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 IOException{
        //BufferedReader f = new BufferedReader(new FileReader("uva.in"));
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int t = Integer.parseInt(f.readLine());
        for(int i = 0; i < t; i++) {
            int n = Integer.parseInt(f.readLine());
            char[] a = f.readLine().toCharArray();
            char[] b = f.readLine().toCharArray();
            ArrayList<Integer> stepsA = new ArrayList<>();
            char firstA = a[0];
            for(int j = 1; j < n; j++) {
                if(firstA != a[j]) {
                    stepsA.add(j);
                }
                firstA = a[j];
            }
            if(firstA != '0') {
                stepsA.add(n);
            }
            ArrayList<Integer> stepsB = new ArrayList<>();
            char firstB = b[0];
            for(int j = 1; j < n; j++) {
                if(firstB != b[j]) {
                    stepsB.add(j);
                }
                firstB = b[j];
            }
            if(firstB != '0') {
                stepsB.add(n);
            }
            Collections.reverse(stepsB);
            out.print(stepsA.size()+stepsB.size());
            for(int j: stepsA) {
                out.print(" " + j);
            }
            for(int j: stepsB) {
                out.print(" " + j);
            }
            out.println();
        }
        f.close();
        out.close();
    }
}