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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Q3 {
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		MScanner s = new MScanner(System.in);
		int t = s.nextInt();
		while (t-- > 0) {
			int n = s.nextInt();
			char [] str1 = s.next().toCharArray();
			char []str2 = s.next().toCharArray();
			ArrayList<Integer> ans = new ArrayList<Integer>();
		        for(int i = n - 1; i >= 0; i--){
		            if(str1[i] == str2[i])
		                continue;
		            else{
		                if(str1[0] != str1[i]){
		                    ans.add(1);
		                    if(str1[0] == '1')
		                        str1[0] = '0';
		                    else
		                        str1[0] = '1';
		                }
		                ans.add(i + 1);
		                for(int j = 0; j <= i; j++){
		                    if(str1[j] == '0')
		                        str1[j] = '1';
		                    else
		                        str1[j] = '0';
		                }
		                for(int j = 0; j <= i / 2; j++){
		                	char temp = str1[j];
		                	str1[j]= str1[i-j];
		                	str1[i-j]=temp;
		                }
		            }
		        }
		        System.out.print(ans.size()+" ");
		        for(int i = 0; i < ans.size(); i++){
		            System.out.print(ans.get(i)+" ");
		        }
		        System.out.println();
		}
	}

	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[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public long[] longArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		public int[] intSortedArr(int n) throws IOException {
			int[] in = new int[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public long[] longSortedArr(int n) throws IOException {
			long[] in = new long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			shuffle(in);
			Arrays.sort(in);
			return in;
		}

		public Integer[] IntegerArr(int n) throws IOException {
			Integer[] in = new Integer[n];
			for (int i = 0; i < n; i++)
				in[i] = nextInt();
			return in;
		}

		public Long[] LongArr(int n) throws IOException {
			Long[] in = new Long[n];
			for (int i = 0; i < n; i++)
				in[i] = nextLong();
			return in;
		}

		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[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * in.length);
			int tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}

	static void shuffle(long[] in) {
		for (int i = 0; i < in.length; i++) {
			int idx = (int) (Math.random() * in.length);
			long tmp = in[i];
			in[i] = in[idx];
			in[idx] = tmp;
		}
	}
}