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:
// package com.company;
import java.util.*;
import java.lang.*;
import java.io.*;
//****Use Integer Wrapper Class for Arrays.sort()****
public class EE3 {
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String[] Args)throws Exception{
        FastReader scan=new FastReader(System.in);
        int t=1;
        t=scan.nextInt();
        while(t-->0){
            int n=scan.nextInt();
            String a=scan.next();
            String b=scan.next();
            ArrayList<Integer> ops=new ArrayList<>();
            if(n==1) {
                ops.add(1);
                if(a.charAt(0)==b.charAt(0)){
                    ops.add(1);
                }
            }else{
                for (int i = 0; i < n; i++) {
                    if (a.charAt(i) != b.charAt(i)) {
                        if (i == n - 1) {
                            ops.add((i + 1));
                            ops.add(1);
                            ops.add((i + 1));
                        } else {
                            if (a.charAt(i + 1) != b.charAt(i + 1)) {
                                if(a.charAt(i)!=a.charAt(i+1)) {
                                    if (i == 0) {
                                        ops.add(1);
                                        ops.add(2);
                                        ops.add(1);
                                        i++;
                                    } else {
                                        ops.add(i);
                                        ops.add(i + 1);
                                        ops.add(i + 2);
                                        ops.add(i + 1);
                                        i++;
                                    }
                                }else{
                                    if(i==0){
                                        ops.add(2);
                                        i++;
                                    }else{
                                        ops.add(i+2);
                                        ops.add(2);
                                        ops.add(i+2);
                                        i++;
                                    }
                                }
                            } else {
                                ops.add((i + 1));
                                ops.add(1);
                                ops.add((i + 1));
                            }
                        }
                    }
                }
            }
            out.print(ops.size()+" ");
            for(Integer i:ops){
                out.print(i+" ");
            }
            out.println();
        }
        out.flush();
        out.close();
    }
    static class FastReader {

        byte[] buf = new byte[2048];
        int index, total;
        InputStream in;

        FastReader(InputStream is) {
            in = is;
        }

        int scan() throws IOException {
            if (index >= total) {
                index = 0;
                total = in.read(buf);
                if (total <= 0) {
                    return -1;
                }
            }
            return buf[index++];
        }

        String next() throws IOException {
            int c;
            for (c = scan(); c <= 32; c = scan()) ;
            StringBuilder sb = new StringBuilder();
            for (; c > 32; c = scan()) {
                sb.append((char) c);
            }
            return sb.toString();
        }

        int nextInt() throws IOException {
            int c, val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
        long nextLong() throws IOException {
            int c;
            long val = 0;
            for (c = scan(); c <= 32; c = scan()) ;
            boolean neg = c == '-';
            if (c == '-' || c == '+') {
                c = scan();
            }
            for (; c >= '0' && c <= '9'; c = scan()) {
                val = (val << 3) + (val << 1) + (c & 15);
            }
            return neg ? -val : val;
        }
    }
}
//