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:
'''      ___           ___                         ___                       ___           ___                         ___     
     /\__\         /\  \         _____         /\  \                     /\  \         /\  \                       /\__\    
    /:/ _/_        \:\  \       /::\  \        \:\  \       ___         /::\  \       |::\  \         ___         /:/ _/_   
   /:/ /\  \        \:\  \     /:/\:\  \        \:\  \     /\__\       /:/\:\__\      |:|:\  \       /\__\       /:/ /\  \  
  /:/ /::\  \   ___  \:\  \   /:/  \:\__\   ___ /::\  \   /:/__/      /:/ /:/  /    __|:|\:\  \     /:/  /      /:/ /::\  \ 
 /:/_/:/\:\__\ /\  \  \:\__\ /:/__/ \:|__| /\  /:/\:\__\ /::\  \     /:/_/:/__/___ /::::|_\:\__\   /:/__/      /:/_/:/\:\__\
 \:\/:/ /:/  / \:\  \ /:/  / \:\  \ /:/  / \:\/:/  \/__/ \/\:\  \__  \:\/:::::/  / \:\~~\  \/__/  /::\  \      \:\/:/ /:/  /
  \::/ /:/  /   \:\  /:/  /   \:\  /:/  /   \::/__/       ~~\:\/\__\  \::/~~/~~~~   \:\  \       /:/\:\  \      \::/ /:/  / 
   \/_/:/  /     \:\/:/  /     \:\/:/  /     \:\  \          \::/  /   \:\~~\        \:\  \      \/__\:\  \      \/_/:/  /  
     /:/  /       \::/  /       \::/  /       \:\__\         /:/  /     \:\__\        \:\__\          \:\__\       /:/  /   
     \/__/         \/__/         \/__/         \/__/         \/__/       \/__/         \/__/           \/__/       \/__/    
'''
"""
░░██▄░░░░░░░░░░░▄██
░▄▀░█▄░░░░░░░░▄█░░█░
░█░▄░█▄░░░░░░▄█░▄░█░
░█░██████████████▄█░
░█████▀▀████▀▀█████░
▄█▀█▀░░░████░░░▀▀███
██░░▀████▀▀████▀░░██
██░░░░█▀░░░░▀█░░░░██
███▄░░░░░░░░░░░░▄███
░▀███▄░░████░░▄███▀░
░░░▀██▄░▀██▀░▄██▀░░░
░░░░░░▀██████▀░░░░░░
░░░░░░░░░░░░░░░░░░░░
"""
import sys
import math
import collections
import operator as op
from collections import deque
from math import gcd, inf, sqrt, pi, cos, sin, ceil, log2
from bisect import bisect_right, bisect_left

# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')

from functools import reduce
from sys import stdin, stdout, setrecursionlimit
setrecursionlimit(2**20)


def factorial(n):
    if n == 0:
        return 1
    return n * factorial(n - 1)


def ncr(n, r):
    r = min(r, n - r)
    numer = reduce(op.mul, range(n, n - r, -1), 1)
    denom = reduce(op.mul, range(1, r + 1), 1)
    return numer // denom  # or / in Python 2


def prime_factors(n):
    i = 2
    factors = []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(i)
    if n > 1:
        factors.append(n)
    return (list(factors))


def isPowerOfTwo(x):
    return (x and (not(x & (x - 1))))


def factors(n):
    return list(set(reduce(list.__add__, ([i, n // i] for i in range(1, int(n**0.5) + 1) if n % i == 0))))

MOD = 1000000007
PMOD = 998244353
T = 1
T = int(stdin.readline())
for _ in range(T):
    # n, m = list(map(int, stdin.readline().rstrip().split()))
    n = int(stdin.readline())
    # a = list(map(int, stdin.readline().rstrip().split()))
    # b = list(map(int, stdin.readline().rstrip().split()))
    # q = int(stdin.readline())
    # c = list(map(int, stdin.readline().rstrip().split()))
    a = list(stdin.readline().strip('\n'))
    b = list(stdin.readline().strip('\n'))
    c = a[0]
    ans = []
    for i in range(1, n):
        if a[i] != a[i - 1]:
            ans.append(i)
            c = a[i]
    for i in range(n - 1, -1, -1):
        if b[i] != c:
            ans.append(i + 1)
            c = b[i]
    print(len(ans), *ans)