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.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.Locale;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) throws Exception {
        try (BufferedInputStream in = new BufferedInputStream(System.in);
             PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out))) {

            Scanner sc = new Scanner(in).useLocale(Locale.US);

            int T = sc.nextInt();
            for (int t = 0; t < T; t++) {
                sc.nextInt();
                char[] a = sc.next().toCharArray();
                char[] b = sc.next().toCharArray();

                List<Integer> ps = new ArrayList<>();
                solve(a, b, 0, a.length, b.length, ps);

                out.println(ps.size());
                for (Integer p : ps) out.print(p + 1 + " "); out.println();
            }
        }
    }
    
    private static void solve(char[] a, char[] b, int as, int ae, int bl, List<Integer> ps) {
        int signum = (int) Math.signum(as - ae);
        
        for (int i = 1; i <= bl; i++) {
            if (!eq(b[bl - i], a[ae + signum * i], signum)) {
                if (eq(b[bl - i], a[as], signum)) {
                    ps.add(0);
                }
                ps.add(bl - i);

                solve(a, b, ae + signum * i, as, bl - i, ps);
                return;
            }
        }
    }

    private static boolean eq(char a, char b, int signum) {
        return (signum < 0) == (a == b);
    }
}