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

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

input = sys.stdin.readline


T = int(input())
for t in range(T):
	# Read
	N = int(input())
	A = list(map(int, input().strip()))
	B = list(map(int, input().strip()))

	# Solve
	flips = []
	left = 0
	right = N - 1
	i = N - 1
	big_flips = 0
	while i >= 0:
		if big_flips % 2 == 0:
			bit = A[right]
			opposite_bit = A[left]
		else:
			bit = 1 - A[left]
			opposite_bit = 1 - A[right]
		# no need to flip number
		if bit == B[i]:
			i -= 1
			if big_flips % 2 == 0:
				right -= 1
			else:
				left += 1
			continue


		if 1 - opposite_bit == B[i]:
			flips.append(right - left + 1)
			if big_flips % 2 == 0:
				left += 1
			else:
				right -= 1
		else:
			flips.append(1)
			flips.append(right - left + 1)
			if big_flips % 2 == 0:
				left += 1
			else:
				right -= 1
		big_flips += 1
		i -= 1
	# Print ans
	if flips:
		print(len(flips), end=' ')
		print(' '.join(map(str, flips)))
	else:
		print(0)