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.*;
import java.util.*;

public class Main{
	static void main() throws Exception{
		int n=sc.nextInt();
		char[]a=sc.nextLine().toCharArray(),b=sc.nextLine().toCharArray();
		int cnt=0;
		StringBuilder ans=new StringBuilder();
		int toggle=0;
		int reverse=-1;
		for(int i=n-1;i>0;i--) {
			int idx;
			if(reverse==-1) {
				reverse=0;
				idx=i;
			}
			else {
				int sign=toggle==1?-1:1;
				idx=reverse+sign*i;
			}
			char ai=a[idx];
			if(toggle==1) {
				ai=(ai=='0'?'1':'0');
			}
			if(ai==b[i])continue;
			if(b[i]==a[0]) {
				cnt++;
				ans.append(1+" ");
			}
			a[0]=ai=='0'?'1':'0';
			cnt++;
			ans.append((i+1)+" ");
			int sign=toggle==1?-1:1;
			toggle^=1;
			reverse+=sign*i;
		}
		if(a[0]!=b[0]) {
			cnt++;
			ans.append(1+" ");
		}
		pw.print(cnt+" ");
		pw.println(ans);
	}
	public static void main(String[] args) throws Exception{
		sc=new MScanner(System.in);
		pw = new PrintWriter(System.out);
		int tc=1;
		tc=sc.nextInt();
		while(tc-->0)
			main();
		pw.flush();
	}
	static PrintWriter pw;
	static MScanner  sc;
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]inArr=new int[n];for(int i=0;i<n;i++)inArr[i]=nextInt();
	        return inArr;
		}
		public long[] longArr(int n) throws IOException {
	        long[]inArr=new long[n];for(int i=0;i<n;i++)inArr[i]=nextLong();
	        return inArr;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]inArr=new int[n];for(int i=0;i<n;i++)inArr[i]=nextInt();
	        shuffle(inArr);
	        Arrays.sort(inArr);
	        return inArr;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]inArr=new long[n];for(int i=0;i<n;i++)inArr[i]=nextLong();
	        shuffle(inArr);
	        Arrays.sort(inArr);
	        return inArr;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]inArr=new Integer[n];for(int i=0;i<n;i++)inArr[i]=nextInt();
	        return inArr;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]inArr=new Long[n];for(int i=0;i<n;i++)inArr[i]=nextLong();
	        return inArr;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void shuffle(int[]inArr) {
		for(int i=0;i<inArr.length;i++) {
			int idx=(int)(Math.random()*inArr.length);
			int tmp=inArr[i];
			inArr[i]=inArr[idx];
			inArr[idx]=tmp;
		}
	}
	static void shuffle(long[]inArr) {
		for(int i=0;i<inArr.length;i++) {
			int idx=(int)(Math.random()*inArr.length);
			long tmp=inArr[i];
			inArr[i]=inArr[idx];
			inArr[idx]=tmp;
		}
	}
}