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.ArrayList;
import java.util.Scanner;

public class p3hard {
	static boolean flip;
	static int fInd;
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		
		int t = in.nextInt();
		for (int ti = 0; ti < t; ti++) {
			int N = in.nextInt();
			String a = in.next();
			String b = in.next();
			int opers = 0;
			ArrayList<Integer> seq = new ArrayList<>();
			flip = false;
			fInd = 0;
			int b1 = a.charAt(0)-'0';
			for (int i = N-1; i >= 1; i--) {
				if (apply(a, i) != b.charAt(i)-'0') {
					int req = b.charAt(i)-'0';
					if (b1 == req) {
						opers++;
						seq.add(1);
						b1 = 1-b1;
					}
					opers++;
					seq.add(i+1);
					b1 = 1-apply(a, i);
					fInd += flip?-i:i;
					flip = !flip;
				}
			}
			if (b1 != b.charAt(0)-'0') {
				opers++;
				seq.add(1);
			}
			System.out.print(opers);
			for (int x : seq) System.out.print(" "+x);
			System.out.println();
		}
		
		in.close();

	}
	
	static int apply(String a, int x) {
		int i = flip ? fInd-x : fInd+x;
		int v = a.charAt(i)-'0';
		return flip ? 1-v : v;
	}
}