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.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class TaskA {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st;
        PrintWriter pw = new PrintWriter(System.out);
        
        try {
            int t = Integer.parseInt(br.readLine());
            while(t-->0) {
                int n = Integer.parseInt(br.readLine());
                char[] ca = br.readLine().toCharArray();
                char[] cb = br.readLine().toCharArray();
                int[] a = new int[n];
                int[] b = new int[n];
                for(int i=0 ; i<n ; i++) {
                    a[i] = ca[i]-'0';
                    b[i] = cb[i]-'0';
                }

                int turn = 0;
                int l = 0;
                int r = n-1;
                ArrayList<Integer> al = new ArrayList<>();
                for(int i=n-1 ; i>=0 ; i--) {
                    if(turn%2 == 0) {
                        if(a[r] != b[i]) {
                            if(a[l] == b[i]) {
                                al.add(1);
                                al.add(i+1);
                            }
                            else {
                                al.add(i+1);
                            }
                            turn++;
                            l++;
                        }
                        else r--;
                    }
                    else {
                        if((1-a[l]) != b[i]) {
                            if((1-a[r]) == b[i]) {
                                al.add(1);
                                al.add(i+1);
                            }
                            else {
                                al.add(i+1);
                            }
                            turn++;
                            r--;
                        }
                        else l++;
                    }
                }

                pw.print(al.size() + " ");
                for(int x: al) {
                    pw.print(x + " ");
                }
                pw.println();
            }
        }
        finally {
            pw.flush();
            pw.close();
        }
    }
}