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:
# dic = {4:5,2:2,1:8,3:4,5:1}
# dic = sorted(dic,key = dic.keys())
# print(dic)

# print((2|3|32|43|8)|(43), 2|32|8)
# print(2|3|32|43|8, 3|43, 32|8, 43, 8)


for _ in range(int(input())):
	n = int(input())
	m = 0
	a = input()
	b = input()
	if a==b:
		print(0)
	else:
		b = list(b[::-1])
		for i in range(len(b)):
			if b[i]=='0':
				b[i] = '1'
			else:
				b[i] = '0'
		l = 1
		k = []
		for i in range(1,len(a)):
			if  a[i]!=a[i-1]:
				k.append(l)
				m+=1
			l+=1
		b = ''.join(b)
		# print(b)
		if a[-1]==b[-1]:
			a = a[-1]*len(a)
		else:
			a = str(int(not int(a[-1])))*len(a)
			m +=1
			k.append(n)
		l = 1
		k2 = []
		for i in range(1,len(a)):
			if  b[i]!=b[i-1]:
				k2.append(l)
				m+=1
			l+=1
		k2 = k2[::-1]
		k+=k2
		m+=1
		k.append(n)
		print(m,*k)