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.util.*;
import java.io.*;

public class PrefixFlipEasy {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        int t = in.nextInt();

        for (int i = 0; i < t; i++) {
            int n = in.nextInt();
            String a = in.next();
            String b = in.next();
            ArrayList<Integer> flips = new ArrayList<>();

            for (int j = 1; j < n; j++) {
                if (a.charAt(j) != a.charAt(j - 1)) {
                    flips.add(j);
                }
            }
            if (a.charAt(n - 1) == '1') {
                flips.add(n);
            }
            if (b.charAt(n - 1) == '1') {
                flips.add(n);
            }

            for (int j = n - 1; j >= 1; j--) {
                if (b.charAt(j) != b.charAt(j - 1)) {
                    flips.add(j);
                }
            }

            System.out.print(flips.size());
            for (int x : flips) System.out.print(" " + x);
            System.out.println();
        }
    }

    static String flipString(String s) {
        String ret = "";
        for (int i = 0; i < s.length(); i++) {
            ret = s.charAt(i) + ret;
        }
        return ret;
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i));
            st = new StringTokenizer("");
        }
        public String next() throws IOException {
            if (st.hasMoreTokens()) {
                return st.nextToken();
            }
            else
                st = new StringTokenizer(br.readLine());
            return next();
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public int[] nextIntArr(int size) throws IOException {
            int[] arr = new int[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        public long[] nextLongArr(int size) throws IOException {
            long[] arr = new long[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
        public double[] nextDoubleArr(int size) throws IOException {
            double[] arr = new double[size];
            for (int i = 0; i < arr.length; i++) {
                arr[i] = nextDouble();
            }
            return arr;
        }
    }
}