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 collections  
def input():
	return sys.stdin.readline().rstrip()
 
def split_input():
	return [int(i) for i in input().split()]

# tests = 1
tests = int(input())

def flip(s):
	if s == '1':
		return '0'
	else:
		return '1'

for _ in range(tests):
	n = int(input())
	a = (input())
	b = (input())
	picked = 0
	ans = []
	for i in range(n-1,-1,-1):
		# if a[0] == b[i]:
		# 	ans.append(1)
		# a[0] = flip(a[0])
		# ans.append(i+1)
		# for j in range(len(a)):
		# 	a[j] = flip(a[j])
		# a.reverse()
		# a.pop()
		if picked % 2 == 0:
			num = a[picked//2] 
		else:
			num = flip(a[n - 1 - picked//2])
		if num == b[i]:
			ans.append(1)
		ans.append(i+1)
		picked += 1
	print("%d "%len(ans), end = "")
	print(*ans, sep = " ")