(i) - '0';
                    temp = (temp + cnt % 2) % 2;
                    if(temp == 1)
                        {
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i - 1;
                        i = temp;
                        }
                    else
                        {
                        ans.add(1);
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i - 1;
                        i = temp;
                        }
                    }
                else if(t == 0 && b.charAt(r) == '1')
                    {
                    int temp = a.charAt(i) - '0';
                    temp = (temp + cnt % 2) % 2;
                    if(temp == 0)
                        {
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i - 1;
                        i = temp;
                        }
                    else
                        {
                        ans.add(1);
                        ans.add((r + 1));
                        ++cnt;
                        temp = j;
                        j = i - 1;
                        i = temp;
                        }
                    }
                --r;
                }
            }
        else if(j == i)
            {
            if((t == 1 && b.charAt(r) == '0') || (t == 0 && b.charAt(r) == '1'))
                {
                ans.add(1);
                }
            break;
            }
        }
    output.write(ans.size() + " ");
    for(i=0;i<ans.size();++i)
        output.write(ans.get(i) + " ");
    output.write("\n");  
    output.flush();
    }
    public static void main(String[] args) throws Exception
    {
    int t = 1;
    t = scan.nextInt();
    while(t-- > 0)
        tc();
    }
}