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.*;
import java.math.*;

public class A {
    static final boolean RUN_TIMING = false;
    static char[] inputBuffer = new char[1 << 20];
    static PushbackReader in = new PushbackReader(new BufferedReader(new InputStreamReader(System.in)), 1 << 20);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    public void go() throws IOException {
        // in = new PushbackReader(new BufferedReader(new FileReader(new File("test.txt"))), 1 << 20);
        // out = new PrintWriter(new FileWriter(new File("output.txt")));
        int zzz = ipar();
        for (int zz = 0; zz < zzz; zz++) {
            int n = ipar();
            char[] s = spar().toCharArray();
            char[] ss = Arrays.copyOf(s, n);
            char[] t = spar().toCharArray();
            ArrayList<Integer> moves = new ArrayList<>();
            int[] order = new int[n];
            for (int i = 0; i*2 < n; i++) {
                order[i*2] = i;
                if (i*2+1 < n) {
                    order[i*2+1] = n-i-1;
                }
            }
            // out.println(Arrays.toString(order));
            for (int i = n-1; i >= 0; i--) {
                int j = order[n-1-i];
                boolean flip = (n-1-i) % 2 == 1;
                if (s[j] == t[i] ^ flip) {
                    moves.add(0);
                    // change(ss, 0);
                }
                moves.add(i);
                // change(ss, i);
            }
            // out.println(ss);
            // out.println(t);
            out.print(moves.size());
            for (int x : moves) {
                out.print(" ");
                out.print(x+1);
            }
            out.println();
        }
    }

    public void change(char[] s, int j) {
        for (int i = 0; i <= j/2; i++) {
            char temp = s[i];
            s[i] = s[j-i];
            s[j-i] = temp;
        }
        for (int i = 0; i <= j; i++) {
            s[i] = s[i] == '0' ? '1' : '0';
        }
    }

    public int ipar() throws IOException {
        return Integer.parseInt(spar());
    }

    public int[] iapar(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = ipar();
        }
        return arr;
    }

    public long lpar() throws IOException {
        return Long.parseLong(spar());
    }

    public long[] lapar(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = lpar();
        }
        return arr;
    }

    public double dpar() throws IOException {
        return Double.parseDouble(spar());
    }

    public String spar() throws IOException {
        int len = 0;
        int c;
        do {
            c = in.read();
        } while (Character.isWhitespace(c) && c != -1);
        if (c == -1) {
            throw new NoSuchElementException("Reached EOF");
        }
        do {
            inputBuffer[len] = (char)c;
            len++;
            c = in.read();
        } while (!Character.isWhitespace(c) && c != -1);
        while (c != '\n' && Character.isWhitespace(c) && c != -1) {
            c = in.read();
        }
        if (c != -1 && c != '\n') {
            in.unread(c);
        }
        return new String(inputBuffer, 0, len);
    }

    public String linepar() throws IOException {
        int len = 0;
        int c;
        while ((c = in.read()) != '\n' && c != -1) {
            if (c == '\r') {
                continue;
            }
            inputBuffer[len] = (char)c;
            len++;
        }
        return new String(inputBuffer, 0, len);
    }

    public boolean haspar() throws IOException {
        String line = linepar();
        if (line.isEmpty()) {
            return false;
        }
        in.unread('\n');
        in.unread(line.toCharArray());
        return true;
    }

    public void shuffle(int[] arr) throws IOException {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int)(Math.random() * (n-i) + i);
            int temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(long[] arr) throws IOException {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int)(Math.random() * (n-i) + i);
            long temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public void shuffle(Object[] arr) throws IOException {
        int n = arr.length;
        for (int i = 0; i < n; i++) {
            int j = (int)(Math.random() * (n-i) + i);
            Object temp = arr[i];
            arr[i] = arr[j];
            arr[j] = temp;
        }
    }

    public static void main(String[] args) throws IOException {
        long time = 0;
        time -= System.nanoTime();
        new A().go();
        time += System.nanoTime();
        if (RUN_TIMING) {
            System.out.printf("%.3f ms%n", time / 1000000.0);
        }
        out.flush();
        in.close();
    }
}