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.lang.*;
import java.io.*;
 
 
public class A
 
{
    class Pair<S extends Comparable<S>, T extends Comparable<T>> implements Comparable<Pair<S, T>> {
        S first;
        T second;
    
        Pair(S f, T s) {
            first = f;
            second = s;
        }

        @Override
        public int compareTo(Pair<S, T> o) {
            int t = first.compareTo(o.first);
            if (t == 0) return second.compareTo(o.second);
            return t;
        }
    
        @Override
        public int hashCode() {
            return (31 + first.hashCode()) * 31 + second.hashCode();
        }
    
        @Override
        public boolean equals(Object o) {
            if (!(o instanceof Pair)) return false;
            if (o == this) return true;
            Pair p = (Pair) o;
            return first.equals(p.first) && second.equals(p.second);
        }
    
        @Override
        public String toString() {
            return "Pair{" + first + ", " + second + "}";
        }
    }
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            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; 
        } 
    } 
    public static void main (String[] args) throws java.lang.Exception
    {
        try {
            System.setIn(new FileInputStream("input.txt"));
            System.setOut(new PrintStream(new FileOutputStream("output.txt")));
        } catch (Exception e) {
            System.err.println("Error");
        }
        
        FastReader sc = new FastReader();
        int t =sc.nextInt();
        PrintWriter out=new PrintWriter(System.out);
        while(t-->0){
            solve(sc,out);
        }
         out.close();
    }
    static void solve(FastReader sc,PrintWriter out) {
        int n = sc.nextInt();
        char a[] = sc.next().toCharArray();
        char b[] = sc.next().toCharArray();
        ArrayList<Integer> list = new ArrayList<>();
        int cnt =0;
        for(int i=n-1;i>=0;i--){
            if(a[i]!=b[i]){
                if(a[0]==b[i]){
                    list.add(1);
                    a[0]=a[i];
                    for(int j=0;j<=i;j++){
                        if(a[j]=='1'){
                            a[j]='0';
                        }
                        else{
                            a[j]='1';
                        }
                    }
                    list.add(i+1);
                    for(int j=0;j<(i+1)/2;j++){
                        char temp=a[j];
                        a[j]=a[i-j];
                        a[i-j]=temp;
                    }
                }
                else{
                    for(int j=0;j<=i;j++){
                        if(a[j]=='1'){
                            a[j]='0';
                        }
                        else{
                            a[j]='1';
                        }
                    }
                    list.add(i+1);
                    for(int j=0;j<(i+1)/2;j++){
                        char temp=a[j];
                        a[j]=a[i-j];
                        a[i-j]=temp;
                    }
                }
            }
        }
        out.print(list.size()+" ");
        for(int i=0;i<list.size();i++){
            out.print(list.get(i)+" ");
        }
        out.println();

        
    }
}