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:
// package codeforces.round653;
import java.io.*;
import java.util.*;
import java.lang.*;

public class q1 {
    static class Print
    {
        private final OutputStream out;
        /*public Print(OutputStream outputStream)
        {
            writer=new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }*/
        public Print()
        {
            this.out=System.out;
        }
        public void print(String str)throws IOException
        {
            //buf=str.getBytes();
            for (int i = 0; i < str.length(); i++)
            {
			/*if (i != 0)
			out.write(' ');*/
                out.write(str.charAt(i));
            }
        }
        public void printLine(String str)throws IOException
        {
            print(str);
            out.write('\n');
        }
        public void close()throws IOException
        {
            out.close();
        }
    }
    static class Scan
    {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
                throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                    return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
                n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
                n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
                n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
                return true;
            return false;
        }
    }
    public static void main(String[] args) throws IOException
    {
        Scan scn = new Scan();
        Print print=new Print();
        BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
        int t =scn.scanInt();
        while(t-->0) {
          int n=scn.scanInt();
          String str1=scn.scanString();
          String str2=scn.scanString();
          char[] s1=new char[n];
          char[] s2=new char[n];
          for(int i=0;i<n;i++){
              s1[i]=str1.charAt(i);
              if(s1[i]=='0')
              s2[n-i-1]='1';
              else s2[n-1-i]='0';
          }
          int s1lo=0;
          int s1hi=n-1;
          int s2lo=0;
          int s2hi=n-1;
          int[] arr=new int[2*n];
          int idx=0;
          for(int i=0;i<=str1.length()-1;i++){
              if(i%2==0){
                  if(str2.charAt(n-1-i)==s1[s1lo]){
                      arr[idx]=1;
                      idx++;
                      arr[idx]=n-i;
                      idx++;
                  }
                  else{
                      arr[idx]=n-i;
                      idx++;
                  }
                  s1lo++;
                  s2hi--;
              }
              else{
                  if(str2.charAt(n-1-i)==s2[s2lo]){
                      arr[idx]=1;
                      idx++;
                      arr[idx]=n-i;
                      idx++;
                  }
                  else{
                      arr[idx]=n-i;
                      idx++;
                  }
                  s2lo++;
                  s1hi--;
              }
          }
          bw.append(idx+" ");
          for(int i=0;i<idx;i++){
              bw.append(arr[i]+" ");
          }
          bw.append("\n");

        }
        bw.close();
    }
    public static int gcd(int a,int b){
        if(b==0){
            return a;
        }
        return gcd(b,a%b);
    }
    static boolean isPrime(int n)
    {
        // Corner cases
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;

        // This is checked so that we can skip
        // middle five numbers in below loop
        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;

        return true;
    }
}