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 math
# from sys import stdin, stdout
# import numpy as np

if __name__ == '__main__':
	for t in range(int(input())):
		n = int(input())
		a = list(map(int, list(input())))
		b = list(map(int, list(input())))

		index = n-1
		move = 0
		hist = []

		flipped, reverse = False, False
		start, end = 0, n-1

		while index > -1:
			if index == 0:
				if (a[end] == b[index] and not flipped) or (a[end] != b[index] and flipped):
					pass
				else:
					move = move + 1
					hist.append(1)

				index = index - 1

			elif (a[end] == b[index] and not flipped) or (a[end] != b[index] and flipped):
				index = index - 1

				if start < end:
					end = end - 1
				else:
					end = end + 1

			else:
				if (a[start] == b[index] and not flipped) or (a[start] != b[index] and flipped):
					move = move + 1
					hist.append(1)
					
					a[start] = 1 - a[start]

				else:
					move = move + 1
					hist.append(abs(start-end)+1)

					if start < end:
						start, end = end, start+1
					else:
						start, end = end, start-1

					if flipped:
						flipped = False
					else:
						flipped = True

					index = index - 1

		print(move, ' '.join(list(map(str, hist))))