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.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.StringTokenizer;

public class D {

    static class Task {
        private void swap(char[] arr, int i, int j) {
            char tmp = arr[i];
            arr[i] = arr[j];
            arr[j] = tmp;
        }

        private void invert(char[] arr, int i) {
            arr[i] = arr[i] == '0' ? '1' : '0';
        }

        private void createData(char[] arr1, char[] arr2) {
            for (int i = 0; i < 100000; i++) {
                arr1[i] = i % 2 == 0 ? '0' : '1';
                arr2[i] = i % 2 == 0 ? '1' : '0';
            }
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {

            int t = in.nextInt();
            while ((t--) > 0) {
                int n = in.nextInt();
                char[] arr1 = in.next().toCharArray();
                char[] arr2 = in.next().toCharArray();
//                char[] arr1 = new char[100000];
//                char[] arr2 = new char[100000];
//                createData(arr1, arr2);

                List<Integer> list = new ArrayList<>();

                int invertCount = 0;
                int l = 0;
                int r = n - 1;
                boolean isFromRight = true;

                for (int i = n - 1; i >= 0; i--) {
                    int curNum1 = -1;
                    if (isFromRight) {
                        curNum1 = arr1[r];
                    } else {
                        curNum1 = arr1[l];
                    }

                    if (invertCount % 2 != 0) {
                        curNum1 = curNum1 == '0' ? '1' : '0';
                    }

                    if (curNum1 == arr2[i]) {
                        if (isFromRight) {
                            r--;
                        } else {
                            l++;
                        }
                        continue;
                    }

                    int firstNum1 = -1;
                    if (isFromRight) {
                        firstNum1 = arr1[l];
                    } else {
                        firstNum1 = arr1[r];
                    }

                    if (invertCount % 2 != 0) {
                        firstNum1 = firstNum1 == '0' ? '1' : '0';
                    }

                    if (firstNum1 == arr2[i]) {
                        // 第一位先处理
                        list.add(1);
                    }

                    list.add(i + 1);
                    invertCount++;
                    if (isFromRight) {
                        l++;
                    } else {
                        r--;
                    }
                    isFromRight = !isFromRight;
                }

                int size = list.size();
                if (size == 0) {
                    out.println(0);
                    continue;
                }

                out.print(size + " ");
                for (Integer num : list) {
                    out.print(num + " ");
                }
                out.println();
            }
        }
    }

    private static void sort(double[] arr) {
        Double[] objArr = Arrays.stream(arr).boxed().toArray(Double[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(int[] arr) {
        Integer[] objArr = Arrays.stream(arr).boxed().toArray(Integer[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void sort(long[] arr) {
        Long[] objArr = Arrays.stream(arr).boxed().toArray(Long[]::new);
        Arrays.sort(objArr);
        for (int i = 0; i < arr.length; i++) {
            arr[i] = objArr[i];
        }
    }

    private static void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task task = new Task();
        task.solve(1, in, out);
        out.close();
    }

    public static void main(String[] args) {
        new Thread(null, () -> solve(), "1", 1 << 26).start();
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }

}