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:
from __future__ import division, print_function

import sys
from atexit import register

if sys.version_info[0] < 3:
    from io import BytesIO as stream
else:
    from io import StringIO as stream


sys.stdin = stream(sys.stdin.read())
input = lambda: sys.stdin.readline().rstrip('\r\n')

sys.stdout = stream()
register(lambda: sys.__stdout__.write(sys.stdout.getvalue()))


def read_int():
    return int(input())


def read_ints():
    return list(map(int, input().split(' ')))


def flip(a):
    return 0 if a == 1 else 1


def solve():
    """
    a1 = 11 reverse whole
         01

    a0
    """
    n = read_int()
    a = list(map(int, input()))
    b = list(map(int, input()))
    end = n-1
    operations = []
    while end > -1:
        if a[end] != b[end]:
            if a[0] == a[end]: # just flip
                flipped = list(map(flip, a[:end+1]))
                flipped.reverse()
                a[:end+1] = flipped
                operations.append(end+1)
            else:
                a[0] = flip(a[0]) # flip first
                operations.append(1)
                flipped = list(map(flip, a[:end+1]))
                flipped.reverse()
                a[:end+1] = flipped
                operations.append(end+1)
            a[end] = b[end]
        end -= 1
    print(len(operations), ' '.join(map(str, operations)))


if __name__ == '__main__':
    T = read_int()
    for _ in range(T):
        solve()