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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class LongInteger {

	public static void main(String[] args) throws NumberFormatException, IOException {

		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		int t = Integer.parseInt(reader.readLine());
		while (t-- > 0) {
			int n = Integer.parseInt(reader.readLine());
			//String input1 = reader.readLine();
			//String[] nk = input1.split(" ");
			//long k = Long.parseLong(nk[1]);
			/*String input2 = reader.readLine();
			String[] splits = input2.split(" ");
			int[] in = new int[splits.length];
			for( int i = 0; i < splits.length;i++){
				in[i] = Integer.parseInt(splits[i]);
			}*/
			String in = reader.readLine();
			String bin = reader.readLine();
			//solve(Integer.parseInt(splits[0]),Integer.parseInt(splits[1]),Integer.parseInt(splits[2]));
			//solve(in,bin);
			solve(in.split(""), bin.split(""));
		}
	}	

	private static void solve(String[] s, String[] t) {
		
		List<Integer> pref = new ArrayList<>();
		for(int i = 0; i < s.length; i++) {
			if(!s[i].equals(t[i])) {
				pref.add(i);
				pref.add(0);
				pref.add(i);
			}
		}
		
		System.out.print(pref.size());
		for(int i :pref) {
			System.out.print(" "+(i+1));
		}
		
		System.out.println();
		
		
	}
}