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:
#!/usr/bin/env python3

# need 0:
#
# 0 ... 0 - ok
# 0 ... 1 - prefix 1, than prefix n
# 1 ... 0 - ok
# 1 ... 1 - prefix n
#
# need 1:
#
# 0 ... 0 - prefix n
# 0 ... 1 - ok
# 1 ... 0 - prefix 1, than prefix n
# 1 ... 1 - ok

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

    p = []

    j1 = 0
    j2 = n - 1
    inc = -1
    flip = False
    for i in range(n - 1, -1, -1):
        val1 = a[j1]
        val2 = a[j2]
        if flip:
            if val1 == '0':
                val1 = '1'
            else:
                val1 = '0'
            if val2 == '0':
                val2 = '1'
            else:
                val2 = '0'

        if b[i] == val2:
            j2 += inc
            continue

        if val1 != val2:
            p.append(1)

        p.append(i + 1)
        j1 -= inc
        j1, j2 = j2, j1

        if inc == -1:
            inc = 1
        else:
            inc = -1

        flip = not flip

    # a1 = [int(i) for i in a]
    # b1 = [int(i) for i in b]
    # for p_i in p:
    #     for i in range(p_i):
    #         a1[i] += 1
    #         a1[i] %= 2
    #     for i in range(p_i // 2):
    #         a1[i], a1[p_i - 1 - i] = a1[p_i - 1 - i], a1[i]

    # print(' '.join(map(str, a1)))
    # print(' '.join(map(str, b1)))

    s = str(len(p))
    if len(p) > 0:
        s += ' '
        s += ' '.join(map(str, p))
    print(s)