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;

public final class CodeForces {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(br.readLine());
        while(t-->0) {
            int n = Integer.parseInt(br.readLine());
            char[] s1 = br.readLine().toCharArray();
            char[] s2 = br.readLine().toCharArray();
            int[] ans = solve(s1, s2, n);
            if(ans[0] == 0) {
                System.out.println(0);
            } else {
                StringBuilder sb = new StringBuilder();
                for(int i=0; i<ans.length; i++)
                    sb.append(ans[i]).append(" ");
                System.out.println(sb.toString());
            }
        }
        br.close();
    }

    private static int[] solve(char[] s1, char[] s2, int n) {
        if(n == 1) {
            int[] ans = new int[2];
            if(s1[0] == s2[0]) {
                return ans;
            } else {
                ans[0] = 1;
                ans[1] = 1;
                return ans;
            }
        }
        ArrayList<Integer> list = new ArrayList<>();
        for(int i=n-1; i>=0; i--) {
            if(i == 0) {
                if(s1[0] != s2[0]) {
                    list.add(1);
                }
            } else {
                if (s1[i] != s2[i]) {
                    if (s1[0] == s1[i]) {
                        list.add(i + 1);
                        for (int j = 0; j <= i; j++) {
                            if (s1[j] == '0')
                                s1[j] = '1';
                            else
                                s1[j] = '0';
                        }
                        for (int j = 0; j < (i+1) / 2; j++) {
                            char temp = s1[j];
                            s1[j] = s1[i - j];
                            s1[i - j] = temp;
                        }
                    } else {
                        if (s1[0] == '0')
                            s1[0] = '1';
                        else
                            s1[0] = '0';
                        list.add(1);
                        list.add(i+1);
                        for (int j = 0; j <= i; j++) {
                            if (s1[j] == '0')
                                s1[j] = '1';
                            else
                                s1[j] = '0';
                        }
                        for (int j = 0; j < (i+1) / 2; j++) {
                            char temp = s1[j];
                            s1[j] = s1[i - j];
                            s1[i - j] = temp;
                        }
                    }
                }
            }
        }
        if(list.size() == 0) {
            int[] ans = new int[1];
            return ans;
        } else {
            int[] ans = new int[list.size()+1];
            ans[0] = list.size();
            for(int i=0; i<list.size(); i++)
                ans[i+1] = list.get(i);
            return ans;
        }
    }
}