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.OutputStream;
    import java.io.IOException;
    import java.io.InputStream;
    import java.io.PrintWriter;
    import java.nio.channels.ClosedByInterruptException;
    import java.util.*;
    import java.io.IOException;
    import java.io.BufferedReader;
    import java.io.InputStreamReader;
    import java.io.InputStream;

    /*
    @author kalZor
     */
    public class TaskB {
        public static void main(String[] args) {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastReader in = new FastReader(inputStream);
            PrintWriter out = new PrintWriter(outputStream);
            Solver solver = new Solver();
            int testCount = 1;
            testCount = Integer.parseInt(in.next());
            for (int i = 1; i <= testCount; i++)
                solver.solve(i, in, out);
            out.close();
        }

        static class Solver {
            public void fastSort(int[] a){
                Random random = new Random();
                for(int i=0;i<a.length;i++){
                    int nextInd = random.nextInt(a.length);
                    int temp = a[nextInd];
                    a[nextInd] = a[i];
                    a[i] = temp;
                }
                Arrays.sort(a);
                return;
            }
            public int gcd(int a,int b){
                if(a==0) return b;
                else return gcd(b%a,a);
            }
            public void solve(int testNumber, FastReader in, PrintWriter out) {
                int n = in.nextInt();
                String a = in.next();
                String b = in.next();
                ArrayList<Integer> ans = new ArrayList<>();
                if(a.charAt(0)!=b.charAt(0)){
                    ans.add(1);
                }
                for(int i=1;i<n;i++){
                    if(a.charAt(i)!=b.charAt(i)){
                        ans.add(i+1);
                        ans.add(1);
                        ans.add(i+1);
                    }
                }
                out.print(ans.size()+" ");
                for(int x:ans) out.print(x+" ");
                out.println();
            }
        }

        static class FastReader {
            BufferedReader br;
            StringTokenizer st;

            public FastReader(InputStream stream){
                br = new BufferedReader(new
                        InputStreamReader(stream));
            }

            public String next(){
                while (st == null || !st.hasMoreElements()){
                    try{
                        st = new StringTokenizer(br.readLine());
                    }
                    catch (IOException e){
                        e.printStackTrace();
                    }
                }
                return st.nextToken();
            }

            public int nextInt(){
                return Integer.parseInt(next());
            }

            public long nextLong(){
                return Long.parseLong(next());
            }

            public double nextDouble(){
                return Double.parseDouble(next());
            }

            public String nextLine(){
                String str = "";
                try{
                    str = br.readLine();
                }
                catch (IOException e){
                    e.printStackTrace();
                }
                return str;
            }

            public int[] nextArray(int n) {
                int[] a=new int[n];
                for (int i=0; i<n; i++) a[i]=nextInt();
                return a;
            }
        }
    }