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.lang.*;
import java.io.*;
import java.util.*;

//author : s a n 1 d h y a

//Date : 21-07-2020 

public class C1382 {
    static long Mod = 1000000007;

    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 ni() {
            return Integer.parseInt(next());
        }

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

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

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


    public static void sortbyColumn(int arr[][], int col) {
        Arrays.sort(arr, new Comparator<int[]>() {

            @Override
            public int compare(final int[] entry1, final int[] entry2) {

                if (entry1[col] > entry2[col])
                    return 1;
                else
                    return -1;
            }
        });
    }

    public static long modex(long x, long y) {
        x = x % Mod;
        long ret = 1;
        while (y > 0) {
            if (y % 2 != 0) {
                ret = ret * x % Mod;
            }
            x = x * x % Mod;
            y >>= 1;
        }
        return ret;
    }

    public static long mplr(long x, long y) {
        long ret = 0;
        while (y != 0) {
            if (y % 2 != 0) {
                ret = (ret + x) % Mod;
            }
            x = (x + x) % Mod;
            y >>= 1;
        }
        return ret;
    }

    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.ni();
        while (t-- > 0) {
        int n=sc.ni();
        String a=sc.next();
        String b=sc.next();
        char ar[]=a.toCharArray();
        char br[]=b.toCharArray();
        int d=n;
        for(int i=n-1;i>=0;i--){
            if(ar[i]==br[i])
                continue;
            else
            {
                d=i;
                break;
            }
        }
        if(d==n){
            System.out.println("0");
            continue;
        }
        int op=0;
        int x=d;
        List<Integer> l=new ArrayList<>();
        for(int i=d;i>0;i--){
            if(ar[0]==br[i])
            {
                l.add(1);
                l.add(x+1);
                for(int j=1;j<=x;j++){
                    if(ar[j]=='1')
                        ar[j]='0';
                    else
                        ar[j]='1';
                }
                char tm[]=Arrays.copyOfRange(ar,0, 1 + x);

                for(int j=x;j>=0;j--){
                    ar[x-j]=tm[j];

                }

                x--;
            }
            else
            {
                l.add(x+1);
                for(int j=0;j<=x;j++){
                    if(ar[j]=='1')
                        ar[j]='0';
                    else
                        ar[j]='1';
                }
                char tm[]=Arrays.copyOfRange(ar,0, 1 + x);
                for(int j=x;j>=0;j--){
                    ar[x-j]=tm[j];

                }
                x--;
            }
        }
        if(ar[0]!=br[0])
            l.add(1);
        String s="";
    //    s+=Integer.toString(l.size())+" ";
        System.out.print(l.size()+" ");
        for(int i=0;i<l.size();i++)
        {//   s+=Integer.toString(l.get(i))+" ";
            System.out.print(l.get(i)+" ");
        }

        System.out.println(s);
        }
    }
}