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.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        
        var sc = new Scanner(System.in);
    
        int T = Integer.parseInt(sc.next());
        var pw = new PrintWriter(System.out);
        for(int t = 0; t < T; t++){
            int n = Integer.parseInt(sc.next());
            String c = sc.next();
            String d = sc.next();
            var b = new int[n];
            var deque = new ArrayDeque<Integer>();
            for(int i = 0; i < n; i++){
                if(c.charAt(i) == '1'){
                    deque.addLast(1);
                }else{
                    deque.addLast(0);
                }
                if(d.charAt(i) == '1') b[i] = 1;
            }
            int k = 0;
            var p = new ArrayList<Integer>();
            var e = new int[n];
            boolean reverse = false;
            for(int i = n; i > 0; i--){
                if(reverse){
                    if(deque.removeLast() != b[i-1]){
                        k++;
                        p.add(1);
                    }
                }else{
                    if(deque.removeFirst() == b[i-1]){
                        k++;
                        p.add(1);
                    }
                }
                k++;
                p.add(i);
                reverse = !reverse;
            }
            pw.print(k + " ");
            for(int i = 0; i < k; i++){
                pw.print(p.get(i) + " ");
            }
            pw.println();
        }
        pw.flush();
    }
}