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:
t = int(input())
while t>0:
	n = int(input())
	a = list(str(input()))
	b = list(str(input()))
	a = list(map(int,a))
	b = list(map(int,b))
	level = []
	aclone = []
	for i in range(n):
		if a[i] == 0:
			aclone.append(1)
		else:
			aclone.append(0)
	for i in range(n-1,-1,-1):
		# print(a)
		# print(aclone)
		if a[i] != b[i]:
			if i != 0:
				if a[0] != b[i]:
					level.append(i+1)
					# print("level=",i+1)
					d = list(a)
					a = aclone[::-1]
					aclone = d[::-1]
					# a.pop()
					# aclone.pop()
					# for j in range(i+1):
					# 	if a[j] == 0:
					# 		a[j] = 1
					# 	else:
					# 		a[j] = 0
					# a.pop()
				else:
					# print("hey")
					level.append(1)
					if a[0] == 1:
						a[0] = 0
						aclone[0] = 1
					else:
						a[0] = 1
						aclone[0] = 0
					# print("level=",i+1)
					level.append(i+1)
					# a[0] = a[i]
					# a = a[::-1]
					d = list(a)
					a = aclone[::-1]
					aclone = d[::-1]
					# a.pop()
					# aclone.pop()

					# for j in range(i+1):
					# 	if a[j] == 0:
					# 		a[j] = 1
					# 	else:
					# 		a[j] = 0
					# a.pop()
			else:
				# print("hello")
				level.append(1)
		a.pop()
		aclone.pop()
	print(len(level),' '.join(map(str,level)))						
	t = t-1