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:
'''     ░░█ ▄▀█ █   █▀ █░█ █▀█ █▀▀ █▀▀   █▀█ ▄▀█ █▀▄▀█  
        █▄█ █▀█ █   ▄█ █▀█ █▀▄ ██▄ ██▄   █▀▄ █▀█ █░▀░█     '''


# [cf-1382-c.py] => [21-07-2020 @ 20:28:34] 
# Author & Template by : Udit "luctivud" Gupta
# https://www.linkedin.com/in/udit-gupta-1b7863135/


import math;   from collections import *
import sys;    from functools import reduce
import time;   from itertools import groupby

# sys.setrecursionlimit(10**6)

def input()         : return sys.stdin.readline()
def get_ints()      : return map(int, input().strip().split())
def get_list()      : return list(get_ints())
def get_string()    : return list(input().strip().split())
def printxsp(*args) : return print(*args, end="")
def printsp(*args)  : return print(*args, end=" ")


DIRECTIONS = [(+0, +1), (+0, -1), (+1, +0), (+1, -1)] 
NEIGHBOURS = [(-1, -1), (-1, +0), (-1, +1), (+0, -1),\
              (+1, +1), (+1, +0), (+1, -1), (+0, +1)]


CAPS_ALPHABETS = {chr(i+ord('A')) : i for i in range(26)}
SMOL_ALPHABETS = {chr(i+ord('a')) : i for i in range(26)}
INF = float('inf')


# Custom input output is now piped through terminal commands.


S34t = time.time()
for _testcases_ in range(int(input())): 
    n = int(input())
    a = list(input())
    b = list(input())
    j = n-1
    moves = 0
    ans = []
    while j >= 0:
        if a[j] != b[j]:
            if a[0] == b[j]:
                moves += 1
                if a[0] == '1':
                    a[0] = '0'
                else:
                    a[0] = '1'
                ans.append(1)
            for i in range((j+2)//2):
                if i == j-i:
                    if a[i] == '1':
                        a[i] = '0'
                    else:
                        a[i] = '1'
                else:
                    a[i], a[j-i] = a[j-i], a[i]
                    if a[i] == '0':
                        a[i] = '1'
                    else:
                        a[i] = '0'
                    if a[j-i] ==  '0':
                        a[j-i] = '1'
                    else:
                        a[j-i] = '0'
            moves += 1
            ans.append(j+1)
        j -= 1
    print(moves, *ans)




S34p = time.time()
# print("Time Elapsed: {}".format(float(S34p-S34t)))
''' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                             SHREE RAM JAI RAM, JAI JAI RAM 
                                             ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'''