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.math.BigInteger;
import java.util.*;

public class B
{
    public static int goCode(int a[], int b[])
    {
        int n = a.length;
        for(int i = n-1; i >= 0; i--)
        {
            if(a[i] != b[i])
                return i;
        }
        return -1;
    }
    public static int[] flip(int a[], int l)
    {
        int n = a.length;
        for(int i = 0; i < l; i++)
        {
            if(a[i] == 1)
                a[i] = 0;
            else if(a[i] == 0)
                a[i] = 1;
        }        
        ArrayList<Integer> arr = new ArrayList<>();
        for(int i = 0; i < l; i++)
        {
            arr.add(a[i]);
        }
        int j = 0;
        for(int i = arr.size()-1; i >= 0; i--)
        {
            a[j] = arr.get(i);
            j++;
        }
        return a;
    }
    public static void main(String [] args) throws Exception
    {
        Foster sc = new Foster();
        PrintWriter p = new PrintWriter(System.out);
        int t = sc.nextInt();
        while(t-- != 0)
        {
            int n = sc.nextInt();
            char A[] = sc.next().toCharArray();
            char B[] = sc.next().toCharArray();
            int a[] = new int[n];
            int b[] = new int[n];
            for(int i = 0; i < n; i++)
            {
                if(A[i] == '1')
                    a[i] = 1;
                if(A[i] == '0')
                    a[i] = 0;
                if(B[i] == '1')
                    b[i] = 1;
                if(B[i] == '0')
                    b[i] = 0;
            }
            int count = 0;
            for(int i = 0; i < n; i++)
            {
                if(a[i] == b[i])
                    count++;
            }
            if(count == n)
            {
                p.println("0");
            }
            else
            {
                ArrayList<Integer> ans = new ArrayList<>();
                while(goCode(a,b) != -1)
                {
                    int idx = goCode(a,b);
                    if(b[idx] != a[0])
                    {
                        flip(a, idx+1);
                        ans.add(idx+1);
                    }
                    else
                    {
                        ans.add(1);
                        flip(a, 1);
                        ans.add(idx+1);
                        flip(a,idx+1);
                    }
                }
                p.print(ans.size() + " ");
                for(int i : ans)
                {
                    p.print(i + " ");
                }
                p.println();
            }
        }
        p.close();
    }

/*
    Move to top!!
*/
    static class Foster 
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() 
        {
            while (!st.hasMoreTokens())
                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());
        }
        int[] intArray(int n)
        {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++)
            {
                arr[i] = nextInt();
            }
            return arr;
        }
        long[] longArray(int n)
        {
            long arr[] = new long[n];
            for(int i = 0; i < n; i++)
            {
                arr[i] = nextLong();
            }
            return arr;
        }
        long pow(long... a)
        {
            long mod = Long.MAX_VALUE;
            if(a.length == 3)   mod = a[2];
            long res = 1;
            while(a[1] > 0)
            {
                if(a[1] % 2 != 0)
                    res = (res * a[0]) % mod;
                a[1] /= 2;
                a[0] = (a[0] * a[0]) % mod;
            }
            return res;
        }
        void print(Object... o) 
        {
            for(Object next : o)
            {
                System.out.print(next + " ");
            }
        }
        void println(Object... o) 
        {
            for(Object next : o)
            {
                System.out.print(next + " ");
            }
            System.out.println();
        }
        void watch(Object...a) throws Exception 
        {
            int i = 1;
            for (Object o: a) 
            {
                boolean found = false;
                if (o.getClass().isArray()) 
                {
                    String type = o.getClass().getName().toString();
                    switch (type) 
                    {
                        case "[I":
                        {
                            int[] test = (int[]) o;
                            println(i + " : " + Arrays.toString(test));
                            break;
                        }
                        case "[[I":
                        {
                            int[][] obj = (int[][]) o;

                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[J":
                        {

                            long[] obj = (long[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[J":
                        {

                            long[][] obj = (long[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[D":
                        {

                            double[] obj = (double[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[D":
                        {

                            double[][] obj = (double[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[Ljava.lang.String":
                        {

                            String[] obj = (String[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[Ljava.lang.String":
                        {

                            String[][] obj = (String[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        case "[C":
                        {
                            char[] obj = (char[]) o;
                            println(i + " : " + Arrays.toString(obj));
                            break;
                        }
                        case "[[C":
                        {

                            char[][] obj = (char[][]) o;
                            println(i + " : " + Arrays.deepToString(obj));
                            break;
                        }
                        default:
                        {
                            println(i + " : type not identified");
                            break;
                        }
                    }
                    found = true;
                }
                if (o.getClass() == ArrayList.class) 
                {
                    println(i + " : LIST = " + o);
                    found = true;
                }
                if (o.getClass() == TreeSet.class) 
                {
                    println(i + " : SET = " + o);
                    found = true;
                }
                if (o.getClass() == TreeMap.class) 
                {
                    println(i + " : MAP = " + o);
                    found = true;
                }
                if (o.getClass() == HashMap.class) 
                {
                    println(i + " : MAP = " + o);
                    found = true;
                }
                if (o.getClass() == LinkedList.class) 
                {
                    println(i + " : LIST = " + o);
                    found = true;
                }
                if (o.getClass() == PriorityQueue.class) 
                {
                    println(i + " : PQ = " + o);
                    found = true;
                }
                if (!found) 
                {
                    println(i + " = " + o);
                }
                i++;
            }
        }
    }
}