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:
def readints():
    return [int(e) for e in input()]


def main():
    n = int(input())
    a = [int(e) for e in input()]
    b = [int(e) for e in input()]
    ans = []

    left, right, rev, flip, b_last_pos = 0, n - 1, False, False, n

    while b_last_pos > 0:
        b_last_pos -= 1
        if rev:
            a_last = a[left]
            a_zero = a[right]
        else:
            a_last = a[right]
            a_zero = a[left]
        
        if flip:
            a_last = 1 - a_last
            a_zero = 1 - a_zero

        if a_last != b[b_last_pos]:
            if a_zero == b[b_last_pos]:
                ans.append(1)

            flip = not flip
            rev = not rev
            ans.append(b_last_pos + 1)
    
        if rev:
            left += 1
        else:
            right -= 1


    print(len(ans), end=' ')
    print(*ans, sep=' ')


tests = int(input())
for _ in range(tests):
    main()