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 _1381a1 {
    FastScanner scn;
    PrintWriter w;
    PrintStream fs;

    long MOD = 1000000007;
    int N=100000+10;
    long mul(long x, long y) {long res = x * y; return (res >= MOD ? res % MOD : res);}
    long power(long x, long y) {if (y < 0) return 1; long res = 1; x %= MOD; while (y!=0) {if ((y & 1)==1)res = mul(res, x); y >>= 1; x = mul(x, x);} return res;}
    boolean LOCAL;
    void debug(Object... o){if(LOCAL)System.err.println(Arrays.deepToString(o));}
    
    // void reverse(StringBuilder sb,int idx){
    //     int k=idx;
    //     for(int i=0;i<=idx;i++)
    //     {
    //         sb.setCharAt(i, (char)((~(sb.charAt(k)-'0'))+'0'));
    //         k--;
    //     }
    // }

    void solve(){

        int t=scn.nextInt();
        while(t-->0)
       {    int n=scn.nextInt();
            String s1=scn.next(),s2=scn.next();
                ArrayList<Integer> ans=new ArrayList<>();
                for(int i=0;i<n;i++){
                    if(s1.charAt(i)!=s2.charAt(i)){
                        ans.add(i+1);
                        // reverse(sb1,i);
                        // sb1.setCharAt(0, (char)((~(sb1.charAt(0)-'0'))+'0'));
                        // reverse(sb1,i);
                        ans.add(1);
                        ans.add(i+1);
                    }
                }

                w.print(ans.size()+" ");
                for(int e:ans) w.print(e+" ");
                w.println();
        }
    }
 
    void run() {
        try {
            long ct = System.currentTimeMillis();
            scn = new FastScanner(new File("input.txt"));
            w = new PrintWriter(new File("output.txt"));
            fs=new PrintStream("error.txt");
            System.setErr(fs);
            LOCAL=true;
 
            solve();
 
            w.close();
            System.err.println(System.currentTimeMillis() - ct);
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
    }
 
    void runIO() {
 
        scn = new FastScanner(System.in);
        w = new PrintWriter(System.out);
        LOCAL=false;
 
        solve();
 
        w.close();
    }
 
    class FastScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
 
        public FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }
 
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return null;
                st = new StringTokenizer(s);
            }
            return st.nextToken();
        }
 
        boolean hasMoreTokens() {
            while (st == null || !st.hasMoreTokens()) {
                String s = null;
                try {
                    s = br.readLine();
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (s == null)
                    return false;
                st = new StringTokenizer(s);
            }
            return true;
        }
 
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        long[] nextLongArray(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
 
        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
 
    public static void main(String[] args) {
        new _1381a1().runIO();
    }
}