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 index(m, start, end, reversed):
#     if not reversed:
#         return start + m
#     else:
#         return end - m

test = False

def get_end(start, end, reversed):
    if not reversed:
        return end
    else:
        return start

def get_start(start, end, reversed):
    if not reversed:
        return start
    else:
        return end

def invert(bit, inverted):
    if not inverted:
        return bit
    else:
        return (not bit)


"""
Main
"""

t = int(input())

for test_case in range(t):
    n = int(input())
    a = list(map(lambda x: bool(int(x)), input()))
    b = list(map(lambda x: bool(int(x)), input()))

    start, end = 0, n-1
    reversed, inverted = False, False
    instr = "" #Instructions
    k = 0

    for m in range(n-1, -1, -1):
        # if test:
        #     print("m = ", m)
        #     print("start, end = ", start, ", ", end)
        #     print("inverted, reversed = ", inverted, ", ", reversed)
        target = b[m]
        real_m_in_a = get_end(start, end, reversed)
        cand = invert(a[real_m_in_a], inverted)

        if cand == target:
            if not reversed:
                end -= 1
            else:
                start += 1
        else:
            first_index = get_start(start, end, reversed)
            cand = invert(a[first_index], inverted)
            if (not cand) != target:
                instr += "1 "
                k += 1
                # if test:
                #     print(1)
            instr += str(m+1) + " "
            k += 1
            # if test:
            #     print(m+1)
            reversed = not reversed
            inverted = not inverted
            if not reversed:
                end -= 1
            else:
                start += 1

    print(k, instr)