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:
###############################################
#                                             #
#   author: raghav_0901 (Raghav Dalmia)       #
#   updated on: 21-07-2020,  9:10:28 pm IST   #
#                                             #
###############################################

from math import *

inf = 10**10


def _in():
    return [int(x) for x in input().split(' ')]


def perform(s):
    out = ""
    for i in s:
        out = out + ("1" if i == "0" else "0")
    return out[::-1]


def main():
    n = int(input())
    a = input()
    b = input()

    ans = []
    j = n - 1
    while(j >= 0 and a != b):

        # print(a, b)

        while(j >= 0 and a[j] == b[j]):
            j = j - 1

        if(j < 0):
            break

        a = a[:j + 1]
        b = b[:j + 1]

        # print(a, b)

        if(len(a) == 1):
            ans.append(1)
            break

        if(a[0] == b[j]):
            ans.append(1)
            a = ("0" if a[0] == "1" else "1") + a[1:]
        if(len(a) > 1):
            ans.append(j + 1)
            a = perform(a)

    print(len(ans), end=" ")
    for i in ans:
        print(i, end=" ")
    print()


if __name__ == "__main__":
    tt = 1
    tt = int(input())
    for _ in range(tt):
        main()