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.*;

public class file {

    private static final Scanner scn = new Scanner(System.in);

   
    public static void foo(int cas){
        int n = scn.nextInt();
        String a = scn.next();
        String b = scn.next();
        ArrayList<Integer> lis = new ArrayList<>();
        Stack<Integer> stk = new Stack<>();
        for (int i = 0; i < n-1; i++) {
            if (a.charAt(i) != a.charAt(i+1)){
                lis.add(i+1);
            }
            if (b.charAt(i) != b.charAt(i+1)) {
                stk.push(i+1);
            }
        }
        if (a.charAt(n-1) != '0') lis.add(n);
        if (b.charAt(n-1) != '0') stk.push(n);
        System.out.printf("%d ", lis.size()+stk.size());
        for (int k : lis) {
            System.out.printf("%d ", k);
        }
        while (!stk.isEmpty()) {
            System.out.printf("%d ", stk.pop());
        }
        System.out.println();
        
    }


    public static void main(String[] args) {

        int t = scn.nextInt();
        for (int i = 0; i < t; i++) {
            foo(i);
        }
    }
}