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.InputStreamReader;
import java.util.ArrayList;
import java.util.List;

public class T2 {

    public static void main(String[] args) {
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            int t = Integer.parseInt(br.readLine());
            for (int t_ = 0; t_ < t; t_++) {
                int n = Integer.parseInt(br.readLine());
                String a = br.readLine();
                String b = br.readLine();
                solve(a,b);
            }
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private static StringBuilder _a;
    private static StringBuilder _aOrder = new StringBuilder();

    private static void transform(int l) {
//        StringBuilder s = new StringBuilder(_a.substring(0, l));
//        s.reverse();
//        for (int i = 0; i < l; i++) {
//            s.setCharAt(i, s.charAt(i) == '1' ? '0' : '1');
//        }
//        _a = s.append(_a.substring(l,_a.length()));
//
//        StringBuilder sOrder = new StringBuilder(_aOrder.substring(0, l));
//        sOrder.reverse();
//        _aOrder = sOrder.append(_aOrder.substring(l, _aOrder.length()));
//        System.out.printf("flipping %d: %s\n", l, _a.toString());
//        System.out.printf("order: %s\n", _aOrder.toString());
//        System.out.println("###");
    }

    public static void solve(String a, String b) {
        _aOrder = new StringBuilder();
        for (int i = 0; i < a.length(); i++) {
            _aOrder.append(i);
        }
        _a = new StringBuilder(a);
        int count = 0;
        StringBuilder result = new StringBuilder();
        int bottom = 0;
        int top = a.length()-1;
        boolean flipped = false;
        for (int i = b.length()-1; i >= 1; i--) {
            if (!flipped) {
                if (b.charAt(i) == a.charAt(top)) {
                    top--;
                    continue;
                }
                if (a.charAt(bottom)==b.charAt(i)) {
                    count++;
                    result.append(1).append(" ");
                    transform(1);
                }
                result.append(i+1).append(" ");
                transform(i+1);
                flipped = true;
                count++;
                bottom++;
            } else {
                if (b.charAt(i)!=a.charAt(bottom)) {
                    bottom++;
                    continue;
                }
                if (a.charAt(top)!=b.charAt(i)) {
                    count++;
                    result.append(1).append(" ");
                    transform(1);
                }
                result.append(i+1).append(" ");
                transform(i+1);
                flipped = false;
                count++;
                top--;
            }
        }
        if (flipped) {
            if (a.charAt(top)==b.charAt(0)) {
                count++;
                result.append(1);
                transform(1);
            }
        } else {
            if (a.charAt(bottom)!=b.charAt(0)) {
                count++;
                result.append(1);
                transform(1);
            }
        }
        System.out.print(count + " ");
        System.out.println(result.toString());
    }
}