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:
t = int(input())

for i in range(t):
	n = int(input())
	a = [int(val) for val in list(input())]
	b = [int(val) for val in list(input())]
	if a == b:
		print(0)
	else:
		count = 0
		res = []
		is_flip = False
		left = 0
		right = n-1
		j = n-1
		a_zero = a[0]

		while left < right:
			if is_flip:
				curr_j = 1-a[left]
			else:
				curr_j = a[right]

			if curr_j != b[j]:
				if is_flip:
					a_zero = 1-a[right]
				else:
					a_zero = a[left]

				if curr_j == a_zero:
					count += 1
					res.append(str(j+1))
					is_flip = not is_flip

				else:
					count += 2
					res.append('1')
					if is_flip:
						a[right] *= -1
					else:
						a[left] *= -1
					res.append(str(j+1))
					is_flip = not is_flip

			if is_flip:
				left += 1
			else:
				right -= 1

			j -= 1

		if is_flip:
			a_zero = 1-a[right]
		else:
			a_zero = a[left]

		if a_zero != b[0]:
			count += 1
			res.append('1')

		print(count, ' '.join(res))