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:
/**
 * ******* Created  on 21/7/20 7:58 PM*******
 */

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

public class C1382 implements Runnable {

    private static final int MAX = (int) (1E5 + 5);
    private static final int MOD = (int) (1E9 + 7);
    private static final long Inf = (long) (1E14 + 10);
    private static final double eps = (double) (1E-9);
    char[] ansC;
    private void solve() throws IOException {
        int t = 1;
        t = reader.nextInt();
        while (t-- > 0) {
            int n = reader.nextInt();
            String a = reader.next();
            String b = reader.next();
            ansC = new char[n];
            boolean flag = false;
            List<Integer> ans = new ArrayList<>();
            for(int i = a.length()-1, j =b.length()-1, k=0;j>=0; j--){

                if(a.charAt(i) == b.charAt(j) && !flag){
                    ansC[j] = b.charAt(j);
                    i--;
                    continue;
                }
                if(a.charAt(k) != b.charAt(j) && flag ){
                    ansC[j] =b.charAt(j);
                    k++;
                    continue;
                }

                if(flag){
                        char y = check(a,b, i,j,ans, flag);
                        ansC[j] = y;
                        i--;
                }else{
                        ansC[j]= check(a,b, k,j,ans, flag);
                        k++;
                }
                flag = !flag;
            }

            writer.print(ans.size()+" ");
            for(int a1 : ans)writer.print( (a1+1) +" ");
            writer.println();
          //  writer.println(ansC);
        }
    }

    private char check(String a, String b, int i, int j, List<Integer> ans, boolean flag) {
        char re = 'a';
        if(flag)
            if(b.charAt(j) == a.charAt(i) || j==0){
                ans.add(j);
                re = a.charAt(i)=='1'?'1':'0';
            }else{
                ans.add(0);
                ans.add(j);
                re = a.charAt(i)=='1'?'0':'1';
            }
        else
            if(b.charAt(j) != a.charAt(i) || j ==0){
                ans.add(j);
                re = a.charAt(i)=='1'?'0':'1';
            }else{
                ans.add(0);
                ans.add(j);
                re = a.charAt(i)=='1'?'1':'0';
            }
            return re;
    }

    public static void main(String[] args) throws IOException {
        try (Input reader = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            new C1382().run();
        }
    }

    StandardInput reader;
    PrintWriter writer;

    @Override
    public void run() {
        try {
            reader = new StandardInput();
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }


    interface Input extends Closeable {
        String next() throws IOException;

        String nextLine() throws IOException;

        default int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        default long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        default double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        default int[] readIntArray() throws IOException {
            return readIntArray(nextInt());
        }

        default int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        default long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextLong();
            }
            return array;
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }

        @Override
        public String nextLine() throws IOException {
            return reader.readLine();
        }
    }

}