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.io.*;
public class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw=new PrintWriter(System.out);
        int t=Integer.parseInt(br.readLine());
        while(t-->0)
        {
            int n=Integer.parseInt(br.readLine());
            char c1[]=br.readLine().toCharArray();
            char c2[]=br.readLine().toCharArray();
            ArrayList<Integer> al=new ArrayList<>(); 
            /*int i;
            for(i=0;i<n;i++)
            {
                if(arr[i]!=1)
                break;
            }
            if(i!=n)
            {
                al.add(i);
                for(;i<n;i++)
                {
                    int j;
                    for(j=i;j<n;j++)
                    {
                        if(arr[j]==0)
                        break;
                    }
                    if(j!=n)
                    {
                        al.add(j);
                        int k;
                        for(k=j;k<n;k++)
                        {
                            if(arr[k]==1)
                            break;
                        }
                        al.add(k);
                        
                    }
                }
            }*/
            //ArrayList<Integer> o=new ArrayList<>();
            boolean take=true;
            int i;
            for(i=0;i<c1.length;i++)
            {
                if(c1[i]!='0')
                {
                    if(i>0)
                    al.add(i);
                    break;
                }
            }
            //int last=-1;
            //pw.println(al);
            for(;i<c1.length;i++)
            {
                if(c1[i]=='1')
                {
                    //o.add(i);
                    int j;
                    for(j=i+1;j<c1.length;j++)
                    {
                        if(c1[j]!='1')
                        break;
                    }
                    al.add(j);
                    i=j-1;
                }
                else
                {
                    int j;
                    for(j=i;j<c1.length;j++)
                    {
                        if(c1[j]!='0')
                        {
                            al.add(j);
                            //take=true;
                            break;
                        }
                    }
                    i=j-1;
                }
            }
            for(int j=c2.length-1;j>=0;j--)
            {
                if(c2[j]=='1')
                {
                    al.add(j+1);
                    if(j>0)
                    al.add(j);
                }
            }
            pw.print(al.size()+" ");
            for(int x:al)
            pw.print(x+" ");
            pw.println();
        }
        pw.flush();
        pw.close();
    }
}