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:
def inv(st):
	s=[]
	for i in st:
		if i=="1":
			s=["0"]+s
		else:
			s=["1"]+s
	return "".join(s)
def match(ar,br,k,li):
		n=len(ar)
		
		for i in range(n-1,-1,-1):
			if ar[i]!=br[i]:
				break
		else:
			return k,li
		x=br[i]
		if ar[0]!=x:
			k+=1
			li.append(i+1)
			return match(inv(ar[:i+1]),br[:i+1],k,li)
		else:
			for j in range(i-1,-1,-1):
				if ar[j]==x:
					a=inv(ar[j+1:i+1])+ar[:j+1]
					k+=2
					li+=[j+1,i+1]
					return match(a,br[:i+1],k,li)
					
t=int(input())
for _ in range(t):
					n=int(input())
					ar=input()
					br=input()
					m,ls=match(ar,br,0,[])
					ls=[m]+ls
					print(*ls)