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 find(s1,s2):
    if len(s1) == 1:
        if s1 == s2:
            return []
        else:
            return [1]
    
    indices = [-1]*len(s1)
    cur = len(s1) - 1
    val = 0
    for i in range(len(s1)):
        indices[cur] = val
        cur -= 2
        val += 1
        if cur < 0:
            break
    if indices[0] == -1:
        cur = 0
        for i in range(len(s1)):
            indices[cur] = val
            val += 1
            cur += 2
            if cur > len(s1) - 1:
                break
    else:
        cur = 1
        for i in range(len(s1)):
            indices[cur] = val
            val += 1
            cur += 2
            if cur > len(s1) - 1:
                break
#     print(indices)
    ans = []
    temp = 1
    for i in range(len(s1)-1,-1,-1):
        if (int(s1[indices[i]])+temp)%2 == int(s2[i])%2:
            ans += [i+1]
        else:
            ans += [1,i+1]
        temp += 1
    return ans

ANS = []
for _ in range(int(input())):
    input()
    s1 = input()
    s2 = input()
    ans = find(s1,s2)
    ans = [str(x) for x in ans]
    ans = [str(len(ans))] + ans
    ANS += [" ".join(ans)]
print("\n".join(ANS))