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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;

public class C {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintStream out = System.out;

        int t = Integer.parseInt(br.readLine());

        for (int i = 0; i < t; i++) {
            int n = Integer.parseInt(br.readLine());
            String[] arr = br.readLine().split("");
            int[] a = new int[n];
            for (int x = 0; x < n; x++) a[x] = Integer.parseInt(arr[x]);
            int[] b = new int[n];
            arr = br.readLine().split("");
            for (int x = 0; x < n; x++) b[x] = Integer.parseInt(arr[x]);
            ArrayList<Integer> ops = new ArrayList<>();
            int pos = n-1;
            while (pos >= 0) {
                if (a[pos] == b[pos]) {
                    pos--;
                    continue;
                }
                if (a[pos] == a[0]) {
                    ops.add(pos+1);
                    a = reverse(a, pos+1);
                    pos--;
                    continue;
                }
                ops.add(1);
                if (a[0] == 1) a[0] = 0;
                else a[0] = 1;
            }
            out.print(ops.size());
            for (int x : ops) out.print(" " + x);
            out.println();
        }

        System.out.flush();
    }
    private static int[] reverse(int[] a, int x) {
        int[] next = new int[a.length];
        for (int i = 0; i < a.length; i++) {
            if (i < x) {
                if (a[i] == 0) {
                    next[x - i - 1] = 1;
                }
            } else {
                next[i] = a[i];
            }
        }
        return next;
    }
}