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.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.io.*;

public class StringMan {
	static char[] a;
	static StringBuilder sb;
	static ArrayList<Integer> sb2;
	static int c;

	public static void main(String[] args) throws NumberFormatException, IOException, InterruptedException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int t = sc.nextInt();
		while (t-- > 0) {
			sb = new StringBuilder();
			sb2=new ArrayList<Integer>();
			c = 0;
			int n = sc.nextInt();
			String str = sc.nextLine();
			a = str.toCharArray();
			str = sc.nextLine();
			char[] b = str.toCharArray();
			// System.out.println(Arrays.toString(a));

//			for (int i = b.length - 1; i >= 0; i--) {
//				if (a[i] != b[i]) {
//					if (b[i] == a[0]) {
//						change(1);
//					}
//					change(i + 1);
//				}
//			}
//			
//			if (sb.length() != 0) {
//				String s = sb.substring(0, sb.length() - 1);
//				pw.println(c + " " + s);
//			}else {
//				pw.println(c);
//			}
			for (int i = 0; i < a.length-1; i++) {
				if(a[i]!=a[i+1]) {
					change(i+1);
				}
			}
			if(a[a.length-1]=='1')
				change(a.length);
		//	System.out.println(sb);
			for (int i = 0; i < a.length-1; i++) {
				if(b[i]!=b[i+1]) {
					change2(i+1);
				}
			}
			if(b[b.length-1]=='1')
				change2(a.length);
			Collections.reverse(sb2);
			for (Integer x : sb2) {
				sb.append(x+" ");
			}
			if (sb.length() != 0) {
				String s = sb.substring(0, sb.length() - 1);
				pw.println(c + " " + s);
			}else {
				pw.println(c);
			}
		}
		pw.close();
	}

	static void change(int n) {
		sb.append(n + " ");
		c++;
	}
	static void change2(int n) {
		sb2.add(n);
		c++;
	}

	static void shuffleArray(int[] ar) {
		// If running on Java 6 or older, use `new Random()` on RHS here
		Random rnd = ThreadLocalRandom.current();
		for (int i = ar.length - 1; i > 0; i--) {
			int index = rnd.nextInt(i + 1);
			// Simple swap
			int a = ar[index];
			ar[index] = ar[i];
			ar[i] = a;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < arr.length; i++)
				arr[i] = nextInt();
			return arr;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}

}