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.*;
import java.util.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(in.readLine());
        char[] arr = { '1', '0', '0', '1', '0'};
        for(int rc=0; rc<t; rc++) {
            int n = Integer.parseInt(in.readLine());
            char[] a = in.readLine().toCharArray();
            char[] b = in.readLine().toCharArray();
            ArrayList<Integer> lis = new ArrayList<>();
            for(int i=n-1; i>=0; i--) {
                if(a[i]==b[i]) continue;
                if(a[0]==b[i]) {
                    lis.add(1);
                    a = flip(a,0);
                }
                lis.add(i+1);
                a = flip(a,i);
            }
            System.out.print(lis.size()+" ");
            for(int i:lis) System.out.print(i+" ");
            System.out.println();
        }
    }
    public static char[] flip(char[] orig, int i) {
        char[] flipped = new char[orig.length];
        for(int j=0; j<=i; j++) {
            flipped[j] = orig[i-j];
            if(flipped[j]=='0') flipped[j]='1';
            else flipped[j]='0';
        }
        for(int j=i+1; j<orig.length; j++) {
            flipped[j] = orig[j];
        }
        return flipped;
    }
}