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.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class PrefixFlipEasy {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int numTests = sc.nextInt();
        PrintWriter pw = new PrintWriter(System.out);
        for (int t = 0; t < numTests; t++) {
            int n = sc.nextInt();
            char[] A = sc.next().toCharArray(), B = sc.next().toCharArray();
            int[] a = new int[n], b = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = A[i] - '0';
                b[i] = B[i] - '0';
            }
            ArrayList<Integer> flips = new ArrayList<>();
            for (int i = n - 1; i >= 0; i--) {
                if (a[i] == b[i]) {
                    continue;
                }
                if (i == 0) {
                    flips.add(1);
                    continue;
                }
                if (i == 1) {
                    flips.add(i + 1);
                    flips.add(1);
                    flips.add(i + 1);
                    continue;
                }
                if (i == 2) {
//                    if (a[i - 1] == b[i - 1]) {
//                        flips.add(3);
//                        flips.add(1);
//                        flips.add(3);
//                        if (a[0] != b[0]) {
//                            flips.add(1);
//                        }
//                    } else {
//                        if (1 - a[0] == b[2]) {
//                            flips.add(3);
//                            if (a[2] == b[0]) {
//                                flips.add(1);
//                            }
//                        } else {
//                            flips.add(1);
//                            flips.add(3);
//                            if (a[2] == b[0]) {
//                                flips.add(1);
//                            }
//                        }
//                    }
                    addForLength3(a[0], a[1], a[2], b[0], b[1], b[2], flips);
                    break;
                }
                // i >= 3
                flips.add(i + 1);
                // deal with i, i-1, i-2
                addForLength3(a[i], a[i - 1], a[i - 2], b[i], b[i - 1], b[i - 2], flips);
                flips.add(i + 1);
                i -= 2;
//                if (a[i - 1] == b[i - 1]) {
//                    flips.add(i + 1);
//                    flips.add(1);
//                    flips.add(i + 1);
//                } else {
//                    if (a[i] == a[i - 1]) {
//                        flips.add(i + 1);
//                        flips.add(2);
//                        flips.add(i + 1);
//                    } else {
//                        flips.add(i + 1);
//                        flips.add(1);
//                        flips.add(2);
//                        flips.add(1);
//                        flips.add(i + 1);
//                    }
//                    i--;
//                }
            }
            pw.print(flips.size());
            for (int f : flips) {
                pw.print(" " + f);
            }
            pw.println();
            //pw.println(check(a, b, flips));
        }
        pw.flush();
        pw.close();
        sc.close();
    }

    private static void addForLength3(int a, int b, int c, int x, int y, int z,
                               ArrayList<Integer> flips) {
        if (c == z) {
            addForLength2(a, b, x, y, flips);
            return;
        }
        // c != z
        if (b == y) {
            flips.add(3);
            flips.add(1);
            flips.add(3);
            if (a != x) {
                flips.add(1);
            }
        } else {
            // b != y
            if (1 - a == z) {
                flips.add(3);
                if (c == x) {
                    flips.add(1);
                }
            } else {
                flips.add(1);
                flips.add(3);
                if (c == x) {
                    flips.add(1);
                }
            }
        }
    }

    private static void addForLength2(int a, int b, int x, int y, ArrayList<Integer> flips) {
        if (b == y) {
            if (a != x) {
                flips.add(1);
            }
            return;
        }
        flips.add(2);
        flips.add(1);
        flips.add(2);
        if (a != x) {
            flips.add(1);
        }
    }

    private static boolean check(int[] a, int[] b, List<Integer> flips) {
        for (int f : flips) {
            flip(a, f);
        }
        boolean eq = Arrays.equals(a, b);
        if (!eq) {
            System.out.println("WRONG");
            System.out.println(Arrays.toString(a));
            System.out.println(Arrays.toString(b));
        }
        return eq;
    }

    private static void flip(int[] a, int len) {
        for (int i = 0; i < len - 1 - i; i++) {
            int fir = a[i], last = a[len - 1 - i];
            a[i] = 1 - last;
            a[len - 1 - i] = 1 - fir;
        }
        if (len % 2 == 1) {
            a[(len - 1) / 2] ^= 1;
        }
    }
}