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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.StringReader;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Random;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;

public class Main {
    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;
        }
    }  
    static int gcd(int no, int sum) {
        if (sum == 0)
            return no;
        return gcd(sum, no % sum);
    }
    static int lcm(int a , int b){
        return (a / gcd(a , b))*b;
    }
    static void countSort(int[] arr)
    {
        int max = Arrays.stream(arr).max().getAsInt();
        int min = Arrays.stream(arr).min().getAsInt();
        int range = max - min + 1;
        int count[] = new int[range];
        int output[] = new int[arr.length];
        for (int i = 0; i < arr.length; i++) {
            count[arr[i] - min]++;
        }
 
        for (int i = 1; i < count.length; i++) {
            count[i] += count[i - 1];
        }
 
        for (int i = arr.length - 1; i >= 0; i--) {
            output[count[arr[i] - min] - 1] = arr[i];
            count[arr[i] - min]--;
        }
 
        for (int i = 0; i < arr.length; i++) {
            arr[i] = output[i];
        }
    }
    static void RandomShuffleSort(int [] a , int start , int end){
        Random random = new Random();
        for(int i = start; i<end; i++){
            int j = random.nextInt(end);
            int temp = a[j];
            a[j] = a[i];
            a[i] = temp;
        }
        Arrays.sort(a , start , end);
    }
    static char a[];
    public static void main(String[] args) throws IOException {               
        BufferedWriter out = new BufferedWriter(
            new OutputStreamWriter(System.out)); 
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        while(t-->0){
            int n = sc.nextInt();
            a= sc.next().toCharArray();
            char b[] = sc.next().toCharArray();
            ArrayList<Integer> al = new ArrayList<>();
            int count = 0;
            for(int i = n-1; i>0; i--){
                if(a[i]!=b[i]){
                    if(a[0] == b[i]){
                       if(a[0] == '0') a[0] = '1';
                       else a[0] = '0';
                       al.add(1);
                       count++;
                    }
                    stringReverse(i);
                    al.add(i+1);
                    count++;
                }
            }
            if(a[0]!=b[0]){
                a[0] = b[0];
                al.add(1);
                count++;
            }    
            System.out.print(count + " ");
            for(int i : al) System.out.print(i + " ");
            System.out.println();
        }
    }   
    private static  void stringReverse(int i){
        for(int j = 0; j<=i/2; j++){
            if(a[j] == '0') a[j] = '1';
            else a[j] = '0';
            
            if(i-j!=j){
                if(a[i-j] == '0') a[i-j] = '1';
                else a[i-j] = '0';
            }
            char c = a[j];
            a[j] = a[i-j];
            a[i-j] = c;
        }
    }
}