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.BitSet;
import java.util.List;
import java.util.Scanner;

public class ProblemC1_658 {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int tt = 0; tt < t; tt++) {
            int n = sc.nextInt();
            sc.nextLine();
            String a = sc.nextLine();
            String b = sc.nextLine();
            List<Integer> operations = new ArrayList<>();
            int current = n-1;
            BitSet c = new BitSet(n);
            for(int i = 0; i < n; i++) if(a.charAt(i) == '1') c.set(i);
            while (current >= 0) {
                char aChar = c.get(current)? '1' : '0';
                char sChar = c.get(0)? '1' : '0';
                if(aChar != b.charAt(current)) {
                    if(sChar == b.charAt(current)) {
                        operations.add(1);
                        c.flip(0);
                        operations.add(current+1);
                        c.flip(0, current+1);
                        int start = 0;
                        int end = current;
                        while (start < end) {
                            boolean e = c.get(start);
                            c.set(start, c.get(end));
                            c.set(end, e);
                            start++;
                            end--;
                        }
                    } else {
                        operations.add(current+1);
                        c.flip(0, current+1);
                        int start = 0;
                        int end = current;
                        while (start < end) {
                            boolean e = c.get(start);
                            c.set(start, c.get(end));
                            c.set(end, e);
                            start++;
                            end--;
                        }
                    }
                }
                current--;
            }


            System.out.print(operations.size() + " ");
            for(int i = 0; i < operations.size(); i++) {
                System.out.print(operations.get(i));
                if(i != operations.size()-1) {
                    System.out.print(" ");
                }
            }
            System.out.println();
        }
    }
}