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:
t = int(input())

for _ in range(t):
    n = int(input())
    a = str(input())
    b = str(input())

    a_pref0 = [n] * n
    a_pref1 = [n] * n
    b_pref0 = [n] * n
    b_pref1 = [n] * n

    a_ans = []
    b_ans = []

    for i in range(n - 2, -1, -1):
        if a[i + 1] == '0':
            a_pref0[i] = i + 1
        else:
            a_pref0[i] = a_pref0[i + 1]

        if a[i + 1] == '1':
            a_pref1[i] = i + 1
        else:
            a_pref1[i] = a_pref1[i + 1]

        if b[i + 1] == '0':
            b_pref0[i] = i + 1
        else:
            b_pref0[i] = b_pref0[i + 1]

        if b[i + 1] == '1':
            b_pref1[i] = i + 1
        else:
            b_pref1[i] = b_pref1[i + 1]

    a_pos = 0

    for i in range(n):
        x = a[i]

        if x == '0':
            if a_pref0[i] == i + 1:
                continue

            else:
                a_ans.append(i + 1)

        else:
            if a_pref1[i] == i + 1:
                continue
            else:
                a_ans.append(i + 1)

    if a[-1] == '1':
        a_ans.append(n)

    for i in range(n):
        x = b[i]

        if x == '0':
            if b_pref0[i] == i + 1:
                continue

            else:
                b_ans.append(i + 1)

        else:
            if b_pref1[i] == i + 1:
                continue
            else:
                b_ans.append(i + 1)

    if b[-1] == '1':
        b_ans.append(n)

    b_ans.reverse()
    a_ans += b_ans
    if len(a_ans) > 0:
        print(len(a_ans), *a_ans)

    else:
        print(0)