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 PrefixFlip {

    static List<Integer> solve(int[] a, int[] b) {
        int i = a.length - 1;
        List<Integer> moves = new ArrayList<>(a.length * 2);
        while(i >= 0) {
            if(a[i] == b[i]) {
                i--;
                continue;
            }
            if(a[0] == b[i] && i != 0) {
                moves.add(1);
                a[0] = a[0] ^ 1;
            }
            moves.add(i + 1);
            for(int j = 0; j <= i / 2; j++) {
                int t = a[i - j];
                a[i - j] = a[j] ^ 1;
                a[j] = t ^ 1;
            }
            i--;
        }
        return moves;
    }

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        final int tests = Integer.parseInt(reader.readLine());
        for(int test = 0; test < tests; test++) {
            int n = Integer.parseInt(reader.readLine());
            String aStr = reader.readLine();
            String bStr = reader.readLine();

            int[] a = new int[n];
            int[] b = new int[n];

            for(int i = 0; i < n; i++) {
                a[i] = Integer.parseInt(aStr.charAt(i) + "");
                b[i] = Integer.parseInt(bStr.charAt(i) + "");
            }
            List<Integer> res = solve(a, b);
            System.out.print(res.size() + " ");
            for(int i = 0; i < res.size(); i++) {
                System.out.print(res.get(i));
                if(i != res.size() - 1) {
                    System.out.print(" ");
                }
            }
            if(test != tests - 1) {
                System.out.println();
            }
        }

    }
}