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:

// Working program with FastReader 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
import java.io.*;

public class A2_Prefix_Flip_Hard_Version_ {
    public static void main(String[] args) {
        FastReader sc = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        int test = sc.nextInt();
        for (int t = 0; t < test; t++) {
            int n = sc.nextInt();
            String a = sc.next();
            String b = sc.next();
            int[] array1 = new int[n];
            int[] array2 = new int[n];
            for(int i =0;i<n;i++){
            array1[i] = a.charAt(i)-'0';
            array2[i] = b.charAt(i)-'0';
            }
            int[] index = new int[n];
            index[0]=-1;
            int k = 0;
            for (int i = n - 1; i >= 0; i -= 2) {
                index[i] = k;
                k++;
            }
            if (index[0] == -1) {
                for (int i = 0; i < n; i += 2) {
                    index[i] = k;
                    k++;
                }
            } else {
                for (int i = 1; i < n; i += 2) {
                    index[i] = k;
                    k++;
                }
            }
            // for (int i = 0; i < n; i++) {
            //     out.print(index[i] + " ");
            // }
            int left = 0;
            int right = n-1;
            int ans = 0;
            int noOfInverts = 0;
            List<Integer> result = new ArrayList<>();
            while(right>=left){
                int tempIndex = (right-1);
                if(right==left)tempIndex=n-1;
                int temp = array1[index[tempIndex]];
                
                if(noOfInverts%2!=0){
                    if(temp==0)temp=1;
                    else temp=0;
                }
                if(temp!=array2[right]){
                    if(temp!=array1[left]){
                        array1[left] = temp;
                        ans++;
                        result.add(1);
                    }
                    ans++;
                    result.add(right+1);
                    if(array1[left]==0)array1[left]=1;
                    else array1[left]=0;
                }
                else{
                    if(temp==array1[left]){
                        if(array1[left]==0)array1[left]=1;
                        else array1[left]=0;
                        ans++;
                        result.add(1);
                    }
                    ans++;
                    result.add(right+1);
                }
                right--;
                noOfInverts++;
            }
            out.print(ans+" ");
            for(int i =0;i<result.size();i++){
            out.print(result.get(i)+" ");
            }
            out.println();
        }
        out.close();
    }

    public static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}