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.lang.Math;
import java.util.*;

public class Main  {

    public BufferedReader in;
    public PrintStream out;

    public boolean log_enabled = false;
    
    public boolean multiply_tests = true;

    public static boolean do_gen_test = false;
    
    public void gen_test() {
            
        
    }
    
    private class TestCase {

        public Object solve() {
            
            int n = readInt();
            String sa = readLn();
            String sb = readLn();
            
            int i;
            
            int[] a = new int[n];
            int[] b = new int[n];
            
            for (i=0; i<n; i++)
            {
                a[i] = sa.charAt(i)-'0';
                b[i] = sb.charAt(i)-'0';
            }
            
            int[] ops  = new int[2*n];
            int k = 0;
            int l = 0;
            int r = n-1;
            int d = 0;
            int x,y;
            
            for (i=n-1; i>=0; i--)
            {
                x = a[d==0 ? r : l];
                y = a[d==0 ? l : r];
                if ((x ^ d)!= b[i])
                {
                    if (y!=x)
                    {
                        ops[k++] = 1;
                    }
                    
                    ops[k++] = i+1;
                  
                    d = 1-d;
                }
                //else
                {
                    if (d==0)
                    {
                        r --;
                    }
                    else
                    {
                        l++;
                    }
                }
            }
            
            out.print(k);
            if (k>0)
            {
                out.print(' ');
                printArray(ops, k);
            }
            else
            {
                out.println();
            }
            
                
            
                          
            
            return null;
            
            //return strf("%f", 0);
            
            //out.printf("Case #%d: \n", caseNumber);
            //return null;
        }
        
        public int caseNumber;
        
        TestCase(int number) {
            caseNumber = number;
        }
        
        public void run(){
            Object r = this.solve();
            
            if ((r != null))
            {
                //outputCaseNumber(r);
                out.println(r);
            }
        }
        
        public String impossible(){
            return "IMPOSSIBLE";
        }
        
        public String strf(String format, Object... args)
        {
            return String.format(format, args);
        }
        
//        public void outputCaseNumber(Object r){
//            //out.printf("Case #%d:", caseNumber);
//            if (r != null)
//            {
//              //  out.print(" ");
//                out.print(r);
//            }
//            out.print("\n");
//        }
    }

    public void run() {
        //while (true)
        {
            int t = multiply_tests ?  readInt() : 1;
            for (int i = 0; i < t; i++) {
                TestCase T = new TestCase(i + 1);
                T.run();
            }
        }
    }
    

    
    public Main(BufferedReader _in, PrintStream _out){
        in = _in;
        out = _out;
    }
    

    public static void main(String args[]) {
        Locale.setDefault(Locale.US);
        Main S;
        try {
            S = new Main(
                        new BufferedReader(new InputStreamReader(System.in)),
                        System.out
                );
        } catch (Exception e) {
            return;
        }
        
        S.run();
        
    }

    private StringTokenizer tokenizer = null;

    public int readInt() {
        return Integer.parseInt(readToken());
    }

    public long readLong() {
        return Long.parseLong(readToken());
    }

    public double readDouble() {
        return Double.parseDouble(readToken());
    }

    public String readLn() {
        try {
            String s;
            while ((s = in.readLine()).length() == 0);
            return s;
        } catch (Exception e) {
            return "";
        }
    }

    public String readToken() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(in.readLine());
            }
            return tokenizer.nextToken();
        } catch (Exception e) {
            return "";
        }
    }

    public int[] readIntArray(int n) {
        int[] x = new int[n];
        readIntArray(x, n);
        return x;
    }
    
    public int[] readIntArrayBuf(int n) {
        int[] x = new int[n];
        readIntArrayBuf(x, n);
        return x;
    }

    public void readIntArray(int[] x, int n) {
        for (int i = 0; i < n; i++) {
            x[i] = readInt();
        }
    }
    
    public long[] readLongArray(int n) {
        long[] x = new long[n];
        readLongArray(x, n);
        return x;
    }
    
    public long[] readLongArrayBuf(int n) {
        long[] x = new long[n];
        readLongArrayBuf(x, n);
        return x;
    }

    public void readLongArray(long[] x, int n) {
        for (int i = 0; i < n; i++) {
            x[i] = readLong();
        }
    }

    public void logWrite(String format, Object... args) {
        if (!log_enabled) {
            return;
        }

        out.printf(format, args);
    }
    
    public void readLongArrayBuf(long[] x, int n) {
        
        char[]buf = new char[1000000];
        long r = -1;
        int k= 0, l = 0;
        long d;
        
        while (true)
        {
            try{
                l = in.read(buf, 0, 1000000);
            }
            catch(Exception E){};
            
            for (int i=0; i<l; i++)
            {
                if (('0'<=buf[i])&&(buf[i]<='9'))
                {
                    if (r == -1)
                    {
                        r = 0;
                    }
                    d = buf[i] - '0';
                    r = 10 * r + d;
                }
                else
                {
                    if (r != -1)
                    {
                        x[k++] = r;
                    }
                    
                    r = -1;
                }
            }
            
            if (l<1000000)
                return;
        }
    }
    
    public void readIntArrayBuf(int[] x, int n) {
        
        char[]buf = new char[1000000];
        int r = -1;
        int k= 0, l = 0;
        int d;
        
        while (true)
        {
            try{
                l = in.read(buf, 0, 1000000);
            }
            catch(Exception E){};
            
            for (int i=0; i<l; i++)
            {
                if (('0'<=buf[i])&&(buf[i]<='9'))
                {
                    if (r == -1)
                    {
                        r = 0;
                    }
                    d = buf[i] - '0';
                    r = 10 * r + d;
                }
                else
                {
                    if (r != -1)
                    {
                        x[k++] = r;
                    }
                    
                    r = -1;
                }
            }
            
            if (l<1000000)
                return;
        }
    }
    
    public void printArray(long[] a, int n)
    {
        printArray(a, n, ' ');
    }
    
    public void printArray(int[] a, int n)
    {
        printArray(a, n, ' ');
    }
            
    public void printArray(long[] a, int n, char dl)
    {
        long x; 
        int i, l = 0;
        for (i=0; i<n; i++)
        {
            x = a[i];
            
            if (x<0)
            {
                x = -x;
                l++;
            }
            
            if (x==0)
            {
                l++;
            }
            else
            {
                while (x>0)
                {
                    x /= 10;
                    l++;
                }
            }
        }
        
        l += n-1;
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            x = a[i];
            z = false;            
            if (x<0)
            {
                x = -x;
                z = true;
            }
            
            do{
                s[l--] = (char)('0' + (x % 10));
                x /= 10;
            } while (x>0);
            
            if (z)
            {
                s[l--] = '-';
            }
            
            if (i>0)
            {
                s[l--] = dl;
            }
        }
        
        out.println(new String(s));
    }
    
    public void printArray(int[] a, int n, char dl)
    {
        int x; 
        int i, l = 0;
        for (i=0; i<n; i++)
        {
            x = a[i];
            
            if (x<0)
            {
                x = -x;
                l++;
            }
            
            if (x==0)
            {
                l++;
            }
            else
            {
                while (x>0)
                {
                    x /= 10;
                    l++;
                }
            }
        }
        
        l += n-1;
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            x = a[i];
            z = false;            
            if (x<0)
            {
                x = -x;
                z = true;
            }
            
            do{
                s[l--] = (char)('0' + (x % 10));
                x /= 10;
            } while (x>0);
            
            if (z)
            {
                s[l--] = '-';
            }
            
            if (i>0)
            {
                s[l--] = dl;
            }
        }
        
        out.println(new String(s));
    }
    
    public void printMatrix(int[][] a, int n, int m)
    {
        int x; 
        int i,j, l = 0;
        for (i=0; i<n; i++)
        {
            for (j=0; j<m; j++)
            {
                x = a[i][j];
            
                if (x<0)
                {
                    x = -x;
                    l++;
                }

                if (x==0)
                {
                    l++;
                }
                else
                {
                    while (x>0)
                    {
                        x /= 10;
                        l++;
                    }
                }
            }
            
            l += m-1;
        }
        
        l += n-1;
        
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            for (j=m-1; j>=0;  j--)
            {
                x = a[i][j];
                z = false;            
                if (x<0)
                {
                    x = -x;
                    z = true;
                }

                do{
                    s[l--] = (char)('0' + (x % 10));
                    x /= 10;
                } while (x>0);

                if (z)
                {
                    s[l--] = '-';
                }

                if (j>0)
                {
                    s[l--] = ' ';
                }
            }
            
            if (i>0)
            {
                 s[l--] = '\n';
            }
        }
        
        out.println(new String(s));
    }
    
    public void printMatrix(long[][] a, int n, int m)
    {
        long x; 
        int i,j, l = 0;
        for (i=0; i<n; i++)
        {
            for (j=0; j<m; j++)
            {
                x = a[i][j];
            
                if (x<0)
                {
                    x = -x;
                    l++;
                }

                if (x==0)
                {
                    l++;
                }
                else
                {
                    while (x>0)
                    {
                        x /= 10;
                        l++;
                    }
                }
            }
            
            l += m-1;
        }
        
        l += n-1;
        
        
        char[] s = new char[l];
        
        l--;
        boolean z;
        for (i=n-1; i>=0;  i--)
        {
            for (j=m-1; j>=0;  j--)
            {
                x = a[i][j];
                z = false;            
                if (x<0)
                {
                    x = -x;
                    z = true;
                }

                do{
                    s[l--] = (char)('0' + (x % 10));
                    x /= 10;
                } while (x>0);

                if (z)
                {
                    s[l--] = '-';
                }

                if (j>0)
                {
                    s[l--] = ' ';
                }
            }
            
            if (i>0)
            {
                 s[l--] = '\n';
            }
        }
        
        out.println(new String(s));
    }
    
    
}