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
input = lambda: sys.stdin.readline().rstrip('\n\r')

def read():
	return [int(c == '1') for c in input()]

from collections import deque

for _ in range(int(input())):
	n = int(input())
	a, b = deque(read()), read()

	flip = 0
	rev = False

	moves = []
	for i in range(n-1, -1, -1):
		first = a[0]^flip
		last = a[-1]^flip

		if rev: first, last = last, first

		if i == 0:
			if first != b[0]:
				moves.append(1)
			break

		#print(f'i: {i}, first: {first}, last: {last}, b[i]: {b[i]}, flip: {flip}')
		#print(moves)

		if last != b[i]:
			if first == b[i]:
				moves.append(1)

			if not rev:
				a.popleft()
			else:
				a.pop()

			moves.append(i+1)
			rev = not rev
			flip ^= 1
		else:
			if not rev:
				a.pop()
			else:
				a.popleft()

	print(len(moves), *moves)
	#print(''.join(a), b)