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 PYTHON3):

Solution:
from sys import stdin, stdout

# 0 1 2 3 4 5 6 7 8 9
# 9 8 7 6 5 4 3 2 1 (0) 9
# 1 2 3 4 5 6 7 8 (9)   8
# 8 7 6 5 4 3 2 (1)     7
# 2 3 4 5 6 7 (8)       6
# 7 6 5 4 3 (2)         5
# ..........
t = int(stdin.readline())
for _ in range(t):
    n = int(stdin.readline())
    a = stdin.readline().strip()
    b = stdin.readline().strip()

    ans = []
    idx = 0
    flip = False
    for i in range(n-1, -1, -1):
        if (not flip and a[idx] == b[i]) or (flip and a[idx] != b[i]):
            ans.append(1)
        ans.append(i+1)

        if flip:
            idx -= i
        else:
            idx += i

        flip = not flip

    stdout.write(str(len(ans)) + ' ')
    if len(ans) > 0:
        stdout.write(' '.join(map(str, ans)) + '\n')