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 cp;
import java.io.*;
import java.math.*;
import java.util.*;
public class Cf_three {
	long gcd(long a,long b) {if(b==0)return a;else return gcd(b,a%b);}
	void swap(long a,long b) {long temp=a;a=b;b=temp;}
	StringBuilder sb=new StringBuilder();
	BigInteger RES=new BigInteger("0");
//	StringBuilder temp=new StringBuilder(str[i-1]);
//	String rev=temp.reverse().toString(); convert sb to string
//	if(str[i].compareTo(rev)>=0)minn=0;-compare two Strings
	//(Initialize as string) - (a.add(b)) - (array initialized with null and not 0)
	Integer[] ARR=new Integer[5];
	//Integer sort-TLE-Initialize object elements i.e a[0].
	void divisor(long n,int start) {
		int cnt=0;for(int i=start;i<=Math.sqrt(n);i++) {
		if(n%i==0) {if(i==n/i)cnt++;else cnt+=2;}}}
	public static void main(String[] args) throws IOException {	
		PrintWriter out = new PrintWriter(System.out);
		Readers.init(System.in);
		Cf_three obj=new Cf_three();
		int t=Readers.nextInt();
		while(t-->0) {
			int n=Readers.nextInt();
			String s1=Readers.next();
			char[] p=new char[n];
			p=s1.toCharArray();
			String s2=Readers.next();
			int cnt=0;
			char[] q=new char[n];
			q=s2.toCharArray();
			char[] num= {0,1};
			int change=0;
			ArrayList<Integer> arr=new ArrayList<>();
			for (int i = n-1; i >=0; i--) {
		
				if(p[i]==q[i])continue;
				else {
//					System.out.println(change+"Oh"+i);
					
					if(p[0]==p[i]) {
						cnt=cnt+1;
						arr.add(i+1);
					}
					else {
						cnt=cnt+2;
						arr.add(1);
						arr.add(i+1);
						p[0]=p[i];
					}
					change++;
					char[] copy=new char[n];
					copy=Arrays.copyOf(p,n);
					for (int j = 0; j <=i; j++) {
						if(copy[i-j]=='0')p[j]='1';
						else p[j]='0';
					}
//					p[0]=q[i];
				}
				
				p[i]=q[i];
//				p[0]=q[i];
				
//				System.out.println(Arrays.toString(p));
			}
			System.out.print(cnt+" ");
			for (int i = 0; i < arr.size(); i++) {
				System.out.print(arr.get(i)+" ");
			}
			System.out.println();
		}
		out.flush();
	}
}
class Readers {
 
    static BufferedReader reader;
 
    static StringTokenizer tokenizer;
 
 
 
    /** call this method to initialize reader for InputStream */
 
    static void init(InputStream input) {
 
        reader = new BufferedReader(
 
                     new InputStreamReader(input) );
 
        tokenizer = new StringTokenizer("");
 
    }
 
 
 
    /** get next word */
 
    static String next() throws IOException {
 
        while ( ! tokenizer.hasMoreTokens() ) {
 
            //TODO add check for eof if necessary
 
            tokenizer = new StringTokenizer(
 
                   reader.readLine() );
 
        }
 
        return tokenizer.nextToken();
 
    }
 
 
 
    static int nextInt() throws IOException {
 
        return Integer.parseInt( next() );
 
    }
 
	
 
    static double nextDouble() throws IOException {
 
        return Double.parseDouble( next() );
 
    }
    
    
    static long nextLong() throws IOException{
    	
		return Long.parseLong(next());
	}
 
}